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Integrated model for highway -based travel time forecasting with application to truck transportation

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Integrated model for highway -based travel time forecasting with application to truck transportation

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Content INTEGRATED MODEL FOR HIGHWAY-BASED TRAVEL TIME FORECASTING WITH APPLICATION TO TRUCK TRANSPORTATION Copyright 2004 by Shih-Che Lo A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (INDUSTRIAL & SYSTEMS ENGINEERING) August 2004 Shih-Che Lo R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. UMI Number: 3145237 Copyright 2004 by Lo, Shih-Che All rights reserved. INFORMATION TO USERS The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. ® UMI UMI Microform 3145237 Copyright 2004 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Acknowledgments First, the most earnest, acknowledgment must go to my advisor Dr. Randolph W. Hall. For four years he has supplied me with his creative insight, encouragement, sense of humor and enthusiastic attitude towards research and life. I like to discuss my work with him, subject my writing to his critical eye, listen to his suggestions and simply hang around with him. This kept me motivated through the tough times and the thesis would not be possible without his generous efforts. I appreciate this immensely. Next, I would also like to express my gratitude to Dr. James E. Moore and Dr. Richard McBride for taking the time to be on my thesis committee and bringing their knowledge and expertise to help me refine the concepts of this thesis. Many thanks go to the other graduate students at USC who have helped me through the time in graduate school and made these years as enjoyable as they were. I especially want to thank Ding-Chen Chang, and Jiamin Zhao. Finally, this thesis is dedicated to my parents for their love and support, and for always being there for me. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table of Contents Acknowledgments..................................................................................................... ii List of Tables...............................................................................................................vi List of Figures............................................................................................................ x Abstract.......................................................................................................................xiii 1 Introduction............................................................................................................ 1 1.1 Forecasting................................................................................................ 1 1.2 Express Package Transportation............................................................. 3 1.3 Acquiring Real-time Traffic Data.......................................................... 6 1.4 Truck-to-Air Project Implementation...................................................... 11 1.5 Transit Strike Analysis..............................................................................14 1.6 Research Contributions.............................................................................16 2 Literature Review................................................................................................... 17 2.1 Fundamental Theory of Traffic Flow...................................................... 17 2.2 Point Speed Estimation.............................................................................20 2.3 Link Travel Time Estimation...................................................................22 2.4 Forecasting Methods.................................................................................26 2.5 Fuzzy Theory.............................................................................................28 2.6 Route Planning.......................................................................................... 30 2.7 Summary....................................................................................................32 3 Problem Formulation and Forecasting Methods.............................................. 34 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 3.1 Highway Segmentation............................................................................ 35 3.2 Forecasting Future Loop Detector Speeds..............................................38 3.3 Forecasting Travel Time on a Given Route............................................39 3.4 Weighted Moving Average Model..........................................................42 3.5 Linear Regression Model......................................................................... 44 3.6 Fuzzy Reasoning Model...........................................................................47 3.7 Summary....................................................................................................52 4 Experimental Results and Analysis.....................................................................54 4.1 Vary Time of the Day...............................................................................54 4.1.1 Monday, Tuesday, Wednesday, and Thursday....................... 55 4.1.2 Friday......................................................................................... 57 4.1.3 Saturday, Sunday, and Holidays.............................................. 59 4.1.4 Morning Rush Hour, Noon, and Evening Rush Hour............ 60 4.2 Paths...........................................................................................................63 4.3 Incident Conditions...................................................................................69 4.4 Summary....................................................................................................71 5 Applications to Ground-to-Air Scheduling........................................................73 5.1 Background............................................................................................... 74 5.2 Model for Arrival of Work.......................................................................75 5.3 Sort Starvation and Scheduling................................................................78 5.4 Web-Based Decision Support Tool.........................................................80 5.4.1 Design Methodology...............................................................81 iv R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 5.4.2 Truck-to-Air Dispatch.............................................................. 87 5.4.3 Example Scheduling................................................................ 92 5.5 Real-Time Forecasting Model for Truck-to-Air Scheduling................ 95 5.6 Summary................................................................................................... 99 6 Applications to a Transit Strike............................................................................100 6.1 Background................................................................................................100 6.2 Objectives...................................................................................................103 6.3 Reasons for Strike..................................................................................... 105 6.4 Methodology and Study Design...............................................................107 6.5 Statistics and Finding................................................................................108 6.5.1 Impact on Single Locations...................................................... 109 6.5.2 Impact along Routes..................................................................116 6.5.3 Comparison to Control Group.................................................. 124 6 . 6 Real-Time Forecasting Model during Transit Strike..............................126 6.7 Summary....................................................................................................131 7 Conclusions.............................................................................................................. 132 7.1 Summary of Results..................................................................................132 7.2 Future Research......................................................................................... 134 References....................................................................................................................136 Appendix A The Creation of Fuzzy Inference Rules........................................... 141 Appendix B Reports for Experimental Results.....................................................147 v R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. List of Tables Table 1.1 A 30-second sample data table from 6:00 AM, December 21, 2001....... 9 Table 1.2 A 5-minute sample data table from 6:00 AM, June 28, 2002................. 9 Table 3.1 Data of loop detector stations and loops for major highways in District 7 (Los Angeles and Ventura County)........................................................... 40 Table 4.1 Summary of the Experimental Results on Monday, Tuesday, Wednesday and Thursday, MSE values are the sum of 20 loop detectors each day.................................................................................................................................57 Table 4.2 Summary of the Experimental Results on Friday, MSE values are the sum of 20 loop detectors each day..............................................................................58 Table 4.3 Summary of the Experimental Results on Saturday, Sunday and holiday, MSE values are the sum of 20 loop detectors each day................................................................................................................................. 59 Table 4.4 Summary of the Experimental Results at noon, MSE values are the sum of 20 loop detectors each day..............................................................................63 Table 4.5 Summary of the Experimental Results in the evening, MSE values are the sum of 20 loop detectors each day....................................................................... 63 Table 4.6 Comparison for time of day...................................................................... 63 Table 4.7 Travel Time Forecasting Calculation by Fuzzy Model.......................... 65 Table 4.8 Origin-Destination Routes for the experiments...................................... 6 6 Table 4.9 CHP Record for Traffic Collision............................................................ 69 Table 5.1 The database structure for Normal Schedule and Today’s Schedule.... 85 Table 5.2 The database structure for real-time traffic information........................ 8 6 Table 5.3 The database structure for static database............................................... 8 6 Table 5.4 The database structure for VDS................................................................87 Table 5.5 Curves for Standard Deviation Graph.......................................................90 v i R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 5.6 Terminals for Example Scheduling.......................................................... 92 Table 5.7 Planned Schedules for Example Scheduling........................................... 93 Table 5.8 Real-time Schedules for Example Scheduling......................................... 94 Table 5.9 Update Procedure for Real-time Database System with Real-time Forecasting................................................................................................................... 97 Table 5.10 Real-time Travel Time Calculation Comparisons.................................. 98 Table 6.1 U.S. Census 2000, journey to work table in Los Angeles County, California (United States Census Bureau)..................................................................101 Table 6.2 Los Angeles County's Metropolitan Transportation Authority bus lines and rails ridership during September 2003........................................................102 Table 6.3 Public transit ridership in Los Angeles County from 1999 to 2000, data from California State Controller......................................................................... 102 Table 6.4 Statistics analysis for the impact on single locations............................... I l l Table 6.5 Average speed comparison on 1-101 southbound, ASB data from September 15 to October 10, 2003 and ASD data from October 20 to November 14, 2003........................................................................................................................ 118 Table 6 . 6 Average speed comparison on I-110 northbound, ASB data from September 15 to October 10, 2003 and ASD data from October 20 to November 14, 2003........................................................................................................................ 120 Table 6.7 Average speed comparison on 1-105 eastbound, ASB data from September 15 to October 10, 2003 and ASD data from October 20 to November 14, 2003........................................................................................................................ 123 Table 6 . 8 95% Confidence interval for three highways along three MTA rail routes and compare with highway in Orange County at the same time interval... 125 Table 6.9 Experiments during transit strike. Test data acquired from 6:00 AM to 10:00 AM in the morning on I-10 westbound between 1-405 and I-110. Fuzzy Model was applied to predict traffic speed................................................................ 129 Table 6.10 Experiments during transit strike. Test data acquired from 6:00 AM to 10:00 AM in the morning on I-10 westbound between 1-405 and I-110. Weighted Moving Average Model was applied to predict traffic speed................. 130 vii R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table A.l Sample data for \\={d2, d5, d7) with 11 worked, 2 failed, out of 34 points............................................................................................................................ 142 Table A.2 Sample data for h={d2, d$, d% \ with 8 worked, 2 failed, out of 34 points............................................................................................................................ 143 Table A.3 Sample data for I3={ds, dj, < r /g } with 8 worked, 3 failed, out of total 34 points............................................................................................................................ 144 Table A.4 Sample data for Lt={c? 4 , d5, dj} with 10 worked, 4 failed, out of 34 points............................................................................................................................ 145 Table A.5 Sample data for h={ds, de, d% \ with 12 worked, 5 failed, out of 34 points............................................................................................................................ 146 Table B.l Experiments on Monday, Tuesday, Wednesday and Thursday. Test data acquired from 6:30 AM to 9:30 AM on I-10 westbound between 1-405 and I-110. Fuzzy Model was applied to predict traffic speed. MSE values are the sum of 34 data points each day.................................................................................. 148 Table B.2 Experiments on Monday, Tuesday, Wednesday and Thursday. Test data acquired from 6:30 AM to 9:30 AM on I-10 westbound between 1-405 and I-110. WMA Model was applied to predict traffic speed. MSE values are the sum of 34 data points each day.................................................................................. 149 Table B.3 Experiments on Friday. Test data acquired from 6:30 AM to 9:30 AM on I-10 westbound between 1-405 and I-110. Fuzzy Model was applied to predict traffic speed. MSE values are the sum of 34 data points each day................................................................................................................................ 150 Table B.4 Experiments on Friday. Test data acquired from 6:30 AM to 9:30 AM on I-10 westbound between 1-405 and I-110. WMA Model was applied to predict traffic speed. MSE values are the sum of 34 data points each day.............. 151 Table B.5 Experiments on Saturday, Sunday and holiday. Test data acquired from 6:30 AM to 9:30 AM on 1-10 westbound between 1-405 and 1-110. Fuzzy was applied to predict traffic speed. MSE values are the sum of 34 data points each day....................................................................................................................... 152 Table B . 6 Experiments on Saturday, Sunday and holiday. Test data acquired from 6:30 AM to 9:30 AM on I-10 westbound between 1-405 and 1-110. WMA was applied to predict traffic speed. MSE values are the sum of 34 data points each day....................................................................................................................... 153 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table B.7 Experiments at noon. Test data acquired from 11:00 AM to 2:00 PM on I-10 westbound between 1-405 and I-110. Fuzzy Model was applied to predict traffic speed. MSE values are the sum of 34 data points each day 154 Table B. 8 Experiments at noon. Test data acquired from 11:00 AM to 2:00 PM on I-10 westbound between 1-405 and I-110. WMA Model was applied to predict traffic speed. MSE values are the sum of 34 data points each day 155 Table B.9 Experiments in the evening. Test data acquired from 5:00 PM to 8:00 PM on I-10 westbound between 1-405 and I-110. Fuzzy Model was applied to predict traffic speed. MSE values are the sum of 34 data points each day............. 156 Table B.10 Experiments in the evening. Test data acquired from 5:00 PM to 8:00 PM on 1-10 westbound between 1-405 and 1-110. WMA Model was applied to predict traffic speed. MSE values are the sum of 34 data points each day 157 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. List of Figures Figure 1.1 Data flow for loop detectors from TMCs.............................................. 3 Figure 1.2 Locations of UPS Customer Centers in Los Angeles........................... 5 Figure 1.3 Locations of FedEx Express World Service Centers in Los Angeles... 6 Figure 1.4 Real-time data from loop detectors to TMC.......................................... 8 Figure 1.5 Time delay for real-time data....................................................................10 Figure 3.1 Highway segmentation..............................................................................36 Figure 3.2 The calculation of effective travel distance.............................................38 Figure 3.3 Step function for travel speed...................................................................38 Figure 3.4 Apply Moving Average Model on SR-134, 156.33......................44 Figure 3.5 Apply Linear Regression Model on SR-134...........................................47 Figure 3.6 Three Membership functions....................................................................48 Figure 3.7 Apply Fuzzy Reasoning Model on SR-134, MSE= 120.53.................. 53 Figure 4.1 Locations for test data............................................................................... 55 Figure 4.2 Experiment result on Tuesday, May 13, 2003, DD=716063..................56 Figure 4.3 Experiment result on Friday, May 9, 2003, DD=716063.......................58 Figure 4.4 Experiment result on Sunday, May 25, 2003, ID=718103................... 60 Figure 4.5 Experiment result on Tuesday, May 13, 2003, ID=717036...................61 Figure 4.6 Experiment result on Monday, May 19, 2003, ID=717040................... 62 Figure 4.7 Locations of three Origin-Destination pairs............................................ 6 6 Figure 4.8 Travel time predictions for Route JDY to LAX.................................... 6 6 Figure 4.9 Travel time predictions for Route CVR to LAX................................... 67 Figure 4.10 Travel time predictions for Route EMT to LAX.................................. 67 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Figure 4.11 Traffic accidents on 1-10 eastbound...................................................... 70 Figure 4.12 The experimental results for travel time prediction with incident conditions on I-10 eastbound on August 26, 2003................................ 71 Figure 5.1 Truck-to-Air Dispatch Site Organization............................................... 83 Figure 5.2 The relationship diagram for the database in TAD website.................. 84 Figure 5.3 Member Area Workflow Diagram.......................................................... 85 Figure 5.4 Output Graph for Normal Schedule........................................................ 89 Figure 5.5 Standard Deviation Graph........................................................................ 90 Figure 5.6 Cumulative Graphs Before Change in Departure Time........................ 91 Figure 5.7 Cumulative Graphs After Change in Departure Time............................ 91 Figure 5.8 The difference between two implementations of real-time database system....................................................................................................... 96 Figure 6.1 Los Angeles County highway network....................................................104 Figure 6.2 Single Locations from West/Central Los Angeles.................................. 110 Figure 6.3 Average speed comparisons before strike and during strike on 1-5 southbound between I-10 and SR-134................................................... 110 Figure 6.4 Average speed comparisons before strike and during strike on I-10 eastbound between 1-110 and 1-405.........................................................112 Figure 6.5 Average speed comparisons before strike and during strike on SR- 101 southbound between 1-110 and SR-170........................................... 112 Figure 6 . 6 Average speed comparisons before strike and during strike on SR- 101 southbound between SR-170 and 1-405.......................................... 113 Figure 6.7 Average speed comparisons before strike and during strike on I-110 northbound between I-10 and 1-105....................................................... 113 Figure 6 . 8 Average speed comparisons before strike and during strike on 1-405 southbound between SR-101 and 1-10................................................... 114 xi R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Figure 6.9 Average speed comparisons before strike and during strike on 1-405 southbound between I-10 and 1-105.......................................................114 Figure 6.10 Average speed comparisons before strike and during strike on 1-105 westbound between 1-110 and 1-405...................................................... 115 Figure 6.11 Average flow comparisons before strike and during strike on 1-5 southbound.................................................................................................115 Figure 6 .12 MTA rail: red line and SR-101...............................................................116 Figure 6.13 Average speed comparisons on SR-101 Southbound........................... 117 Figure 6.14 MTA rail: blue line and 1-110.................................................................119 Figure 6.15 Average speed comparisons on I-110 northbound................................ 121 Figure 6.16 MTA rail: green line and 1-105...............................................................122 Figure 6.17 Average speed comparisons on 1-105 Eastbound..................................122 Figure 6.18 Average speed comparisons on 1-5 southbound in Orange County.... 126 Figure 6.19 Experiments during a Transit Strike.......................................................128 Figure 7.1 The integrated structure for future travel time forecasting model 135 Figure A.l Sample data for Ii={ J 2 , d$, c/ 7 } with 11 worked, 2 failed, out of 34 points.......................................................................................................... 141 Figure A.2 Sample data for h={d2, c/ 5 , c/g } with 8 worked, 2 failed, out of 34 points.......................................................................................................... 142 Figure A.3 Sample data for I3 ={c/5, c/7, c/g } with 8 worked, 3 failed, out of 34 points.......................................................................................................... 143 Figure A.4 Sample data for 1 4= { < ^ 4 , c/ 5, c l-/ } with 10 worked, 4 failed, out of 34 points.......................................................................................................... 144 Figure A.5 Sample data for Is={c/5, de, c/g} with 12 worked, 5 failed, out of 34 points.......................................................................................................... 145 xii R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Abstract Highways are increasingly congested in metropolitan areas, especially in major cities that rely on highway transportation. As a consequence, travel time forecasting on highways has become an active research field, playing an important role in Intelligent Transportation Systems (ITS) and Advanced Traveler Information Systems (ATIS). Thousands of sensors have been installed on highways for this purpose. ITS and ATIS utilize data from sensors to mitigate traffic congestion by providing real-time travel time information and forecasts. Based on current traffic information and forecasting techniques, fuzzy methods were created in this thesis to predict highway travel time to support decisions for travelers and transportation industries in real-time. By converting traditional flow-based networks into speed-oriented networks, we can apply fuzzy theory to fuzzify these crisp speed data into the fuzzy traffic network. The method starts from analyzing real-time data from single loop detectors and ultimately provides real-time travel time estimation for whole trips. Two applications, truck-to-air connectivity and forecasts during a transit strike, were used to demonstrate the real-time travel time forecasting model. Express Package Transport carriers operate many local terminals within major cities as well as hub terminals. Trucks depart from local terminals carrying express shipments to airports with sorting facilities at the end of each day. Since aircraft depart according to a rigid schedule, it is important for trucks to arrive on time and for shipments to be xiii R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. processed on time. Truck delay can postpone sorting procedures and transferring processes. If aircraft cannot be fully loaded by their scheduled departure time, they either need to be held for late arrivals or depart without all of their shipments. Either situation will cause late deliveries for the affected shipments. Another application that we investigated is travel time forecasting during a transit strike. Highways are especially susceptible to congestion during strikes because travelers have little opportunity to adjust and equilibrate their travel patterns. Hence, the prediction of travel time becomes more important for transportation industries during strikes. A practical website was implemented along with the application of truck-to- air connectivity. We acquire real-time traffic information from loop detectors on highways and calculate real-time travel times for each truck schedule. By implementing a web-based decision support tool with real-time travel time forecasting, outbound aircraft from express companies can depart on schedule. The experiments conducted show that the fuzzy model can predict travel time during peak periods and abnormal traffic conditions. Morning rush hours, evening rush hours, and incident conditions have been evaluated to test the models. The proposed fuzzy model performed better then a Weighted Moving Average Model for the traffic conditions investigated. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 1 Introduction Highways are increasingly congested in metropolitan areas, especially in major cities that rely on highway transportation. Traffic congestion has grown due to sharply increased vehicle travel and very slow growth of roadway capacity in recent years. Rush periods in major cities have doubled in less than 20 years, rising from nearly three hours (morning and evening combined) in 1982 to almost six hours in 1999 (Schrank and Lomax, 2001). Even holidays and Saturdays have rush periods in big cities. Congestion is now found almost half of the daylight hours on workdays. 1.1 Forecasting Forecasting is a general mathematical tool that has many applications. For example, weather, economics, and stock market analysis need forecasting techniques to predict the future. Gross Domestic Product (GDP), the most commonly used indicator of national income, attempts to measure the sum of incomes received by various components of an economy: manufacturing, agriculture, and service industries. Economists use these data and economic models to calculate current GDP and use current GDP to predict the index that projects a country’s wealth in the future. Stock analysts have used many indexes, like Stochastic KD 1 lines (KD), Relative Strength Index (RSI), Convergence and Divergence Moving Average (MACD), Psychological line (PSY), etc., to predict the future of the stock market. They also 1 K and D are two stochastic indictors. 1 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. predict the goal of stock prices before the year’s start and then adjust their forecasted values after each quarter of the year based on the profitability of object companies. Supply chain management and inventory management are other examples. Sales managers need to forecast their sales volume for future sales periods in order to control their inventory status. Higher inventory level may cause trouble in a company’s cash flow. However, lower inventory level may reduce customer service level that tends to reduce customer satisfaction. Therefore, forecasting techniques have been used in many practical applications. Travel time forecasting is an active research field and plays an important role in Intelligent Transportation Systems (ITS). Intelligent Transportation Systems refer to transportation systems which apply combining hardware and software information systems technologies to address and mitigate transportation congestion problems. ITS is part of the national strategy for improving the operational safety, efficiency, and security of highway systems. ITS also means powerful benefits in managing congestion, reducing crashes and improving the efficiency of the trucking and transit industries. Thousands of sensors have been installed on the highways, especially in urban areas. They usually contain an inductive loop, a pull box, a lead-in cable, and a loop controller. These sensors are called loop detectors. They pass information on many parameters, such as the number of loop detectors, the number of physical lanes, the volume recorded at the loop with respect to a vehicle/sample, the occupancy for the loop as a percent, the status of this loop. These data are sent continuously 2 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. throughout the day to centralized Traffic Management Centers (TMCs) (Dahlgren et. al, 2 0 0 2 ). The performance of loop detectors can be determined by two parameters: response time and recovery time (Sreedevi and Black, 2001). Response time is defined as the time between a vehicle’s arrival and the time when data are sent to TMCs. Recovery time is the time required for a loop to return to normal operation after a period of sustained occupancy. Traffic data can be accessed through TMCs remotely to estimate current traffic status, as shown in Figure 1.1. Today, loop detector technology has become the most widely used and accepted traffic detector technology in America. 1.2 Express Package Transportation Express Package Transport carriers, like UPS and Federal Express, operate many local terminals within major cities and Hub Terminals. Trucks depart from local terminals carrying express shipments to airports with sorting facilities at Sensor Sensor Sensor Sensor use Sensor PATH TMC/CalTrans Figure 1.1 Data flow for loop detectors from TMCs 3 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. the end of each day. They normally travel during evening rush hours from local terminals to airports. Since aircraft depart according to a rigid schedule, it is important for trucks to arrive on time and for shipments to be processed on time. Truck delay can postpone sorting procedures and transferring processes. If aircraft cannot be fully loaded by their scheduled departure time, they either need to be held for late arrivals or depart without all of their shipments. Either situation will cause late deliveries for the affected shipments (Hall, 2001). UPS (http://www.ups.com/) is the largest express carrier and largest package carrier in the world. It processes more than 13 million packages and documents each day. Over 2 million of them are air packages, including Next Day and 2nd Day Air packages and documents. UPS delivery drivers are assigned a specific route, making regularly scheduled stops along the route. The driver usually delivers packages in the morning, and picks up packages in the afternoon. UPS has many central sorting facilities located throughout the world, called “Hubs.” Each Hub is connected with a number of local operating centers, which serve as a home base for UPS pickup and delivery vehicles. Packages from the local operating centers are transported to the Hub, sorted in the Hub by zip code and consolidated on conveyor belts. Packages bound for a specific geographical region are all consolidated on the same conveyor belt. Air Hubs are the system to process air packages located around the world. Louisville, Kentucky, is the main UPS Air Hub in America and has approximately 100 flights per day. In the Los Angeles area, the major Air Hub of UPS is located at Ontario Airport. However, many shipments from UPS Customer Centers in Los 4 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Angeles (Figure 1.2) are also transported to Los Angeles International Airport every day. Travel time varies from about 10 minutes to more than one hour. With real-time travel time information available, trucks could potentially depart from local centers, depending on current traffic conditions at the end of each day, and arrive at the airport on time without delaying the sorting process. Federal Express (http://www.fedex.com/) has 6 6 FedEx World Service Centers within the Los Angeles area. Thirteen of them are local terminals (Figure 1.3). Most of the express shipments from these 13 terminals are transported to and processed at the Los Angeles International Airport at the end of each day. As with UPS, travel time varies from about 10 minutes to one hour. Federal Express is 210 118 210 101 Ontario Los Angelesj LAX 105 7ib Figure 1.2 Locations of UPS Customer Centers in Los Angeles 5 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. similar to UPS in that trucks could potentially depart from local terminals depending on real-time conditions and arrive at the airport on schedule without delaying the sorting operation. The real-time travel time forecasting model can be applied to these freight carriers to support their truck schedules. 1.3 Acquiring Real-time Traffic Data Many hardware devices of highway traffic surveillance are installed in metropolitan areas. One of the backbone devices is the single loop detector. 210 118 210 101 Los Angelesi l a ; 105 lib 7ib Figure 1.3 Locations of FedEx Express World Service Centers in Los Angeles 6 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Thousands of these detectors have been installed on the highways. In urban areas, there are as many as 2 detector locations per mile. The principal components of a loop detector are an inductive loop, a pull box, a lead-in cable, and a loop controller. The inductive loop consists of one or more turns of insulated wire that are buried in a shallow cutout in the roadway. Next, the lead-in cable runs from a roadside pull box to the controller. The electronics unit is located in the controller cabinet. The wire loop is triggered by a signal ranging in frequency from 10 kHz to 200 kHz. It functions as an inductive element in conjunction with the electronics unit. When a vehicle stops on or passes over the loop, its inductance decreases. As inductance decreases, the frequency of oscillation increases and causes the electronics unit to send a pulse to the controller, indicating the presence or passage of a vehicle (Sreedevi and Black, 2001). Single-trap loop detectors do not directly measure vehicle speed. They pass many parameters, such as the number of loop detectors, the number of physical lanes, the volume for the loop in vehicle/sample, the occupancy for this loop in percent, the status of this loop to the ATMS spell. These data are sent periodically throughout the day to centralized Traffic Management Centers, as shown in Figure 1.4. Traffic data can be accessed through TMCs remotely to estimate current traffic status. Then, TMCs feed the raw data to local research centers. Two types of data are available from local research centers: raw data and processed data. Raw data are the data collected by single loop detectors that are acquired in a 30-second period. The 30- second raw data provide the flow and occupancy, loop detector data, lane-by-lane, as 7 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. we mentioned earlier. A sample data table for 30-second raw data is shown in Table 1.1. Next, processed data are the average data from ten 30-second raw data files in a 5-minute period. The 5-minute processed loop is the flow, occupancy and speed loop data aggregated across all lanes. A sample data table for 5-minute processed data is shown in Table 1.2. Loop Detectors on the Highway TMC Server TMC Figure 1.4 Real-time data from loop detectors to TMC R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 1.1 A 30-second sample data table from 6:00 AM, December 21, 2001 VDS_ID LOOP_COUNT LANE_COUNT LOOPl_VOL LOOPl_OCC LOOPl_STATUS LOOP2_VOL LOOP2_OCC LOOP2_S T A T U S LOOP3_VOL LOOP3_OCC LOOP3_STATUS LOOP4_VOL LOOP4_OCC LOOP4_S T A T U S 715900 4 2 0 0 2 0 0 2 0 0 2 0 0 4 715901 4 1 0 0 4 3 .0876 1 1 .2591 1 1 .0219 1 715902 4 1 0 0 2 0 0 2 0 0 3 0 0 2 715904 4 2 0 0 4 0 0 2 0 0 2 0 0 4 715908 4 2 0 0 4 2 .0512 1 2 .129 1 0 0 2 Table 1.2 A 5-minute sample data table from 6:00 AM, June 28, 2002 VDS_ID FLOW OCCUPANCY SPEED VMT VHT a TRAVEL_TIME DELAY NUM_SAMP NUMJVALID 715898 5028 .1002 56.24 2162.04 38.44 0.007645 0 30 30 715915 3696 .1191 58.25 1755.6 30.14 0.008154 0 20 20 715918 5472 .1052 58.9 2736 46.45 0.008489 0 30 30 715922 4440 .0734 65.53 2308.8 35.23 0.007935 0 30 30 715929 5280 .0604 66.94 2481.6 37.07 0.007021 0 40 40 An important issue for real-time traffic data is time delay. Data provided by sensors are collected by centralized Traffic Management Centers first. TMCs need to wait for all sensors to respond within a certain period of time. After that time, TMCs organize only the reliable data into a raw data file. The processing time for the data in TMCs is less than 10 minutes. Following this step, TMCs feed the raw data to local research centers, like Partners for Advanced Transit and Highways (PATH), R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. which collect the raw data and calculate processed data. At this stage, traffic speeds are estimated and recorded in the processed data files utilized by the PeMS algorithm for this purpose (Jia et aL, 2001). Basically, PeMS algorithm uses empirical evidence of the variability in the g-factor and the adaptive algorithms for accurately estimating g-factor and traffic speed. The processing time at this step is less than 5 minutes. Finally, remote servers, such as individual research institutes and commercial companies, can access these raw data files and processed data files after the data are available. The transfer time and processing time is less than 1 minute. The complete time delay graph is shown in Figure 1.5. Several aspects of input data are important to the process of real-time travel time forecasting. First of all, time delay will reduce the quality of forecasting. Since the model that we propose is a real-time model, time delay will convert the real-time model into an off-line model. Therefore, the forecasting method will account for the lag time in processing data. That is, (Forecasting Time) = (Current Time) + (Processing Time) + (Lag Time) Sensors TMCs Remote Servers Local Research Centers 10 minutes : 5 minutes 1 minute Figure 1.5 Time delay for real-time data 10 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Fortunately, by the improvement of technology, time delay is reduced to a minimum. Next, the quality of the input data will also have an impact on the quality of forecasts. As we mentioned earlier, not all loop detectors have a response every 30-second period. Hence, the model needs to estimate travel time by using older traffic data. Finally, the parameters for the algorithm to calculate processed data are assigned in a heuristic manner. The algorithm for calculating processed data is summarized in Chapter 2. 1.4 Truck-to-Air Project Implementation In prior research, “ATIS for Ground to Air Connectivity,” investigated by Hall and Lo, 2000-2002, a queueing process with random bulk arrivals is used to model the airport terminal operation with on-time arrival of trucks from local terminals. The result of this project is a web-based scheduling decision tool for trucks that incorporate with real-time traffic information to estimate travel time for truck routes from local centers to airports. Sample data provided by UPS and FedEx were tested by the system. The website is built to demonstrate the feasibility of a real-time travel time forecasting model. It serves as a tool for predicting the arrival of shipments at a central terminal, based on scheduled departures from a set of remote terminals and real-time travel time information. In order to acquire real-time traffic information, an FTP client program was created and added to the web server that was able to retrieve real-time traffic data from Traffic Management Center. These real-time traffic data 11 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. are the input of the real-time forecasting model and we estimate travel time for the whole route based on the current traffic condition with a real-time forecasting methodology. Several database tables were created to store information, including database for highway entrances and exits, locations of loop detectors, real-time traffic speed tables and user interface data table. The output report contains both tabular and graphical presentation. The calculation procedure was implemented by Active Server Pages (ASP) codes. Also, the dynamic graphic presentations were implemented by Java program. The website provides access to a range of information sources and truck patterns at the airport terminal. The biggest concern of trucking companies is the delays on entire fleets. The shipments need to depart from remote terminals and arrive at the airport on time. The web-based scheduling decision tool for trucks incorporates real-time traffic information to estimate travel time for truck routes from local centers to airports. With the decision tools form the website, trucks could potentially depart from local centers, depending on current traffic conditions at the end of each day, and arrive at the airport on time without delaying the sorting process. Although we added a real-time capability in the website, the method to calculate travel time for trucks was at a primitive level initially, based on a snap shot in time. That is, all of the calculations were based on current speeds estimated from real-time traffic data acquired by hardware sensors on highways. Thus, we assumed that traffic conditions would remain the same from origin to destination regardless of 12 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. time change. In short, the travel time estimation procedure in the TAD website was originally calculated by current real-time traffic speed information without any future forecast. In reality, traffic conditions change at all times. Normal traffic patterns consist of two rush hours, morning rush hours and evening rush hours, for any given working day. Also, traffic accidents occur. Sometimes all lanes are blocked due to accidents. Traffic may be jammed in an accident area for both directions. It can take some time for traffic to recover from traffic accidents. Therefore, an efficient travel time forecasting method is necessary in a web-based scheduling decision tool for trucks that incorporates with real-time traffic information to estimate travel time. By applying forecasting techniques, travel time can be predicted more accurately and then the decision tools can better right decisions for trucks, including route selection. This thesis proposes that decision support tools can be improved by adding a fuzzy reasoning model to forecast travel time along routes. It can help not only increase the precision of travel time forecasting, but also make the decision for route planning. The forecasting model can run instantly and efficiently without any time delay, so the TAD website can maintain its real-time characteristic. The complete modification of calculating real-time travel time for the TAD website is shown in Chapter 5. 13 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 1.5 Transit Strike Analysis Highway networks are the backbone of transportation systems in well- developed cities. Connected closely to highway exits is the general road service on which most transit service is operated. Bus transit systems are attractive to meet the growing transportation requirements due to expanding urban area and heavy traffic congestion on highways. However, transit strike shut down buses and trains, and force daily riders to alter their means of transportation. Because travelers have little opportunity to adjust and equilibrate their travel patterns, highways are especially susceptible to congestion during strikes as is possible during ordinary periods of traffic growth. Hence, the control of travel time becomes more important for transportation industries during strikes period. Chapter 6 shows the experimental results for real-time travel time forecasting model during transit strike period. Public transportation is one of the most important services in big cities. According to the 2002 American Community Survey by U.S. Census Bureau, 5% of Americans rely on some form of transit for their journey to work. The Los Angeles County's Metropolitan Transportation Authority (MTA) is the largest transit provider in the Los Angeles area. It serves nearly 400,000 bus riders and 100,000 subway and light-rail riders daily. The mass transit strike in year 2003 in Los Angeles County was the second in three years. The walkout during these 35 days shut down buses and trains, forcing those 500,000 daily riders to scramble for alternate transportation. It was the longest strike in over two decades to hit the public transportation system 14 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. with nearly 2,400 Metro Buses and 73 miles of Metro Rail service. Taxi companies and other bus lines, such as the city of Los Angeles Department of Transportation (LADOT), were overwhelmed by increased demand. But many of those who normally rely on mass transit could not afford the costly alternative and were forced to stay home, walk or rely on friends or relatives for rides. Measured against the total driving population in Los Angeles County, where 7 million motor vehicles are registered, displacement of 500,000 transit riders would seem to have a small effect on roadways. However, delay on congested roadways is highly sensitive to changes in traffic, even a small disruption can have significant impact. According to the sample data collected on highways, average traffic speeds declined during transit strike period. Also, the average length of the rush period increased during transit strike period. It shows that highways are especially susceptible to congestion during transit strikes because travelers have little opportunity to adjust and equilibrate their travel patterns. This situation forms a special kind of driving circumstance on highways. In addition to the experiments from various traffic conditions in Chapter 4, we present the impact of the transit strike through analysis of traffic data gathered from hardware sensors on highways in Chapter 6. The travel time forecasting model was also applied to the sample data during transit strike period. 15 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 1.6 Research Contributions The goal of this research is to build an integrated forecasting model to predict travel time that is implemented by Fuzzy Theory. Based on current traffic data and forecasting techniques, fuzzy methods were created to predict highway travel time in real-time and support decisions for travelers and transportation industries. The method starts from analyzing real-time data from single loop detectors and ultimately provides real-time travel time forecasting for whole trips. By converting traditional flow-based networks into speed-oriented networks, we can apply fuzzy theory to fuzzify these crisp speed data into the fuzzy traffic network. Two applications, truck- to-air connectivity and mass transit strike analysis were used to demonstrate the real time travel time forecasting model. The remainder of the dissertation is organized as follows. Chapter 2 is the review of the literature. Chapter 3 provides the mathematical formulation including weighted moving average model, linear regression model and fuzzy reasoning model, for real-time travel time forecasting. Chapter 4 presents experimental results and analysis of the models from various traffic conditions. Chapter 5 describes an application to the Truck-to-Air scheduling website for the trucking industry. Chapter 6 presents an application from loop detectors data, a transit strike analysis with a case study in Los Angeles County. Chapter 7 offers conclusions. 16 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 2 Literature Review Real-time travel time forecasting is part of the research on intelligent transportation systems. It involves methods for highway capacity analysis, real-time point speed estimation, and travel time prediction. In this chapter, we present literature that examines real-time transportation problems from various stages. Section 2.1 begins with the mathematical formulations from traffic flow theory that have played an important role in initiating research for broad transportation studies. Building on this foundation, Section 2.2 describes the methods to measure traffic speed for single locations either by using hardware sensors or probe cars. Section 2.3 extends travel time estimation from single locations to continuous path. Various forecasting methods to approaching real-time travel time estimation, like neural networks models, time series models, are shown in Section 2.4. Section 2.5 presents fuzzy theories to solve travel time estimation problems. Finally, Section 2.6 provides route-planning algorithms that were developed to find optimal routing and the travel time calculation for complete routes. 2.1 Fundamental Theory of Traffic Flow Traffic flow theory models the interactions between passenger cars, trucks, and buses on roads and highways with mathematical equations. The three primary variables in traffic flow theory are the concentration or the density (k) (measured in vehicles per lane unit distance), the traffic flow (q) on the roadway (measured in 17 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. vehicles per lane per hour), and the traffic speed (v) (measured in unit distance per hour). These three variables obey the relationship q = vk. As early as 1955, Lighthill and Whitham described the flow q and the concentration k as one-dimensional wave motion, kinematic waves, that depend on Newton’s second law of motion. Kinematic waves travel with the velocity dq/dk, and the flow q remains constant on each kinematic wave. Part II of Lighthill and Whitham’s research on kinematic waves presents a theory of traffic flow on long crowded roads. First, the flow q is defined as n!T, where n is the number of vehicles crossing the slice in time T. Next, the concentration k is Y d t k = ^ — , (2.1) Tdx where ^ d t is the sum of the time required by each vehicle to cross the slice. The third quantity v is a dx v = 7 = -j • (2- 2) k '-Y d t According to Traffic Flow Theory: A State of the Art Report (2002), flow (q) is the number of vehicles counted (N), divided by the elapsed time (T). That is, q = n!T. Next, the total elapsed time (T) is the sum of the headways recorded for each vehicle: T= £ > ,(* ), (2.3) i= i 18 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. where headway is calculated by /z,(x) = tj(x) - Hence, the flow can be derived as follows: N N 1 1 C i ~ T ~ N ~ 1 N T ■ (2-4) i=l ™ i=l That is, flow is the reciprocal of the average headway. Newell (1993) proposed a simplified theory of kinematic waves in highway traffic by evaluating the cumulative flow A(x, t). A(x, t) is defined as the cumulative number of vehicles that pass any location x by time t, starting from the passage of a reference vehicle. Then A(x, t), k(x, t) and q(x, t) are calculated as follows: k(x,t)= (2.5) dx q(x,t) = ^ ^ - , (2.6) dt and the identity d2A(x,t) _ d2A(x,t) dxdt dtdx provided that the second derivatives exist. The cumulative flow can be evaluated directly from boundary or initial conditions without evaluation at intermediate times and positions. Daganzo (1994) extended Newell’s method with an alternative way of predicting traffic behavior for one link. This method evaluates the flow at a finite 19 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. number of carefully selected intermediate points, including entrance and exit. The procedure requires more computer memory than Newell’s method, but it can be extended to complex networks readily. By dividing the road into homogeneous sections, called cells, the system obeys the following equation: n,+i(H-l) = nit) (2.8) where nit) is the number of vehicles in cell i at time t. Let Nit) denote the maximum number of vehicles that can be present in cell i at time t, and let Qit) denote the maximum number of vehicles that can flow into cell i when the clock advances from Mo t+1, the amount of empty space in cell i at time t is Nit) - nit). The cell transmission model is based on a recursion where the cell occupancy at time M -l equals its occupancy at time t, plus the inflow and minus the outflow: (f+1) = nit) + yit) - yM(t) (2.9) where the flows are related to the current conditions at time t: yit) = min { t (t), Qit), Nit) - nit)}. (2.10) 2.2 Point Speed Estimation Following traffic flow theory, the mathematical formulations for estimating point speeds have been studied. Based on the relationship q = vk, if we can measure the density (k) and count the traffic flow (q), then traffic speed can be estimated flawlessly. It is easy to count the traffic flow; however, it is not trivial to measure the density. The literature for estimating vehicle speeds from single loop detectors is summarized in this subsection. 20 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Jia, Chen, Coifman and Varaiya (2001) derived the PeMS (Freeway Performance Measurement Project) algorithm for real-time speed estimates from single-loop detectors. They derived that (2-U ) by estimating the g-factor for k(t). So the speed can be calculated by: v(t) = g ( t ) x - ^ p - , (2.12) o(t)xT where T is the duration of the reporting period, c(t) is the number of vehicles that crossed the detector during period t, and the occupancy o(t) is the fraction of time during that period. The authors provide empirical evidence of the variability in the g- factor for PeMS algorithm and the adaptive algorithms for accurately estimating g- factor and speed. They suggest that the estimated travel speed acquired by assuming a common g-factor for all detectors in all single-loop detectors can be off by 50 percent or more. As a result, the use of their PeMS algorithm will reduce forecasting error. This method has been applied to California PATH project as current traffic speed estimator. Moreover, Coifman (2001) proposed an improved algorithm to estimate travel speed from single loop detectors. The traditional calculation for estimating mean velocity is mean length for a vehicle multiplied by the total flow during a sample period and then divided by occupancy during a sample period. However, the estimation for a vehicle’s mean length may be biased depending on the time of day. 21 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Hence, the author suggested that the mean length for the vehicle should be calculated during the free flow period. The results for the improved algorithm worked fairly well except at low flows. Back to 1999, Dailey derived a statistical algorithm to estimate mean traffic speed from single loop detectors. The calculation for mean traffic speed is based on the volume and occupancy data during a specific period of time. The proposed equation for estimating mean speed, that is the ratio of volume and occupancy, has two parts in the calculation, a deterministic component and a stochastic component. The deterministic component is found from the root for a third-order polynomial equation. A filtering approach is presented to measure the stochastic component. Practical traffic data provided by WSDOT Traffic Management System (TMS) on 1-5 in Seattle, Washington, was tested to evaluate the reliability of the algorithm. 2.3 Link Travel Time Estimation Beginning from point speed estimation, the complete travel time for whole trips can be calculated. Link travel time is derived from origin to destination. One approach to calculate total travel is to sum time on segments. Direct measure whole travel time was also used to estimate link travel time. One of the challenges to calculate total travel on segments is that travel condition may change from time to time. Therefore, the accuracy may reduce when estimate longer trips. In this subsection, the first two papers propose neural network models to estimate travel time. Next, a matrix estimation technique and a partial differential equation (PDE) 22 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. model to estimate travel time are described. Finally, algorithms to extract travel time by dual loop detectors are discussed. Fu and Rilett (1995) proposed an artificial neural network (NN) model to estimate dynamic Origin-Destination (O-D) travel time. Three feed forward neural networks were used to model three different time periods: AM peak, PM peak, and off peak. The back-propagation learning algorithm was used in the training of these three NN models. The training data for the NN models was acquired from the city of Edmonton, Alberta, Canada. Based on the simulation data for O-D travel time during the AM peak period, the average relative error is 12.7%, which translates to about 255 seconds for an average trip length of 2260 seconds. The authors conclude that although the NN model is not as accurate as the standard shortest path algorithms, it still has great potential for modeling O-D travel time during non-congested periods. Anderson and Bell (1997) proposed two models to estimate link travel times in urban road networks. The first neural network model was trained from a microscopic traffic simulator of an isolated junction. The second model is a queueing model that was combined with the SCOOT urban traffic control system in Nottingham, England. Preliminary experimental results were shown in the paper. Matsumura, Yamashita, Iwaki and Sugimura (1998) developed a travel-time prediction method based on the comparison between statistical travel time and current status travel time on a given link. The method calculates a difference between the current travel time and statistical travel time of the link and adds the difference to the statistical travel time at a point in time, i.e., the prediction point, for 23 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. travel time prediction or subtracts the difference from the statistical travel time if the difference is a negative value. Moreover, as the prediction point becomes further ahead, the added or subtracted value of the difference decreases linearly and eventually goes to 0 when the prediction point goes beyond a certain point. Probe vehicle methods were applied to acquire measured travel time data in Osaka Prefecture, Japan. The experimental results show that the average error in the predicted travel time data calculated by the prediction method was about 10 minutes plus or minus the actual measured travel time data on routes. Palacharla and Nelson (1999) proposed a fuzzy reasoning model and a fuzzy neural networks model to estimate travel time from loop detectors data. The input data of both models were fuzzified data from occupancy and flow measured by loop detectors. A set of fuzzy inference rules applied to convert the data into travel times. Finally, a simple weighted sum approach was used to defuzzify the travel time from fuzzy rules. The proposed models worked as single speed estimation instead of travel time estimation. The authors shown that the fuzzy neural networks model had estimated travel time 87% more accurately than fuzzy reasoning model. Ashok and Ben-Akiva (2000) developed a dynamic O-D matrix estimation technique that estimated each O-D flow exactly once for dynamic traffic management systems. The study used two different approaches to predict real-time O-D flows. The first approach was the extension of previous work, which used state- vector from the deviation in O-D flows to replace O-D flows themselves. The second approach used state-vector from the deviation of departure rates to replace O-D flows 24 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. themselves. Based on their case study (1-880 near Hayward, California), the results showed that the approximation was robust, as expected. Kachroo, Ozbay, and Hobeika (2001) developed macroscopic traffic flow models for real-time travel time estimation. The study modeled the traffic flow as partial differential equations (PDE) which shown a static velocity relationship with density. Then, they extended the models to estimate real-time travel time by utilizing the infinitesimal section with length dx and then integrating it over the entire length to acquire the travel time. The authors account for non-uniform density of traffic sensors on highways. Therefore, the accuracy of the data is higher in some areas than others. However, their model does not require input from loop detectors. Hence, real time issues and the models are not impregnable without practical experiments and proofs. Rice and Zwet (2001) proposed a simple and effective method for predicting travel times on freeways. Their linear regression model is done on the basis of the current traffic situation in combination with historical data. Their model arises from the empirical fact that there exists a linear relationship between any future travel time and current status travel time. The slope and intercept of the relationship is observed to change subject to the time of day and the time until departure. Hence, the prediction scheme is linear regression with time varying coefficient. According to the experimental results and comparing to Principal Components Predictor and Nearest Neighbors Predictor, the linear regression model performs better with smaller root mean squared (RMS) error. 25 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Coifman and Cassidy (2001), and Coifman (2001) presented algorithms to identify vehicles and extract travel time by dual loop detectors, both on congested freeways and on uncongested freeways. The proposed algorithms could be easily implemented based on the existing traffic surveillance and computer technology. Coifman (2002) extended their research from single loop detectors to dual loop detectors for link travel time forecasting. The study applied basic traffic flow theory for estimating link travel time by integrating the signals from dual loop detectors. Their major consideration is that travel time forecasting should be more informative to users who need to know traffic conditions rather than average velocity, flow, or occupancy. The proposed model could be used to produce a robust incident detection system. 2.4 Forecasting Methods Forecasting is a general mathematical tool that has many applications. For example, weather, economics, and stock market analysis need forecasting techniques to predict the future. Several the latest forecasting methods focusing on transportation science were summarized in this subsection. Mekky (1996) demonstrated how to use spreadsheets to forecast traffic flows in the year 2011 based in the observed flow volume in 1986. Two simple techniques based on the well know Furness methods were used in the spreadsheets, with and without transportation modeling software. The advantage of this spreadsheet method is to solve large-scale problems quickly and easily. 26 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Lan and Miaou (1999) derived recursive algorithms to predict short-term arrival flows for signalized intersections. They pointed out that the choice of the Gaussian type probabilistic distribution may be appropriate for highly aggregated flows, but it may be inappropriate when modeling flows in short time interval. Therefore, they proposed a dynamic generalized linear model (DGLM) to predict short time traffic flows and provide the prediction limits. Zhang (2000) proposed a back-propagation neural network model to predict traffic flow based on road occupancy. The input for the model goes to three blocks: traffic flow process, back-propagation, and neural network predictor. The output for the traffic flow process is compared with the output from the neural network predictor. The difference between these two outputs is the feedback to the back- propagation block. With a neural network predictor and feedback mechanism in the system, the proposed model was able to predict accurately with an average percentage error of less than 5%. The author believes that the parameters for the model can be obtained through nonlinear optimization. However, due to the natural behavior of the neural network, the optimal parameters for the model are very difficult to find without doing numerous experiments. This model needs more time and memory space to be realized in a practical way. In contrast to traditional prediction methods, Lin, Su, and Hsu (2001) proposed the Markov-Fourier grey model (MFGM) prediction approach by using the grey theorem. From their simulation results, the MFGM can be used in both short term prediction and long-term prediction. 27 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 2.5 Fuzzy Theory Fuzzy systems can be used to represent human knowledge very well. It has been applied to various applications successfully, especially in the design of fuzzy controllers. Many researchers also used fuzzy theory to design fuzzy signal controllers in transportation research field. Wang and Mendel (1992) developed a general method to generate fuzzy rules from numerical data. The study provided a systemic five-step algorithm beginning with fuzzified numerical data and ending with de-fuzzified data to a real number. The method can be applied to both numerical information and linguistic data. Practical experiments have shown that a fuzzy controller generated by the algorithm is indistinguishable from a pure neural network controller. Song and Chissom (1993) proposed the first fuzzy time series model. They studied the model by observation and built a dynamic process with linguistic values. Ten definitions and two theorems had been defined and proved in the study. Also, the forecasting procedures for fuzzy time series were addressed in the paper. Hellendoorn and Baudrexl (1995) have shown two examples of the use of fuzzy logic in traffic control. The first example deals with traffic flow on highways and accident recognition systems. Then the second example shows that fuzzy logic can be used to estimate the number of cars driving to a number of parking lots. Chen (1996) proposed a fuzzy forecasting model based on fuzzy times series analysis. The model follows these steps: (1) defining minimum value and maximum 28 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. value for the universe of discourse; (2) partition the universe of discourse into even lengthy and equal intervals; (3) For each interval, define corresponding fuzzy sets by linguistic value of the linguistic variable; (4) define the fuzzy logical relationships for each fuzzy sets and divided those relationships into groups; (5) forecasting by three preset rules. The proposed model has been used to forecast the enrollments of University of Alabama with average forecasting error of 3.23%. Kikuchi (2000) developed a method to defuzzify the fuzzy number that adjusts the observed values to meet the relationship. The approach of the method is based on the formulation of fuzzy linear programming model. A highway entrance model is performed to formalize in the fuzzy LP form. It is simple and flexible to adjust to meet the underlying relationship for the model. Chen (2002) proposed an improved fuzzy forecasting method based on a higher order fuzzy times series model. Following from the first order model, the higher order model is acquired by performing numbers of fuzzy logical operations before dividing the fuzzy logical relationships into groups. All other steps remain unchanged. The proposed model was also applied to forecast enrollment at the University of Alabama. Based on the values of mean square errors (MSE) performed by different models, the high-order fuzzy time series model had the smallest MSE value of all the models. Although the proposed model increased the number of fuzzy logical relationships, the time complexity of the higher order model remains the same as the first order model. 29 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 2.6 Route Planning Route planning is also part of real-time travel time forecasting methodology. Route planning is much easier to determine without real-time factors. However, with real-time issues involved, the shortest distance route may not be the fastest route. Also, the origin route may be changed when traveling during the route. Here we summarize several route-planning methods in this subsection. Hall (1986) proposed a method to find the fastest path through a network with random time-dependent travel times. The method is based on the statistical network for finding the least expected travel time path. Two important findings were shown in the paper. First, standard shortest path algorithm do not identify the least expected travel time path on networks with random and time-dependent travel times. Next, the optimal route choice on a random and time-dependent network is not a simple path but an adaptive decision rule, conditioned to the times nodes are actually reached. Guzolek and Koch (1989) presented the idea of a Route Planning Subsystem to determine the best routes in the road networks using different optimization criteria, to incorporate the information from road network database into the route planning, to plan a fast and efficient route, and to perform real-time tactical navigation in conjunction with in-vehicle route guidance. The objectives used to optimize the routes included minimum time, minimum distance, fewest turns, and avoiding or 30 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. encouraging freeways. By combining appropriate software and a navigable database, the Route Planning Subsystem was implemented by a commercial company. Kachroo and Ozbay (1996) addressed real-time dynamic traffic routing (DTR) problem by the formulation of a fuzzy feedback controller. The study shows that a fuzzy feedback controller is suitable for DTR problems because it is nonlinear, time varying, and contains uncertainties. Fuzzifier, Fuzzy Control, Defuzzifier, Variable Message Signs (VMS) Traffic System, are five building blocks in the proposed fuzzy controller system. These five blocks one by one form a feedback loop between link flows and actuation commands. A simple simulation example shows that the fuzzy feedback controller system is a viable and attractive solution to dynamic traffic control/routing problems. Gartner and Stamatiadis (1997) extended a static traffic assignment control system to the quasi-dynamic and dynamic control system with real-time traffic information. They provided a framework for integration of Dynamic Traffic Assignment (DTA) with real-time control in the context of the real-time traffic adaptive control system (RT-TRACS) for generation of signal control strategies. They connected this system with intelligent transportation systems (FTS) using a practical approach to realize their experiments. In addition, Abdelfatah and Mahmassani (1998) presented a central controller to seek time-varying route guidance and signal control to optimize the system performance. They also introduced the mathematical formulations and heuristic 31 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. solution algorithms for the combined problem of time-varying assignments and responsive signal control to optimize the total travel time in the network. They use DYNASMART simulation model as an evaluation tool to study an actual network from the Dallas-Fort Worth area. Doan, Ziliaskopoulos, and Mahmassani (1999) developed an on-line monitoring system for real-time dynamic traffic assignment (RT-DTA) systems. The systems can estimate the traffic flows on a real-rime basis and predict their evolution in the short term. Transportation network, observation process, state estimator, and traffic management and control are four building blocks in the general structure of real-time traffic system. Demand estimation errors, path estimation, traffic propagation errors, and internal traffic model structure errors were identified as the sources of errors in the RT-DTA systems. Jula, Dessouky, Ioannou, and Chassiakos (2001) modeled the container movement by trucks as an asymmetric “multi-Traveling Salesmen Problems with Time Windows” (m-TSPTW). They proposed a two-phase exact algorithm based on dynamic programming (DP) to find the best routes for a fleet of trucks. A hybrid methodology by DP with genetic algorithms was also developed to solve medium to large size problems. 2.7 Summary Travel time forecasting has been studied for many years. Lighthill and Whitham’s kinematic waves (1955) based on Newton’s second law of motion 32 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. initiates the estimation of traffic speed. Traffic flow theory continues to model the interactions between passenger cars, trucks, and buses on roads and highways. By predicting traffic behavior for one spot or one link, traffic speed can be calculated from mathematical equations. The PeMS algorithm, proposed by Jia, Chen, Coifman and Varaiya (2002), is one of the most important traffic speed estimation equations (Equation 2.12) used to approximate traffic speed in real-time from data collected by loop detectors. Their algorithm is the core of California Freeway Performance Measurement Project which provides traffic data for researches throughout California. Total travel time can be calculated by adding individual travel time on segments or directly measuring. Our real-time travel time forecasting model begins with the input from the value of estimated speed by PeMS Algorithm. In order to accurately calculate link travel times, various forecasting methods were proposed to add-in to the travel time forecast model. Generally, forecasting techniques can be applied to many applications, such as weather, economics, or stock market. We will develop a forecast method based on Fuzzy theory to estimate travel time in real-time in Chapter 3. The model will include the spirit of Fuzzy methodology that the senses of human feelings are not crisp, and combine the fundamental knowledge of traffic flow theory to generate the prediction of travel time. 3 3 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 3 Problem Formulation and Forecasting Methods Travel time forecasting has attracted researchers’ attention due to increasing traffic congestion in major cities, and the need to create accurate forecasts in many applications. Beverage delivery to restaurants and bars, wholesale distribution between warehouses and from warehouses to retailers, and transport of fuels are all applications where travel time needs to be manipulated. It is possible to monitor shipments more closely and make deliveries on time by coordinating schedules with real-time travel information. As wireless technology becomes more mature and handheld devices become less expensive, it will be easier to retrieve real-time information for travelers anytime and anywhere in the world. Many technologies have been applied to improve the travel experience for travelers. One of the most famous systems is Advanced Traveler Information Systems (ATIS). ATIS systems rely mostly on real-time traffic information with hardware installed in vehicles and traffic management centers. Traffic data from loop detectors are the major data source for a typical ATIS system. Loop detector data are used to estimate real-time speeds at the locations of loop detectors. Historical data combined with real-time loop detectors’ data can be effective in improving the accuracy of travel time prediction. The content in this chapter is organized as follows. Section 3.1 describes the formulation of a highway-based network. The highway segmentation for the speed- oriented network is based on the location of loop detectors. Section 3.2 provides the 34 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. configurations for loop detectors on highways. Section 3.3 extends forecasting traffic speeds to the calculation of travel time for a given route. Next, the methods for forecasting future loop detector speeds are presented. Three practical methods are described in Section 3.4 to 3.6 to approach travel time forecasting. Section 3.4 develops a method, called weighted moving average model. Section 3.5 derives a linear regression model, and Section 3.6 presents a fuzzy reasoning model. Finally, Section 3.7 is the summary for this chapter. 3.1 Highway Segmentation The first step to approaching highway-based travel time forecasting is to build a transportation network. Our highway-based transportation network is a speed-oriented network, which is different from traditional flow-based networks. The problem formulation begins with the following definitions. Definition 1 A directed network G is a graph with a set of nodes X and an associate set of arcs A, denoted by G=(X, A). An origin-destination route R is a subset of G where R consists of an ordered sequence x\, X 2, ... , xn, xn+ i of vertices from X and an ordered sequence of edges e\, ei, ... , en from A. That is, the endpoints of edge e, are x, and Xi+ i. Moreover, x\ is the origin and xn+ i is the destination. 3 5 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Definition 2 The location of a single loop detector is denoted by LD;, where j is the identity of the loop detector. Let v/f) denote the real-time travel speed detected by LD, at time t that is calculated every 5 minutes, whose its value is the average value (mean) from ten 30-second periods. The arcs in a directed graph G are derived from loop detector locations and interchanges. If a single highway segment has many loop detectors, then the segment is divided into multiple arcs, which results in one loop detector per arc, as shown in Figure 3.1. Moreover, a virtual loop detector is assigned for the arc that has no loop detector on it. Hence, we have the following definition. X j .x Figure 3.1 Highway segmentation 36 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Definition 3 There is one and only one LD, for each < ? , in a directed network G. Moreover, the length of e, is d, and the speed on < ? , at time t is v,(t), where dj denotes the length (Figure 3.2) of LD,. dj is calculated by the following equation: *1 = L D .-L D S LD( -L D . LD( -L D S (3.1) where LDS: the postmile for the previous loop detector immediately before LD/, LD ,: the postmile for LDj, L D ,: the postmile for the next loop detector immediately after LD/. In order to simpify our presentation more easily, the index system i is ordered by its geographic position from the origin to the destination on route R. The following assumptions are made and justified later in the paper: 1. The real-time point speeds are acquired continuously and estimated from single loop detectors every 5-minute interval. 2. There are no time delays in the data transfer period. 3. Speed is constant over each arc as shown in Figure 3.3, which is determined by the loop detector of the arc. 4. Travel time on both highway and local urban roads is continuous and is a strictly increasing function of traffic flow. 3 7 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 5. The lowest traffic speed is 0 miles/hour and the highest traffic speed is the free flow speed. Direction LDS LDi LDt = 0 4 0 = Figure 3.2 The calculation of effective travel distance v,+i Speed V i -1 Xi-1 di-\ Xi di Xj+i d ,+ 1 Xi+2 Figure 3.3 Step function for travel speed 3.2 Forecasting Future Loop Detector Speeds In the state of California, there are 7522 detector stations distributed among 134 freeways; 23138 loops are in these stations. The densities of single loop detectors vary for different districts. There are 10086 loop detectors and 3293 stations in District 7 (Los Angeles and Ventura County). However, there are only 38 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 1375 loop detectors and 470 stations in District 8 (San Bernardino and Riverside County). Table 3.1 shows the data of loop detector stations and loops for major highways in District 7. In California, Partners for Advanced Transit and Highways (PATH), collects the raw data from traffic management center and passes to local research centers, such as Freeway Performance Measurement System (PeMS), to calculate processed data. Traffic speeds are estimated and recorded in the processed data files utilized by the PeMS algorithm. (Jia et al., 2001). In the next three sections, we provide three different mechanisms for forecasting future loop detector speeds: weighted moving average model (Section 3.3), linear regress model (Section 3.4), and fuzzy reasoning model (Section 3.5). The moving average model is a traditional statistical model whereas the fuzzy reasoning model is based on fuzzy logic reasoning. Both models can perform instantly with setup time of less than three time periods, depending on the configurations. However, the linear regression model needs more historical data than other models. The data set for linear regression requires traffic data at the same time interval back to a certain numbers of days. 3.3 Forecasting Travel Time on a Given Route The linear regression model described in Section 3.5 can predict travel time directly regardless of time change. However, the models proposed in Section 3.4 and 3.6 predict the speeds for the next time period from the current loop detector data first. By repeating the calculations, we can forecast speed values for the next n time 39 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. periods, i.e., n-pass calculation. The experiment that we performed in this section is based on this procedure. Travel time calculation on a speed-based highway network can be formulated using the following definition. Table 3.1 Data of loop detector stations and loops for major highways in District 7 (Los Angeles and Ventura County) Highways Total Miles Loop Detector Stations Number of Loops 1-5 N 88.5 92 549 1-5 S 88.6 99 657 I-10E 46.8 117 802 I-10W 46.8 113 802 1-105 E 18.1 36 239 1-105 W 18.1 41 258 I-110N 31.8 36 291 I-110S 31.8 32 232 1-210 E 52.4 37 351 1-210 W 52.4 40 386 1-405 N 48.5 89 681 1-405 S 48.5 89 712 1-605 N 26.1 44 330 1-605 S 26.1 47 357 1-710 N 24.2 24 172 1-710 S 24.2 27 190 SR-60 E 30.6 34 258 SR-60 W 30.6 37 291 SR-91 E 14.7 31 234 SR-91 W 14.7 29 217 SR-101 N 83.1 68 406 SR-101 S 83.0 72 491 SR-118E 48.0 39 281 SR-118 W 48.0 37 261 SR-134 E 13.3 15 143 SR-134W 13.3 13 113 SR-170N 7.6 7 34 SR-170 S 7.6 9 77 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Definition 4 Let Ti denote the estimated travel time from x\ to jc,+ i for a time-dependent origin-destination route R, where jci is the origin and x,+i is the destination. Travel time forecasting is used to find the estimated travel time T = Tn, such that T is the minimum for the time-dependent origin-destination route R. Note that, Tt > 0 for all i, and Tx <T2 <---<Tn. From the above definitions, the estimated travel time T for a time-dependent origin-destination route R can be calculated by the following recursive equation (assume current time is t): t ‘ =t » + , , ! 't , < 3-2> where To = 0 is the initial condition. The equation is obvious and travel distance dt is fixed for all i. Hence, the only variable that will affect the result of estimated travel time is traffic speed forecasting from each loop detector. In order to get forecasted speeds, the Weighted Moving Average Model and the Fuzzy Reasoning Model in the following sections need to be performed recursively. That is, for a specific loop detector LD„ v,(H-5) can be calculated from v,-(t) with 1-pass calculation, v,(H-10) can be calculated from v,(t) with 2-pass calculation, etc.. Also, the speeds remain the same within the same time period. The comparisons of forecasting models are shown in Chapter 4. 41 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 3.4 Weighted Moving Average Model The traditional moving average model treats each piece of data as equally important when calculating the average value, i.e., average weight. However, in real time traffic models, the latest value tends to be the most valuable information in the system. Hence, it would be more useful if we give more weight to the most recent data to emphasize the latest real-time information. The weighted moving average model is constructed as follows: Let V f (t) be the average value for the past n observed data at time t. That is, V/(0 = - £v,. (./)=> '£dviU) = nvi(t), for alii. (3.3) n j= t-n +1 j= t-n +1 Now we add one more point: 1 (+ i ^(t + l) = —— jv ,.(7 ) n + 1 H.n + i = - A < ! > , ( ; ) + v,(( + l» n + 1 j = t - n + 1 -(nvi(t) + vi(t +1)) j=t- 1 (3.4) n + 1 H - v( . (t) H — — v( (t +1), for all i. n + 1 ' n + 1 Then, shift the time index back one time-step from the above equation, i.e., replace t+1 as t. The corresponding expression for forecasting v, is: v,.(0 = v,(f) = v, (t - 1) + — v; .(0, for all i. (3.5) n + 1 n+1 4 2 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Let — — -1 - a , then a = 1 - n + 1 1 . Hence, the basic form for the weighted n + 1 n+1 moving average model is v( (r) = (r -1) + (1 - a)vt (t), for all i. (3.6) By iteration, we can extend the model into a more complex form. v,.(0 = ov;-a-l) + ( l- a ) v | .(0 = «r(«v( . (f - 2) + (1 - a)v,. (t -1)) + (1 - a)v, (t) (3.7) = a 1vi {t- 2) + a (l - a)v( (r -1) + (1 - a)vt (t) Here in our experiments, we use this weighted moving average model with n = 3. We present a preliminary experiment with result to demonstrate the feasibility of the model. The data were collected from TMCs on October 21, 2002, in a three- hour interval, from 6:30 AM to 9:30 AM. We selected one loop detector to perform the calculation and applied n=3 in Equation 3.7. The results were shown in Figure 3.4. Mean Square Error (MSE) was calculated as the performance measure to evaluate the method defined as follows: Where A f,- is measured data and F, is the forecasted data, n is total number of forecasted data. Example (3.8) 4 3 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. SR-134 ID O IO O L O I - W W C O CO o o ■ * T O ID O O v J Od C O ID ID T t Tim e of Day p ^ - O r ig in a l O bserved Data Moving Average Model | Figure 3.4 Apply Moving Average Model on SR-134, MSE= 156.33 3.5 Linear Regression Model Rice and Zwet (2001) proposed a simple and effective method for predicting travel times on freeways. The prediction is done on the basis of the current traffic situation in combination with historical data. According to the empirical fact, there exists a linear relationship between any future travel time and the current status travel time. The slope and intercept of this relationship is observed to change subject to the time of day and the time until departure. This leads to a prediction scheme by means of linear regression with time varying coefficients. The linear regression model is constructed as follows: 44 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Let V(d, I, t) (d e D ,/e L ,t e T ) denote the velocity that was measured on day d at loop I at time t. The travel time from loop a to loop b starting at time t on day d is denoted by X d(a,b,t) for all d e D ,a,be L , t e T . A current status travel time is defined by b-\ 2/j X*d(a,b,t) = ZtTTT— - r t j — (3-8) ^V (d ,i,t) + V(d,i + U) where dt denotes the distance from loop i to loop (z'+l). That is, the current status travel time is calculated by only current traffic velocity at time t on day d. Suppose a number of days d e D before a new day ee D have been observed to calculate V(d,l,t), i.e., a set of historical data. Let t be the current time at day e and V(e,l,t) have been observed for t< t. For a given <?>0, X *e(a,b,r) is a naive predictor of Xe(a,b,T + S). Define the historical mean travel time as ju(a,b,t) = (3.9) |D| d^DM where a^tye L and ai=a, bn=b. ju(a,b,t) is another predictor of Xe(a,b,t + S ) . The linear regression model is based on empirical facts (Rice and Zwet, 2001) that there exist linear relationships between X*(a,b,t) and X(a,b,t + S) for all t and S , and is defined by X (a,b,t + 8 ) = oc(a,b,t,S) + j3(a,b,t,8)X*(a,b,t) + e (3.10) where e is a zero mean random variable modeling random fluctuations and 45 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. measurement errors. Also, a and /? are the intercept and slope corresponding to t and S . Rice and Zwet believe that there exist a linear relationship between any future travel time and the current status travel time. The slope and intercept of this relationship is observed to change subject to the time of day and the time until departure. The model is created by linear regression. Define the pair A (.a(a,b,t,S),/3(a,b,t,S)) to minimize £ ( X d(a,fc,s)- a(a,b,t,S)- 0(a,b,t,S)X*(a,b,t)) 2 K(a,b,t + S - s ) , (3.11) d e D se S where K denotes the Gaussian density with mean zero and a certain variance needs to specify. The actual prediction of Xe(a,b,t + t) becomes X e(a,b,t + S) = a(a,b,t,S) + fi{a,b,t,S)X*(a,b,T). (3.12) Setting a(a,b,t,S) = y(a,b,t,S)ju(a,b,t + S ), then Equation (3.9) expresses a future travel time as a linear combination of the historical mean (Equation (3.8)) and the current status travel time (Equation (3.7)). Example A set of test data has been record from April 14th, 2003, to May 23rd, 2003, a total of 30 consecutive working days. Linear Regression Method was applied on May 24th, 2003, as a preliminary experiment with result to demonstrate the feasibility of the model. All the data were collected from 6:30 AM to 9:30 AM on SR-134 which is the same time period and location as Section 3.4. Figure 3.5 shows the results in the form of travel time instead of traffic speed. 46 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Travel Time Forecast on SR-134 0.7 0.6 ~ 0.5 | 0.4 0.3 0.2 0.1 < 3 O Time of Day — Record Travel Time Forecast Travel Time Figure 3.5 Apply Linear Regression Model on SR-134 3.6 Fuzzy Reasoning Model Before building a fuzzy forecasting model, fuzzy numbers, fuzzy logic, and fuzzy systems need to be explained. A fuzzy number is a quantity with an imprecise value. In contrast to fuzzy numbers, ordinary numbers (single-valued numbers) are called crisp numbers. Any fuzzy number can be thought of as a function whose domain is a specified set (crisp set), and whose range is the span of non-negative real numbers between, and including, 0 and 1. Each numerical value in the domain is assigned a specific continuous membership function where 0 represents the smallest possible grade, and 1 is the largest possible grade. 47 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. In many respects, fuzzy numbers depict the physical world more realistically than crisp numbers. For example, you are driving along a highway where the speeds limit is 65 miles/hour. You try to hold your speed at exactly 65 miles/hour, but your car lacks "cruise control system," so your speed varies from moment to moment. If you plot your instantaneous speed over a period of several minutes, and then plot the result in rectangular coordinates, you may get a function that looks like one of the curves shown below. 1- - 50 65 80 1” 50 65 80 1 " 50 65 80 Figure 3.6 Three Membership functions The left-hand-side curve represents a triangular fuzzy number; the middle curve shows a trapezoidal fuzzy number; the right-hand-side curve illustrates a bell shaped fuzzy number. These three functions are known as membership functions. Their grade starts at zero, rises to a maximum, and then declines to zero again as the domain increases. However, some fuzzy numbers have concave, irregular, or even chaotic membership functions. There is no other restriction on the shape of the membership curve, as long as each value in the domain corresponds to one and only one grade in the range, and the grade is never less than 0 nor more than 1. 48 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Fuzzy logic is an approach to computing based on "degrees of truth," rather than the usual “true or false” (1 or 0) Boolean logic that the modem computer is based on. Dr. Lotfi Zadeh of the University of California, Berkeley first introduced the idea of fuzzy logic in the 1960s. Fuzzy logic includes 0 and 1 as extreme cases of truth (or “the state of matters” or “fact”), but also includes the various states of truth in between, so that, for example, the result of a comparison between two things could be not “tall” or “short” but “.45 of tallness.” Fuzzy logic seems closer to the way our brains work. We aggregate data and form a number of partial truths that we aggregate further into higher truths, which in turn, when certain thresholds are exceeded, cause certain further results such as motor reaction. A similar kind of process is used in artificial computer neural networks and expert systems. It may help to see fuzzy logic as the way reasoning really works and binary or Boolean logic is simply a special case of it. Following the same notation as Section 3.3, v/(t) is the observed speed for loop detector i at time t. is the observed speed for loop detectors /-l, the previous loop detector for loop detector i, at time t. v,+i (t) is the observed speed for loop detectors i+l, the next loop detector for loop detector i, at time t. A sliding time window that memorized current traffic condition at time t along with traffic condition at time t— 1 and t- 2 is defined as 2) V ,.(f- 2) vM (t - 2) i S 1 , s 2 S3 I I 1 ■ K * 7 s i r * 1 + 1 I I S4 S5 S6 i T 1 + ----1 o o o r- 1 4 9 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The speed difference sdj is defined by sdj = sj - so, for j - 1, 2,.8. (3.13) In order to perform fuzzy logic reasoning, two triangular fuzzy sets, POSITIVE (PO) and NEGATIVE (NE), with membership function mpo(u) and /m N e(w) are defined as follows: where h is the free flow speed. Fuzzy logic reasoning follows a set of fuzzy inference rules to forecast vi (t +1). The rules were made by the properties shown in Table A.l to Table A.5 and Figure A.l to Figure A.5 in Appendix A. Each graph in Appendix A shows a collection of successful prediction points (circle sign for positive prediction and plus sign for negative prediction) and failed prediction point (cross sign) by speed difference sdi from a sample data set in a 3-dimension graph. Hence, the fuzzy inference rules that we defined here deal with five particular patterns of neighborhood speeds and historic speeds. There are five index sets defined in the model: \\={d2, d$, di}\ h.={di, d$, d^}', 0, u < 0 and u > 2 h 0 < u< 2 h m? 0 (u) = \ h - \ u - h \ [ h f °> u > 0 and u < - 2 h — 2 h < u < 0 . (3.14) mN E (M ) = “ h-\u + h\ { h 50 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. i3={^5, d-j, J 8}; U={d4, ds, d7}\ 15=1^5, dft, J 8}. Each index set contains a pair of fuzzy rules, positive pattern and negative pattern, designed as follows: IF (d2, PO) AND (d5, PO) AND (d7, PO) THEN (y, PO). IF (d2, NE) AND (d5, NE) AND (d7, NE) THEN (y, NE). IF (d2, PO) AND (ds, PO) AND (d% , PO) THEN (y, PO). IF (d2, NE) AND (d5, NE) AND (d% , NE) THEN (y, NE). IF (d5, PO) AND (d7, PO) AND (d% , PO) THEN (y, PO). IF (d5, NE) AND (d7, NE) AND (cfe, NE) THEN (y, NE). IF (d4, PO) AND (ds, PO) AND (d7, PO) THEN (y, PO). IF (d4, NE) AND (ds, NE) AND (d7, NE) THEN (y, NE). IF (d5, PO) AND (de, PO) AND (ds, PO) THEN (y, PO). IF (d5, NE) AND (de, NE) AND (d8, NE) THEN (y, NE). where output y is calculated by 4 =MAX{MIN{mP0(J.);y e 7(};/ = l,2,--,5} (3.15) ^ =MAX{MIN{m ^idjYJe /,.};/ = 1,2,•••,5} (3.16) \= M A X { 0 ,l-A l -Jl2} (3.17) ^ = (3.18) /tj + Aj + A q 51 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Equation 3.18 is the corresponding defuzzify process. Then, the estimated traffic speed is calculated by vi(t + l) = vi(t) + y. (3.19) That is, y is also a speed difference from v, (t +1) and v, (t). Finally, free flow speed h is determined as follows. We collected a sample data from twelve 5-minute data files from early morning 3:00AM to 3:55 AM. There are total 13235 speed values and then are sorted in descend order. We found out that the 95-percentage speed is 70 miles/hour. Therefore, the free flow speed is set to 70 miles/hour in our experiments. Example The same data set as Section 3.4 were applied as a preliminary experiment with result to demonstrate the feasibility of the model. Moreover, data from up stream loop detector and data from down-stream loop detector were also collected in order to perform the calculation of the model. The results were shown in Figure 3.7. Mean Square Error was calculated as the performance measure to evaluate the method. 3.7 Summary Real-time traffic control strategies are at the core of ATMS/ATIS. To achieve optimal performance, accurate prediction of travel time is essential. In this chapter, we presented three methods to forecast travel time based on real-time traffic 52 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. information. The Weighted Moving Average Model is a traditional statistical model. The Linear Regression Model predicts travel time directly from current traffic conditions without forecasting individual traffic speeds for loop detectors. On the other hand, the Fuzzy Reasoning Model combines time and geographic factors into mathematical equations in order to increase accuracy. Therefore, the Fuzzy Model has potential to generate more accurate predictions for travel time forecasting applications. S R -1 3 4 7 0 ------- S 40 < /> 30 m o m o t j ; in in o m o o 1 7 : m o m o m o T -; cq oj c o < n r t w o o m o 1 - 7 O J T im e o f Day ]--♦—Original O bserved D ata •-&— Fuzzy Reasoning Model j Figure 3.7 Apply Fuzzy Reasoning Model on SR-134, MSE=120.53 5 3 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 4 Experimental Results and Analysis The goal of the experiments is to evaluate and compare the accuracy of travel time forecasting models with real traffic data. We conducted the experiments in accordance with various traffic conditions, including time of day and day of week. The Weighted Moving Average (WMA) Model and the proposed Fuzzy Model are examined and compared. Section 4.1 presents the experiments and results that focus on single locations on highways with various time of day. Section 4.2 presents the experiments and results for entire paths. Non-recurrent traffic conditions, such as traffic accidents, are considered in Section 4.3. All of the experimental data were collected in Caltrans District 7, in the vicinity of downtown Los Angeles, California (Figure 1.2). 4.1 Vary Time of the Day The first set of experiments is designed to test traffic speed forecasting at a single location. Traffic data from May, 2003, were collected and tested in this section. All loop detectors on I-10 westbound between 1-405 and I-110 were examined throughout this section (Figure 4.1). Each experiment contains a three-hour testing period and includes 37 measured traffic speeds from 37 5-minute data sets. Because three measured traffic speeds were needed to initiate the forecasting models, a total of 34 forecasting values were made. Mean Square Error (MSE) is used to measure the accuracy of the models and is defined as follows: 54 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. ( 4 .1 ) where M, is the measured speed (miles/hour), F, is the forecasted speed (miles/hour), and n is the number of data points, which is 34 in this section. Three groups are formed in a week: {Monday, Tuesday, Wednesday, and Thursday}, {Friday}, and {Saturday, Sunday and holiday}. These three groups represent different traffic conditions. The experimental results from these three groups are shown in Section 4.2.1 to Section 4.2.3. Also, there are three groups in a day: {Morning: 6:30 AM - 9:30 AM}, {Noon: 11:00 AM - 2:00 PM}, and {Evening: 5:00 PM - 8:00 PM}, which are shown in Section 4.2.4 to represent different traffic conditions from the time issues. M ---------- I-10 A u Driving Direction T North 4.305 5.655 6.575 8.145 8.545 9.045 10.075 10.445 11.055 11.965 4.1.1 Monday, Tuesday, Wednesday, and Thursday The first testing group in a week is the weekday traffic data from Monday to Thursday. These four weekdays have similar traffic conditions. We tested the models on May 12 to May 15 during morning peak hours from 6:30 AM to 9:30 AM. The 718103 717036 717040 716063 1-405 1-110 Figure 4.1 Locations for test data 5 5 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. summary of experimental results for the Fuzzy Model and the WMA Model are shown in Table 4.1. Detailed reports for the experiments are shown in Appendix B. The total MSE value from the Fuzzy Model is 3612.73 which is lower than the value of 4640.36 from the WMA Model. It is clear from the tables that the predicted values from the Fuzzy Model are close to the measured traffic speeds for every location on this segment. Figure 4.2 shows the comparison graph from Vehicle Detector Station (VDS) ID=716063 in the vicinity to the downtown Los Angeles on May 13 where MSE value from the Fuzzy Model is 56.83 and MSE value from the WMA Model is 117.90. According to the figure, traffic speeds increase sharply from less then 20 miles/hour at 6:45 AM to more than 60 miles/hour after 7:05 AM at this location. Larger forecasting errors occurred during this twenty-minute period whereas more accurate forecasting for the rest of testing period. Traffic Data on Tuesday 60 5 40 I T l o r 4 o I T ) o d o © 0 4 0 0 o in r- o f" o o O ' o 0 0 © 00 o 00 o Time of Day [ - • ♦ ■ • “ Measured Speed Fuzzy Model ~*~WMA Model) Figure 4.2 Experiment result on Tuesday, May 13, 2003, ID=716063 56 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 4.1 Summary of the Experimental Results on Monday, Tuesday, Wednesday and Thursday, MSE values are the sum of 20 loop detectors each day Models 12-May-03 13-May-03 14-May-03 15-May-03 Sum of MSE Fuzzy Model 904.02 1041.18 959.46 708.07 3612.73 WMA Model 1238.24 1257.73 1266.63 877.76 4640.36 4.1.2 Friday The second testing group in a week is the weekday traffic data from Friday. Friday was tested individually because it is the day before the weekend and traffic is usually lighter in the morning and heavier in the evening than other weekdays. We tested the models on May 9 to May 30 for every Friday during morning peak hours from 6:30 AM to 9:30 AM. The experimental results for the Fuzzy Model and the WMA Model are shown in Table 4.2. Detailed reports for the experiments are shown in Appendix B. The total MSE value from the Fuzzy Model is 3746.33 which is lower than the value of 4976.62 from the WMA Model. Figure 4.3 shows the comparison graph from VDS ID=716063, which is the same location as the previous experiment (Section 4.2.1), on May 9 where MSE value from the Fuzzy Model is 53.91 and MSE value from the WMA Model is 122.40. According to the figure, traffic speeds increase from close to 40 miles/hour at 6:45 AM to close to 70 miles/hour after 7:00 AM at this location. The traffic condition around 7:00 AM in the morning is better than on any other weekday. 57 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Heavier traffic flow disappeared after 7:00 AM and the average traffic speed was close to 70 miles/hour afterward on Friday, in contrast heavier traffic flow disappeared after 7:05 AM and the average traffic speed was close to 65 miles/hour afterward on other weekdays. A possible traffic accident occurred close to this location after 9:10 AM, causing traffic speed to decline rapidly afterward. Again, larger forecasting errors occurred during the period of dramatic speed changed. Table 4.2 Summary of the Experimental Results on Friday, MSE values are the sum of 20 loop detectors each day Models 9-May-04 16-May-04 23-May-04 30-May-04 Sum of MSE Fuzzy Model 1055.63 1692.06 593.90 404.74 3746.33 WMA Model 1261.35 2275.86 871.06 568.35 4976.62 Traffic Data on Friday 2 40 « n V ) in © o o m o C N 66 m o » n < N c K o o r — c- o o o o o o o o o o Time of Day | — Measured Speed Fuzzy Model WMA Model | Figure 4.3 Experiment result on Friday, May 9, 2003, DD=716063 5 8 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 4.1.3 Saturday, Sunday and Holidays The last testing group in a week is the weekend traffic data on Saturday, Sunday and holidays. Traffic conditions are usually better during weekends and holidays. We tested the models on May 17, May 18, May 24, and May 25 during morning peak hours from 6:30 AM to 9:30 AM. The experimental results from the Fuzzy Model and the WMA Model are shown in Table 4.3. Detailed reports for the experiments are shown in Appendix B. The total MSE value from the Fuzzy Model is 261.11, which is a little higher than the value of 252.74 from the WMA Model. The MSE values are very small for both models in the experiments because predicted values are very close to measured traffic speeds. There is almost no difference between these two models during the weekend and holiday traffic conditions. Figure 4.4 shows the comparison graph from VDS ID=718103, which is in the middle of I- 10 segment, on May 25 where MSE value from the Fuzzy Model is 3.93 and MSE value from the WMA Model is 6.44. As shown in the figure, both estimated values are close to measured traffic speeds, generating very small forecasting errors. Table 4.3 Summary of the Experimental Results on Saturday, Sunday and holiday, MSE values are the sum of 20 loop detectors each day Models 17-May-03 18-May-04 24-May-04 25-May-04 Sum of MSE Fuzzy Model 64.13 23.56 87.28 86.14 261.11 WMA Model 60.32 21.92 85.92 84.58 252.74 5 9 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Experiment on Sunday « r > O m o © Time of Day |— Measured Speed Fuzzy Model — WMA Model | Figure 4.4 Experiment result on Sunday, May 25, 2003, ID=718103 4.1.4 Morning Rush Hour, Noon, and Evening Rush Hour Section 4.2.1 to Section 4.2.3 show the experiments executed in the morning. In this section, we examined forecasting models during other times for the day. Table 4.4 shows the summary of the experimental results at noon for the Fuzzy Model and the WMA Model on May 12 to May 15. Detailed reports for the experiments are shown in Appendix B. The total MSE value from the Fuzzy Model is 6280.13, which is lower than the value of 8070.56 from the WMA Model. Table 4.5 shows the summary of the experimental results in the evening for the Fuzzy Model and the WMA Model on May 19 to May 22. Detailed reports for the experiments are also 60 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. shown in Appendix B. The total MSE value from the Fuzzy Model is 3472.90, which is lower than the value of 5396.53 by the WMA Model. Figure 4.5 shows the comparison graph for the experiments at noon from VDS ID=717036, which is the same location as Section 4.2.1, on May 13 where the MSE from the Fuzzy Model is 34.56 and the MSE from the WMA Model is 125.33. According to the figure, the results from the Fuzzy Model are very close to the measured speeds, in contrast with the results from the WMA Model. Traffic speeds steady climb to 60 miles/hours at 12:45 PM from 10 miles/hour at 11:15 AM for the Fuzzy Model while forecasts for the WMA Model are relatively unstable in the same time interval. Noon Traffic Experiment 80 70 60 'g' 50 o X & 30 20 10 0 » n Time of Day [— ♦— Measured Speed Fuzzy Model WMA Model) Figure 4.5 Experiment result on Tuesday, May 13, 2003, ID=717036 61 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Figure 4.6 shows the comparison graph for the experiments in the evening data set from VDS DD=717040, which is 2 miles west from the intersection of I-10 and I-110 (the vicinity of the downtown Los Angeles), on May 19 where MSE from the Fuzzy Model is 46.43 and MSE from the WMA Model is 88.04. The results from Figure 4.6 show typical forecasting errors for both models. That is, the forecasts from the Fuzzy Model have one lag period while the forecasts from the WMA Model have two lag periods during dramatic speed adjustment periods. Table 4.6 shows the comparison results for the testing groups from different times of day. The forecasting errors tend to increase in the middle of the day because of uncertainty in traffic patterns. Evening Traffic Experiment 80 - t 3 40 a . 3 0 r r s V~i Tf O m m Time of Day |--♦— Measured Speed Fuzzy Model — WMA Model | Figure 4.6 Experiment result on Monday, May 19, 2003, ID=717040 62 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 4.4 Summary of the Experimental Results at noon, MSE values are the sum of 20 loop detectors each day Models 12-May-03 13-May-03 14-May-03 15-May-03 Sum of MSE Fuzzy Model 1547.82 1364.97 875.41 2491.94 6280.13 WMA Model 1813.55 1846.93 1065.28 3344.80 8070.56 Table 4.5 Summary of the Experimental Results in the evening, MSE values are the sum of 20 loop detectors each day Models 19-May-03 20-May-03 21-May-03 22-May-03 Sum of MSE Fuzzy Model 858.24 661.58 784.21 1168.87 3472.90 WMA Model 1343.75 1017.35 1222.44 1812.99 5396.53 Table 4.6 Comparison for time of day a * a i Total MSE Models — _______Morning___________ Noon___________ Evening Fuzzy Model 3612.73 6280.13 3472.90 WMA Model 4640.36 8070.56 5396.53 4.2 Paths We compared traffic speeds at single locations in the last section. In this section, we focus on predicting travel time for paths. First, we demonstrate the arithmetic of calculating travel time in Table 4.7 for the actual data that we collected on October 22, 2002. The execution of the forecasting model begins at 5:00 PM (current time) on a 12.99 miles segment with 20 loop detectors. 6 3 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. At any current time, we have already measured v,(0 (measured current traffic speeds), v,(t-5) (measured traffic speeds 5 minutes ago), and v,-(f-l0) (measured traffic speeds 10 minutes ago). Next, we execute the arithmetic of calculating travel time to acquire v,-(f+5) (estimated traffic speeds 5 minutes later). That is, the first three speed columns from the table are used to initiate the model and predict traffic speeds for the next column. Then, we execute the arithmetic of calculating travel time again to acquire v,(f+10) (estimated traffic speeds 10 minutes later) from v,(f-5), Vi(t), and Vi(t+ 5). We need to repeat the same procedures until reaching the final destination. Finally, we can calculate total travel time by adding individual travel times. The calculation of cumulative travel time is shown in the last column of the table. For this example, we estimate that it will take 19 minutes to travel 12.99 miles if travel begins at 5:00 PM on the day shown. Three origins have been chosen from twelve FedEx customer service centers in the Los Angeles area for our experiments in this section (Figure 4.7). Los Angeles International Airport (LAX) is our destination for all three origins en route. Detailed travel data for three routes are shown in Table 4.8. Traffic speed data for the experiments were collected from 4:00 PM to 7:00 PM on July 30, 2003. Figure 4.8 to Figure 4.10 show the experimental results for three routes in the form of travel time. For all three experiments, the estimated travel time is calculated by the proposed Fuzzy Model. 6 4 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 4.7 Travel Time Forecasting Calculation by Fuzzy Model d i v,-(f-10) V i{t-5 ) V « (f) v«(f+5) v,-(f+10) v,(M-15) Travel Time D O § 4 — * Q 4:50 PM (M) 4:55 PM (M) 5:00 PM (M) 5:05 PM (F) 5:10 PM (F) 5:15 PM (F) Minutes Cumulative Minutes L D t 0.2 13.45 15.43 14.84 0.41 0.41 l d 2 0.43 7.39 8.82 9.49 1.99 2.40 l d 3 0.48 10.79 11.09 14.51 1.88 4.28 l d 4 1.01 16.05 14.81 21.49 2.08 6.36 l d 5 1.3 17.11 36.67 29.76 49.43 1.89 8.25 l d 6 0.6 34.94 44.63 58.61 56.19 1.28 9.53 l d 7 1.59 52.47 56.95 58.68 55.79 1.12 10.65 l d 8 1.07 60.97 56.73 60.33 60.61 56.77 1.32 11.97 l d 9 0.31 60.84 60.72 60.36 62.59 63.03 0.69 12.66 LDio 0.5 59.3 58.42 58.49 59.57 60 0.42 13.08 L D u 0.5 59.13 58.18 59 60.63 59.66 0.51 13.59 l d 1 2 0.7 65.06 58.66 59.46 60.06 59.32 0.61 14.20 LD,3 0.8 50.32 49.58 50.5 40.19 54.85 0.89 15.09 LD.4 0.7 63.82 56.78 60.78 58.42 60.02 60.85 0.77 15.86 L D 1 5 0.7 61.77 59.99 62.53 61.74 59.06 60.99 0.72 16.58 LD,6 0.8 59.77 57.66 59.93 55.88 58.44 59.6 0.75 17.33 l d 1 7 0.5 60.5 57.37 59.09 60.54 60.22 57.85 0.66 17.99 l d 1 8 0.4 29.88 30.21 26.81 31.68 28.06 29.02 0.46 18.45 L D 1 9 0.3 66.77 59.94 59.96 58.35 59.58 59.85 0.35 18.80 LD2 q 0.1 62.68 63.33 62.68 61.81 62.77 63.12 0.20 19.00 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 4.8 Origin-Destination Routes for the experiments Route Code Origin Location Travel Distance Highway Segment 1 JDY East Los Angeles 20.82 Miles I-605S - I-105W 2 CVR West Los Angeles 14.07 Miles I-10W - I-405S - I-105W 3 EMT Downtown 13.841 Miles I-1 1 OS - I-105W 405 Los Angeles, 605 LAX 105 110 710 Figure 4.7 Locations of three Origin-Destination pairs Travel Time Prediction for Route JDY to LAX 22.5 21.5 - - ? 20.5 H 19.5 - 18.5 18 - 17.5 8 o 8 O o m © © © T O Time of Day (Start Time) | Measured Travel Time Estimated Travel Time | Figure 4.8 Travel time predictions for Route JDY to LAX 66 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. T im e (Minutes) Tim e (Minutes) Travel Time Prediction for Route CVR to LAX 30 25 20 15 10 5 0 o cu 8 O 0 0 1 O c o s 8 O o o co Time of Day (Start Time) Measured Travel Time Estimated Travel Time Figure 4.9 Travel time predictions for Route CVR to LAX Travel Time Prediction for Route EMT to LAX 16.5 15.5 - 14.5 14 -- 13.5 o o < N O c o O CO O 8 O O CO 8 O Time of Day (Start Time) — Measured Travel Time Estimated Travel Time Figure 4.10 Travel time predictions for Route EMT to LAX 67 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. For route JDY to LAX (Figure 4.8), travel time ranges from 19 minutes to 22 minutes with a peak value at 5:30 PM. The largest time prediction errors occurred before 4:30 PM (-0.5 Minute) and after 6:15 PM (+0.5 Minute). That is, there are about 2.5% prediction errors when using the proposed Fuzzy Model for travel time forecasting. For route CVR to LAX (Figure 4.9), travel time ranges from 19 minutes to 25 minutes with a peak value at 5:45 PM. The largest travel time prediction errors occurred between 5:20 PM and 5:50 PM, with the largest 16% prediction errors when using the proposed Fuzzy Model for travel time forecasting. The increase of prediction errors came from the cumulative travel time on the route involving more iterations of travel speeds estimation. That is, the error of travel time prediction is directly proportional to the travel time en route (number of iterations). For route EMT to LAX (Figure 4.10), travel time ranges from 14.5 minutes to 16.5 minutes with a peak value at 6:40 PM. The estimated travel times are very close to the measured travel times along this route during the evening rush period. The largest travel time prediction error occurred at 6:20 PM (-0.5 Minute or 3%). The prediction errors are very small for this experiment because the later half of the route normally does not have heavy traffic in the evening. The major prediction errors occurred when calculating travel time on the first half of the route. 68 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 4.3 Incident Conditions In this section, we investigate the performance of travel time forecasting models under incident conditions. Traffic accidents happen on highways. Speeding, bad weather and drunk driving can all lead to accidents. According to the California Highway Patrol (CHP), there were 198,348 injury collisions in year 2000, and a total of 303,023 persons were involved in the injury collisions. The traffic data for the experiment were collected on August 26, 2003. A traffic collision (ambulance responding) took place on I-10 eastbound close to 1-710 junction at 3:28 PM. The situation completely recovered after 4:35 PM. Table 4.9 shows the CHP record for the traffic collisions and Figure 4.11 shows the locations for the traffic accident. The experiment estimated travel time from postmile=12 to postmile=23(a total travel distance of 1 1 miles), beginning at 3:10 PM and ending at 5:20 PM. Figure 4.12 shows the results of the experiment. Table 4.9 CHP Record for Traffic Collision Start 08/26/2003 15:28 End 08/26/2003 16:35 # 2452 Type Traffic Collision - Ambulance Responding Location EB 110 JWONB 1710 Area East Los Angeles 6 9 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Driving Direction I-110 Junction 1-710 Junction Accident Origin ■ (3-28 PM) I Destination H--------— ol---------- i 12 12.41 19.23 23 Figure 4.11 Traffic accidents on I-10 eastbound According to the experimental results, travel time increases slowly after the accident happened and then decreases slowly before the situation completely recovered. The peak value occurred at 4:10 PM, with the longest travel time of 19 minutes for the 11 miles route. The larger prediction errors happened between 4:05 PM and 4:35 PM; 4:05 PM to 4:20 PM have a -2 minutes difference and 4:20 PM to 4:35 PM have a +2 minutes difference. Measured travel time increased gradually from 3:55 PM to 4:15 PM and then reduced smoothly from 4:15 PM to 4:35 PM due to the traffic accident. In the meantime, the estimated travel time increased gradually from 4:00 PM to 4:25 PM and then reduced smoothly from 4:25 PM to 4:45 PM, contributing the largest prediction errors in the experiment. 70 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Travel Time Prediction Under Incident Conditions 18----- 2 10 — 4 ------- o Time of Day (Start Time) — Measured Travel Time * * ■ * - » Estimated Travel Time Figure 4.12 The experimental results for travel time prediction with incident conditions on I-10 eastbound on August 26, 2003 4.4 Summary In this chapter, we examined travel time forecasting models for real traffic data. We conducted experiments in compliance with various traffic conditions, including time of day, day of week and incident conditions. The proposed Fuzzy Model is superior to the Weighted Moving Average Model in many respects. For the experiments on the single locations, the proposed Fuzzy Model has much smaller mean squared errors than the WMA Model. For the experiments for travel time 71 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. forecasting en route and with incident conditions, the proposed Fuzzy Model can rapidly estimate travel time under any traffic situations. Although the Fuzzy Model performed better than the WMA Model for the experiments, it was not perfect all the time. For example, dramatic speed changes, either increasing or decreasing, will generate larger forecast errors. It is inevitable to have errors for these situations. A possible improvement for the situations is to include more reference points from down-stream speeds and up-stream speeds. Further discussion about improvement of forecasting models will be provided in Chapter 7. 7 2 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 5 Applications to Ground-to-Air Scheduling In the last chapter, we demonstrate the capability of travel time forecasting models by conducting various experiments. In this chapter, we apply travel time forecasting to real-time traffic information and real-time travel time forecasting. We will describe the application to Ground-to-Air scheduling and demonstrate data modeling techniques in this chapter. A critical step in the overnight package delivery industry is the on-time arrival of trucks at airport terminals. Truck delays can delay the package sorting and transfer process, which can in turn delay aircraft departures from the local terminal, as well as aircraft departures from hub terminals that depend on timely aircraft arrivals. This is our motivation for the Ground-to-Air scheduling project. The remainder of this chapter is divided into six sections. Section 5.1 provides background on the application. Section 5.2 summarizes prior work (Hall, 2001), in which models were developed for predicting the arrival of work at a central terminal. Section 5.3 shows the development of the models for predicting the completion of sorting operations at a central terminal. Section 5.4 presents the design for the Truck-to-Air Dispatch (TAD) website. Section 5.5 states the construction of real-time travel time forecasting models for Truck-to-Air scheduling. Summaries are provided in Section 5.6. 73 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 5.1 Background The fastest growing segments of the goods movement industry in the United States have been small shipments and air shipments in recent years. Package delivery companies, such as United Parcel Service (UPS), Federal Express (FedEx), and DHL International (DHL), have prospered in this environment by creating integrated ground/air networks. Air cargo terminals have also developed a capability to rapidly unload trucks, sort shipments, load these shipments into air containers, and load the air containers onto aircraft. The steps are reversed at a destination airport. The first move is to unload aircraft, and then to load trucks within a short time span. High efficiency in sorting and loading has made it economical to send shipments across the country with next day delivery. Express transportation can be divided into several steps. It is desirable to make all of the steps as fast as possible in order to meet time commitments. One of the critical steps is the sorting process at the origin airport. Late truck arrivals can delay sorting with significant repercussions. The issue is especially critical in Southern California for three reasons: (1) west coast shipments have a 3 hour time lag relative to east coast, due to the difference in time zones, (2) Southern California is the dominant population center on the west coast, and (3) congestion in Southern California has both elongated travel times and made them less predictable. 7 4 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The importance of late shipments is magnified by the fact that major hub terminals cannot release their outbound aircraft until all inbound flights have arrived and been processed. Thus, a single delay to a Southern California flight can translate into systemwide delays. Systemwide delays can force an airline to alter its delivery commitment and pickup cutoff times. Thus, airlines that are better at managing their ground operations can offer more competitive service to their customers, and capture a larger share of the express shipment market. The primary analysis in this chapter is a “sort” at an air cargo terminal. Some air cargo terminals schedule multiple sorts at different times, and some terminals have multiple lines that simultaneously complete sorts. Each sort ends when all the packages have been processed for an individual aircraft, or for a group of aircraft that share a sort. Because different sorts process different inbound trucks, and because different sorts feed different aircraft, they can be analyzed independently of each other. 5.2 Model for Arrival of Work This section models the arrival process at the airport freight terminal as a work conserving single server queueing system (Hall, 2002). Work arrives in the form of truckloads of shipments, and is processed by a conveyor sorting line. The amount of work on a truck depends on the number of shipments and their characteristics. One unit of work can be processed in one unit of time. Trucks are 75 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. scheduled to arrive at a reasonably constant rate with the goals of keeping the conveyor line productive and minimizing awaiting processing for the shipments. The variables are defined as follows: n = number of trucks scheduled for a sort, Xi = amount of work on truck i, Ii{t) =1 if truck i has arrived by time t, 0 otherwise, W,(t) = work arrived by time t on truck i, W{t) = cumulative work arrived by time t, among all trucks, where X; and 7,(0 are random variables that depend on the terminal sending shipments, distances, roadway speeds and congestion. W(t) is the measures of cumulative arrival of work that can be derived from X, and /,(?) by Wit) = X /,.(0 X ,, (5.1) 1=1 W(t) = £ w ,( 0 = X w * , . . (5.2) i= i <=i The expectation of W(t) can be calculated by E[W(f)] = X E [/.-(OXJ. (5.3) /= i In the special case where I,{t) and X, are mutually independent, Equation (5.3) reduces to: E [W(t)] = f jPi(t) E(X,), (5.4) ;=i where Pi(t) is the probability that truck i has arrived by time t. Let <r? (t) denote the 76 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. covariance between [/,(f)X,] and [Ij(t)Xj\. Then the variance can be calculated by V[W(t)] = (5.5) U = 1 It is difficult to compute the covariance terms as detailed data are frequently unavailable for estimation of parameters. Here ,we consider the special case where all random variables are mutually independent. Then the variance can be expressed as: V[W(t)] = X Pi(t)[E(Xf) - p,.(0E2(X,.)] T (5-6) = Z a (0[V(X,.) + ( 1 - A.(0)E2(X; .)] (= i Model Extensions The reality is that dependencies do exist among some of the variables 7,(0- Trucks that use the same route at similar times are experience similar travel times and have positively correlated arrival times. Accounting for these dependencies, but still assuming independence with respect to the X, random variables: V[W(t)] = [ £ Pi (0[E(X , 2) - pt (t) E 2 (X; .)] (5.7) + ['ZE(Xi)E(XJ)E{Ii(t)Ij (t)}-pim ( X i)pj (t)E(Xj)] i*j E {7,(07, (0} = P{Tt <t)P(Tj < t|7 ;.< 0 = j / ( 7 } < f |TJfiTJdT (5.8) where T, and 7 } are the arrival times of trucks i and j and f(Tj) is the probability density function for T,. 77 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. If travel times have a multivariate normal distribution, then where //, is E(T,), a} is the standard deviation for arrival time of truck i, and p is the correlation coefficient between arrival times of truck i and truck j. 5.3 Sort Starvation and Scheduling Shipments are processed on a belt sortation system, which operates at a constant rate (defined by the pre-determined belt speed). The sorting process is assumed to begin at a time % corresponding to the time employees arrive for work, and continue until all incoming work is processed. Without loss of generality, the maximum sort rate is assumed to be one unit of work per unit time, and the time of the first scheduled truck arrival equals zero. We assume that incoming loads arrive instantaneously, and that the sorting process continues at the rate 1 whenever work is queued, and the rate 0 otherwise. Sort End Time Modeling Let T represent a practical upper bound on the time when a truck could arrive at a given sort. Then the end time £( f) for the sort can be computed by where S is the length of time that the sort is idled due to the absence of queued work. (5.10) 7 8 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. By making rsmaller, the expectation of £(f) can also be made smaller, thus allowing aircraft to depart earlier on average. However, because S is also a function of T this effect is non-linear. In fact, as r becomes small, E[£(t)] approaches a limiting value, which we denote by the sum W(T)+So. That is, when ris sufficiently small, there is 0 likelihood that a truck will arrive earlier than T , so reducing t further has no effect on EM 2)]. When r is sufficiently large, E(S) approaches 0, so E[£(2)] approaches t + E[W(7)]. Combining these two limiting cases, the following bound is created: E[£(2)]-E[W(7)]>min{So, t} (5.11) The right-hand side of Equation (5.11) can be viewed as the “excess end time,” meaning the amount that E[f(2)] exceeds the expected work, E[W(7)]. (For some distributions, it is possible for the excess end time to be negative.) The performance of the sortation system depends on the rate at which work is scheduled to arrive, along with the start time of the sorting process. If work is scheduled to arrive at a fast rate relative to the sort rate, then work is likely to queue, which has the benefit of minimizing idle time. But beyond a certain point there is little benefit in increasing the arrival rate, as the end time will be dictated by the sorting rate and start time (and not by arrivals). Thus, it may be acceptable to hold back some trucks, reducing pressure on processing shipments at origin terminals and possibly extending the cutoff time for pickup and drop-off of shipments. On the other hand, delaying the start time also reduces idle time (again, because work queues), but 79 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. has the negative effect of extending the end time. Overall, a desirable design would be to pace the arrival of work to roughly match the sorting rate, and to schedule the start of the sort at a time that balances the objectives of maximizing productivity and minimizing the end time. 5.4 Web-based Decision Support Tool The goal of implementing a web-based decision support tool is to schedule and manage the status of trucks in real-time. The website is called Truck-to-Air Dispatch (TAD). TAD follows these design concepts: 1. The site contains a public section and a member-only section. The public section provides links to a variety of data sources related to air/ground shipments, including: (1) Real-time traffic (freeway speeds, lane closures, traffic incidents, directions, traffic information from other regions). (2) Real-time weather. (3) Real-time aviation, including airport delays. (4) Associations and organizations that are involved in air and truck freight shipments. (5) Airports. 2. The member section is open to any individual. The individual who establishes the account acts as the account manager and represents an airport terminal. The member can permit additional users to access and edit terminal data. 80 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. These users may represent local terminals, from where trucks depart for the airport. In this manner, data can be communicated among participants. 3. Data can be easily edited to represent “today’s schedule,” or to represent a planned, or “normal”, schedule. 4. Real-time data are generated to predict the arrival of work (i.e., shipments needing sorting) at the airport terminal. Data are presented both in tabular and graphical formats. 5. “What-if” capability is provided, so the user can easily evaluate the effects of changing the start time for a sort, or changing the processing rate for a sort. A basic goal for the design is to provide a user-friendly interface, and a “one-stop- shopping” location to access a variety of information relevant to ground and air transportation. Figure 5.1 diagrams the site organization, showing six basic functional areas, and an expanded view of the Member Area. Figure 5.2 shows the relationship diagram for database in TAD website. Our focus has been on the Member Area, which is explained in the following sections. 5.4.1 Design Methodology The Member Area is limited to registered users as a means for protecting the confidentiality of user entered data. Immediately after a “New User” form is entered, a new user account is created and an email notification is sent to the user’s email address. This permits the user to enter the Member Area, which provides various 81 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. functions. Figure 5.3 provides an overview of the workflow in the Member Area. We now explain how the functions are performed, beginning with the database. Database Structures Within the Member Area, users can populate four databases; one database is automatically generated, and two are static, created by the developers. All databases are created in Microsoft Access. The four user-populated databases are: 1. Normal truck schedule: database for storing planned truck schedules. 2. Today’s truck schedule: database for storing temporary changes in the truck schedule. 3. Terminal: database for storing a terminal’s physical address. 4. User profiles: database stores user information. The database structures for Normal Schedule and Today’s Schedules are the same. Each record represents an individual truck that is scheduled to travel from a particular terminal to a particular airport, for a particular sort, with given departure and arrival times. These data are represented in 14 fields (Table 5.1). The terminal database is simpler. Each record represents an individual terminal, and there are nine data fields: ID, USERNAME, TERMINALNAME, ADDRESS, CITY, STATE, ZIP, PHONE, and REMARK, which are self explanatory. “REMARK” is used at the discretion of the user to enter comments on a terminal. When a new terminal is entered in the normal schedule database, a record is automatically generated in the terminal database, which the user can later populate with supplemental information (address, phone number, etc.). 82 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Link Traffic Sites Member Area Home Page Contact Information California Lane Closures Frequently Asked Questions Logout First Time User Message Board Travel Advisory News Network User Profile Add New User Share Truck Schedule View Share User Data View User Data Edit User Data Terminal Data Add New Terminal Add From Schedule View Terminal Edit Terminal Delete Terminal Normal Schedule: Add New Truck View All Trucks View Selected Trucks Edit Truck Delete Trucks Table Graph Today’s Schedule Start of Each Day Add New Truck View All Trucks View Selected Trucks Edit Truck Delete Trucks Update Arrival Time Table Graph Figure 5.1 Truck-to-Air Dispatch Site Organization 83 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The user profile database is also simple, and contains the fields: ED , NAME, ADDRESS, PHONENUMBER, EMAIL, AIRLINE, USERNAME, PASSWORD and SUPERIOR. The last field, SUPERIOR, is used to store the relationship between this user and other users. If the user is the root in the group, then a “0” is assigned to this field. Otherwise, this field is assigned a user ID that created the user account and that can share his/her truck schedules with this user. I R elationships ID U5ERNAME TERMINALNAME ADDRESS CITY STATE ZIP PHONE REMARK ID AIRPORT SORTNAME Day Hr Mm STIME PROCRATE USER ID USER AIRPORT 50RTNAME DAY TRUCKNO TERMINAL DEPTIME ARRTIME LOADSIZE R1 R2 ODTIME OATIME ID NAME ADDRESS PHONENUMBER EMAIL AIRLINE SUPERIOR PASSWORD ID USER SORT ID USER AIRPORT SORTNAME DAY TRUCKNO TERMINAL DEPTIME ARRTIME LOADSIZE R1 R2 ODTIME OATIME ID ENTRANCE NAME DISTANCE V D SJD ROUTE ------------- ID V D SJD SPEED ID VD5_ID FREEW AYJD DIRECTION CAL_POSTMILE ABS_POSTMILE DISTANCE NEXT YDS Figure 5.2 The relationship diagram for the database in TAD website 8 4 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 5.1 The database structure for Normal Schedule and Today’s Schedule Fields Meaning ID an automatically generated ordered record number USER user ID AIRPORT name of destination airport SORTNAME name of the terminal sort DAY days of week TRUCKNO truck number TERMINAL name of the origin terminal for the truck DEPTIME scheduled departure time for the truck ARRTIME scheduled arrival time for the truck LOADSIZE load size for the truck R1 the first freeway where the truck enters the highway R2 entrance where the truck enters the highway ODTIME convert departure time from natural time into a time line system, from 1 to 1440 minutes (24 hours) OATIME convert arrival time from natural time into a time line system, from 1 to 1440 minutes (24 hours) Start User Profiles Terminal Data Normal Schedule Table, Graph. Today’s Schedule Table, Graph. Normal Schedule Add, View, Edit, Delete Today’s Schedule Add, View, Edit, Delete Figure 5.3 Member Area Workflow Diagram 85 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. The core of real-time travel time forecasting system contains three databases: real-time traffic database, static database, and VDS database. The automatically generated database maintains information on real-time traffic. Each record represents the state of an individual loop detector (Table 5.2), and updates instantly when user requested. Table 5.3 shows the static database, which provides configurations on loop detectors, highway entrances and routes. This database is used to locate the travel time from origin to highway entrance and from highway exit to destination. Table 5.4 shows the database structure for VDS, which gives the locations of single loop detectors in freeway in Los Angeles area, and the routes to the airport. The data from this database provides necessary information for real-time travel time forecasting models. Table 5.2 The database structure for real-time traffic information Fields Meaning ID ordered number from 1 to 1510 VDS_ID Caltrans detector identification number SPEED Latest speed acquired for the loop detector Table 5.3 The database structure for static database Fields Meaning ID an automatically generated ordered record number ENTRANCE a unique number assigned to the entrance NAME name of the freeway entrance DISTANCE distance from freeway entrance to nearest Single Loop Detector (VDS) in the direction to LAX VDS_ID ID for nearest Single Loop Detector ROUTE freeway ID for the entrance 86 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 5.4 The database structure for VDS Fields Meaning ID an automatically generated ordered record number VDS_ID ID the Single Loop Detector FREEWAY_ID ID for the freeway DIRECTION flow directions for Single Loop Detector in freeway CAL_POSTMILE California post mile for Single Loop Detector ABS_POSTMILE Absolute post mile for Single Loop Detector DISTANCE distance from this Single Loop Detector to next Single Loop Detector in the direction to LAX NEXT_VDS next Single Loop Detector ID in the direction to LAX, which defines the route 5.4.2 Truck-to-Air Dispatch The first step for real-time travel time forecasting is to retrieve real-time traffic data. The Freeway Performance Measurement System (PeMS) FTP site is the source for real-time traffic data. PeMS independently acquires data from California Department of Transportation (Caltrans). When requested by the user, data are transferred to the TAD website with an FTP client, which was created for our web server using Borland C++ Builder. Next, the PeMS file is decompressed. We used a standard gzip program to decompress the file from UNIX system (PeMS) to our Windows operation system environment. After the decompress process is complete, we obtain an ASCII text file that contains the real-time information. Then, we extract relevant data from the ASCII text file (e.g., data from outside the region are discarded), and store the data in our Access database, writing over old data. The total time to complete those steps is about 30 seconds. 87 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Next, to calculate the real-time performance of the airport terminal, truck arrival times must first be estimated. For each highway origin, a normal route is stored in the TAD system, which corresponds to a sequence of loop detectors. Each detector represents a highway segment, with a given length and a current speed. The travel time over the segment is simply the ratio of segment length to speed. In the event of missing data (i.e., a non-functioning detector), the length of an adjacent detector’s segment is increased to cover the missing data segment. The estimated travel time equals the sum of the segment travel times, plus a nominal off-freeway travel time (for which real-time data are unavailable). The arrival time is the sum of the planned departure time and the calculated travel time. Program output is generated in both tabular and graphical forms. Both show when trucks are predicted to arrive for a given sort at a given airport, the cumulative arrival of shipments and cumulative processed shipments. They also provide predictions for when the sort will be completed, and provide “what-if ’ capabilities, with respect to sort rate and sort start time. The calculations are based on the methods presented in Section 5.2. Output graphs are generating by Java Applet, using Java 2 as our programming environment. The size of the applet is 600x400 dots. The actual size of the graph is 450 x300 dots. Figure 5.4 shows the output graph for Normal Schedule. A white line represents the cumulative arrival of loads and a green line represents cumulative processed loads. The sort start time, finish time, rate and total 88 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. shipments processed are also displayed numerically at the top of the page. The start time and the processing rate can be altered by entering the “Reschedule Parameters” at the bottom of the page. A new graph is then created with these parameters. Figure 5.4 Output Graph for Normal Schedule Identical display formats are provided for the normal schedule and the today schedule. An additional option provides an alternative format, showing expected arrival of work ± one standard deviation, and expected completion of work for each of these arrival patterns (Figure 5.5). This graph accounts for variability in truck arrival times at the airport, and is based on Equation (5.6), with a normal arrival time distribution, identical standard deviations for truck arrival times, and a standard deviation in truck load size. Six curves are shown in the SD graph. The meanings for 89 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. the curves are listed in Table 5.5. Adjustable departure time are shown in Figure 5.5 and Figure 5.6. Table 5.5 Curves for Standard Deviation Graph Curves Meaning A+0(t) expected arrival of shipments, plus one standard deviation A(t) expected arrival of shipments A-a(t) expected arrival of shipments, minus one standard deviation P+a(t) expected processed shipments, based on A+0(t) P(t) expected processed shipments P-a(t) expected processed shipments, based on A _a(t) 6 00 1 7'DO 18'QO 10 00 00 00 0 MJO 00 00 0 3 00 04 00 Standard Deviation for Normal Distribution (1 - 40): Figure 5.5 Standard Deviation Graph 90 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Figure 5.6 Cumulative Graphs Before Change in Departure Time Figure 5.7 Cumulative Graphs After Change in Departure Time R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 5.4.3 Example Scheduling Sample data provided by an express carrier were used as an example for demonstration. Table 5.6 shows the locations for 10 terminals in the Los Angeles area. All express shipments from these locations transport to Los Angeles International Airport (LAX). Hence, the sort name for this schedule is called “LAX.” Table 5.7 shows 61 planned truck schedules with their departure time, planned arrival time, and load size. Table 5.6 Terminals for Example Scheduling Terminal Name City State BUR Sun Valley California CCD Beverly Hills California CVR Hollywood California EMT Los Angeles California HHR Hawthorne California JDY Santa Fe Springs California POC City of Industry California SFR Canoga Park California TOA Gardena California VNY North Hills California 9 2 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 5.7 Planned Schedules for Example Scheduling T ruck No. T erm inal D eparture Tim e Arrival Tim e Load Size 1 B U R 1715 1815 100 2 B U R 1715 1815 100 3 B U R 1805 1905 50 4 B U R 1820 1910 40 5 B U R 1745 1845 100 6 B U R 1755 1855 30 7 C C D 1750 1815 80 8 C C D 1805 1830 100 9 C C D 1830 1855 60 10 C C D 1845 1910 60 11 C V R 1805 1835 60 12 C V R 1840 1910 80 13 E M T 1810 1840 30 14 E M T 1830 1900 50 15 E M T 1840 1910 60 16 E M T 1850 1920 40 17 E M T 1820 1850 50 18 H H R 1755 1815 100 19 H H R 1845 1905 80 20 H H R 1840 1900 50 21 H H R 1850 1910 40 22 H H R 1825 1845 100 23 H H R 1905 1925 60 24 H H R 1835 1855 50 25 J D Y 1730 1815 100 26 J D Y 1755 1840 100 27 J D Y 1800 1845 60 28 J D Y 1815 1900 50 29 J D Y 1825 1910 30 30 J D Y 1825 1910 80 31 J D Y 1825 1910 70 32 J D Y 1820 1905 100 33 P O C 1740 1840 100 34 P O C 1755 1855 80 35 P O C 1755 1855 50 36 P O C 1750 1850 60 37 P O C 1755 1855 50 38 P O C 1810 1910 80 39 P O C 1805 1904 60 40 P O C 1800 1900 100 41 S F R 1715 1815 60 42 S F R 1740 1840 100 43 S F R 1800 1900 40 44 S F R 1820 1920 80 45 S F R 1825 1925 60 46 T O A 1745 1815 100 47 T O A 1745 1815 100 48 T O A 1800 1830 60 49 T O A 1755 1825 60 50 T O A 1750 1820 40 51 T O A 1750 1820 40 52 T O A 1820 1850 100 53 T O A 1835 1905 25 54 T O A 1820 1850 60 55 V N Y 1715 1815 30 56 V N Y 1745 1845 100 57 V N Y 1810 1910 100 58 V N Y 1825 1925 50 59 V N Y 1740 1840 60 60 V N Y 1755 1855 65 61 V N Y 1755 1855 65 93 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 5.8 Real-time Schedules for Example Scheduling Arrival Time Truck No. Terminal Load Size Cumulative Load Size Processed Load Size 1 8 1 5 1 B U R 100 7 7 0 0 1 8 1 5 4 1 S F R 6 0 7 7 0 0 1 8 1 5 2 B U R 1 0 0 7 7 0 0 1 8 1 5 4 6 T O A 1 0 0 7 7 0 0 1 8 1 5 4 7 T O A 1 0 0 7 7 0 0 1 8 1 5 5 5 V N Y 3 0 7 7 0 0 1 8 1 5 1 8 H H R 100 7 7 0 0 1 8 1 5 2 5 J D Y 100 7 7 0 0 1 8 1 5 7 C C D 8 0 7 7 0 0 1 8 2 0 5 0 T O A 4 0 8 5 0 2 5 0 1 8 2 0 5 1 T O A 4 0 8 5 0 2 5 0 1 8 2 5 4 9 T O A 6 0 9 1 0 5 0 0 1 8 3 0 8 C C D 100 1 0 7 0 7 5 0 1 8 3 0 4 8 T O A 6 0 1 0 7 0 7 5 0 1 8 3 5 1 1 C V R 6 0 1 1 3 0 1000 1 8 4 0 1 3 E M T 3 0 1 5 2 0 1 1 3 0 1 8 4 0 2 6 J D Y 1 0 0 1 5 2 0 1 1 3 0 1 8 4 0 4 2 S F R 100 1 5 2 0 1 1 3 0 1 8 4 0 5 9 V N Y 6 0 1 5 2 0 1 1 3 0 1 8 4 0 3 3 P O C 1 0 0 1 5 2 0 1 1 3 0 1 8 4 5 2 2 H H R 100 1 8 8 0 1 3 8 0 1 8 4 5 5 6 V N Y 100 1 8 8 0 1 3 8 0 1 8 4 5 5 B U R 1 0 0 1 8 8 0 1 3 8 0 1 8 4 5 2 7 J D Y 6 0 1 8 8 0 1 3 8 0 1 8 5 0 1 7 E M T 5 0 2 1 5 0 1 6 3 0 1 8 5 0 5 2 T O A 100 2 1 5 0 1 6 3 0 1 8 5 0 5 4 T O A 6 0 2 1 5 0 1 6 3 0 1 8 5 0 3 6 P O C 6 0 2 1 5 0 1 6 3 0 1 8 5 5 6 0 V N Y 6 5 2 6 0 0 1 8 8 0 1 8 5 5 6 B U R 3 0 2 6 0 0 1 8 8 0 1 8 5 5 3 7 P O C 5 0 2 6 0 0 1 8 8 0 1 8 5 5 2 4 H H R 5 0 2 6 0 0 1 8 8 0 1 8 5 5 6 1 V N Y 6 5 2 6 0 0 1 8 8 0 1 8 5 5 9 C C D 6 0 2 6 0 0 1 8 8 0 1 8 5 5 3 5 P O C 5 0 2 6 0 0 1 8 8 0 1 8 5 5 3 4 P O C 8 0 2 6 0 0 1 8 8 0 1 9 0 0 2 0 H H R 5 0 2 8 9 0 2 1 3 0 1 9 0 0 2 8 J D Y 5 0 2 8 9 0 2 1 3 0 1 9 0 0 4 3 S F R 4 0 2 8 9 0 2 1 3 0 1 9 0 0 1 4 E M T 5 0 2 8 9 0 2 1 3 0 1 9 0 0 4 0 P O C 1 0 0 2 8 9 0 2 1 3 0 1 9 0 4 3 9 P O C 6 0 2 9 5 0 2 3 3 0 1 9 0 5 3 B U R 5 0 3 2 0 5 2 3 8 0 1 9 0 5 1 9 H H R 8 0 3 2 0 5 2 3 8 0 1 9 0 5 5 3 T O A 2 5 3 2 0 5 2 3 8 0 1 9 0 5 3 2 J D Y 100 3 2 0 5 2 3 8 0 1 9 1 0 1 0 C C D 6 0 3 8 4 5 2 6 3 0 1 9 1 0 1 2 C V R 8 0 3 8 4 5 2 6 3 0 1 9 1 0 4 B U R 4 0 3 8 4 5 2 6 3 0 1 9 1 0 1 5 E M T 6 0 3 8 4 5 2 6 3 0 1 9 1 0 2 1 H H R 4 0 3 8 4 5 2 6 3 0 1 9 1 0 2 9 J D Y 3 0 3 8 4 5 2 6 3 0 1 9 1 0 3 1 J D Y 7 0 3 8 4 5 2 6 3 0 1 9 1 0 3 8 P O C 8 0 3 8 4 5 2 6 3 0 1 9 1 0 5 7 V N Y 1 0 0 3 8 4 5 2 6 3 0 1 9 1 0 3 0 J D Y 8 0 3 8 4 5 2 6 3 0 1 9 2 0 1 6 E M T 4 0 3 9 6 5 3 1 3 0 1 9 2 0 4 4 S F R 8 0 3 9 6 5 3 1 3 0 1 9 2 5 2 3 H H R 6 0 4 1 3 5 3 3 8 0 1 9 2 5 4 5 S F R 6 0 4 1 3 5 3 3 8 0 1 9 2 5 5 8 V N Y 5 0 4 1 3 5 3 3 8 0 94 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 5.5 Real-Time Forecasting Model for Truck-to-Air Scheduling In Section 5.4, a web-based decision support tool was created with a built-in FTP program to acquire real-time traffic information for calculating travel time from terminals to airports. However, the construction of real-time Truck-to-Air scheduling is just part of a real-time environment. Real-time travel time forecasting methods, which we proposed in Chapter 3, need to be integrated into the web-based scheduling tool to complete the real-time Truck-to-Air scheduling tool. We apply the Fuzzy forecasting method to Truck-to Air scheduling in this section. In order to integrate real-time travel time forecasting methods into our web server, a new real-time database system is required for the job. First, a real-time database needs to be able to store historical traffic data for at least three time periods and than update historical traffic data whenever new data arrive. This is because our proposed Fuzzy Model or any time series model, such as WMA model, requires historical data as input data for travel speed prediction. Hence, two sets of historical traffic data along with current traffic data are needed. Next, the real-time database system must be expanded to estimate travel speeds. Every time the forecasting model is executed, a new set of estimated travel speeds is created. The size of the database for storing estimated travel speeds depends on the time of travel. For example, the size of a database for a one-hour prediction is twice the size of the database for an half-hour prediction. Figure 5.8 shows the difference between these two implementations. 95 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. v ; ( 0 Real-time Database System without Real-time Travel Time Forecasting Historical Data Estimated Data < v,<f- 2) V i ( t - 1) V «(0 ^ V,<f+1) v,-(r+2) v,-(r+3) v,(t+4) v,(r+5) v,(r+6) V /(f+ 7 ) V . Real-time Database System with Real-time Travel Time Forecasting Figure 5.8 The difference between two implementations of real-time database system 9 6 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 5.9 Update Procedure for Real-time Database System with Real-time Forecasting Update Procedure for Real-time Database System with Real-time Forecasting Step 0: Acquire real-time traffic speed data for two time periods, and store into v/(f-l), Vi(t) Step 1: Copy data from v,(f— 1) to v,(f-2) and from v,(0 to v ,-(f— 1). Acquire current traffic speed data and store into v,(7) Step 2: Calculate estimate traffic speeds vt(t+ j) for y = 1, 2, n, by V((t+j-\), V i(t+ j-2), V i(t+ j-3 ) Step 3: Calculate real-time travel time by querying appropriate traffic speed data Step 4: Repeat Step 1 to Step 3 whenever new traffic data available. It is obvious that the size of the real-time database system with real-time travel time forecasting is much bigger than the size without real-time travel time forecasting. Next, another consideration for real-time database system with real-time travel time forecasting is the computation time. Since only three sets of historical data are stored inside the database system, all estimated traffic speeds need to be calculated one by one and period by period before we can calculate travel time for the whole route. The computation time is proportional to the number of loop detectors. Finally, the update procedure is summarized in Table 5.9. We use the same example as Section 4.2 to show the difference between real time database systems. Again, the real-time traffic data were collected on October 22, 2002. The execution of the forecasting model begins at 5:00 PM (current time) on a 12.99 miles segment with 20 loop detectors. The total travel time calculated from the real-time travel time database without forecasting is 19.59 minutes and the total 97 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. travel time calculated from the real-time travel time database with forecasting is 19 minutes, whereas 18.69 minutes from measured travel time. That is, the estimated travel time generated by the real-time travel time database without forecasting has larger error than the estimated travel time generated by the real-time travel time database with forecasting. Table 5.10 Real-time Travel Time Calculation Comparisons d, Real-time Travel Time (without Forecasting) Real-time Travel Time (with Forecasting) Real-time Travel Time (Measured) VDS Distance Minutes Cumulative Minutes Minutes Cumulative Minutes Minutes Cumulative Minutes LD, 0 . 2 0.41 0.41 0.41 0.41 0.41 0.41 l d 2 0.43 1.99 2.40 1.99 2.40 1.99 2.40 l d 3 0.48 1 . 8 8 4.28 1 . 8 8 4.28 1 . 8 8 4.28 l d 4 1 . 0 1 2.08 6.36 2.08 6.36 2.08 6.36 l d 5 1.3 2.33 8.69 1.89 8.25 1.40 7.76 l d 6 0 . 6 0.97 9.66 1.28 9.53 1 . 0 1 8.77 l d 7 1.59 1 . 1 2 10.78 1 . 1 2 10.65 1.18 9.95 l d 8 1.07 1.32 1 2 . 1 1.32 11.97 1.41 11.36 l d 9 0.31 0.69 12.79 0.69 1 2 . 6 6 0 . 6 6 1 2 . 0 2 L D io 0.5 0.42 13.21 0.42 13.08 0.41 12.43 LDn 0.5 0.51 13.72 0.51 13.59 0.50 12.93 LD12 0.7 0.61 14.33 0.61 14.20 0.61 13.54 LD.3 0 . 8 0.89 15.22 0.89 15.09 0.82 14.36 LD14 0.7 0.74 15.96 0.77 15.86 0.74 15.1 LD15 0.7 0.67 16.63 0.72 16.58 0.69 15.79 LD,6 0 . 8 0.75 17.38 0.75 17.33 0.76 16.55 LD17 0.5 0 . 6 6 18.04 0 . 6 6 17.99 0.67 17.22 5 0 0 0.4 1 . 0 1 19.05 0.46 18.45 0.93 18.15 LD19 0.3 0.35 19.4 0.35 18.80 0.35 18.5 LD2 o 0 . 1 0.19 ' ■ ■ ■ ; - 49.59 0 . 2 0 19.00 0.19 18.69 98 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 5.6 Summary UPS, Federal Express and other air express companies operate many local terminals within the Los Angeles area. At the end of each day, trucks depart from these terminals carrying express shipments, which are processed at Los Angeles International Airport, Ontario Airport and other local airports in Southern California. Aircraft depart from these airports according to a rigid schedule, so it is important for trucks to arrive on time and for shipments to be processed on time. In this chapter, we model the sorting process at the terminal and the effects of truck arrival time on the completion of the sort. By implementing a web-based decision support tool with real-time travel time forecasting ability, outbound aircraft from express companies can depart on schedule. The tool predicts the completion time of sorting operations, which determines the earliest departure time for the aircraft. A web-based tool (TAD) was created, which both provides access to a range of information sources, and analyzes truck arrival patterns at the airport terminal. The tool demonstrates the possibilities for incorporating real-time traffic measurements in truck scheduling. Unlike personal travel, trucking companies are concerned with the effect of traffic delays on entire fleets. Therefore, it is essential to have tools that enable sets of vehicles to be analyzed, as was accomplished in TAD. The result of utilization of real-time traffic information with real-time forecasting is shown in the previous section that the real-time database system with real-time forecasting can generate more accurate predictions. Hence, the completion time of sorting operations at the airport terminal can be determined efficiently. 99 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 6 Applications to a Transit Strike 6.1 Background Public transportation is one of the important services in big cities. It is estimated that 5% Americans rely on some form of transit system. Table 6.1 shows “journey to work” data table in Los Angeles County, California, from U.S. Census 2000. Bus transit systems are attractive to meet the growing transportation requirements due to expansion of urban areas and heavy traffic congestion on highway. From October 14 to November 17, 2003, 2,200 mechanics at Los Angeles County's Metropolitan Transportation Authority (MTA) walked off the job, joined by 6,000 bus drivers, rail operators and other workers, halting 1,900 buses, as well as light-rail and subway lines. It was the second transit strike in three years in Los Angeles and the fourth since 1982. The MTA is the largest transit provider in the Los Angeles area. It serves nearly 400,000 bus riders and 100,000 subway and light-rail riders daily. Table 6.2 shows MTA’s bus lines and rails ridership comparison during September 2003. The walkout during these 35 days shut down buses and trains forcing those 500,000 daily riders around Los Angeles County to scramble for alternate transportation. It was the longest strike in over two decades to hit the public transportation system with nearly 2,400 Metro Buses and 73 miles of Metro Rail service. The previous walkout in year 2000 by bus drivers shut down the public 100 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. transportation system for 32 days. Taxi companies and other bus lines, like the city of Los Angeles Department of Transportation (LADOT), experienced increased demand. Table 6.3 shows the public transit ridership in Los Angeles County from 1999 to 2000. But many of those who rely on mass transit could not afford the costly alternative and were forced to stay home, walk or rely on friends or relatives for rides. Table 6.1 U.S. Census 2000, journey to work table in Los Angeles County, California (United States Census Bureau) U.S. Census 2000: Los Angeles County, California Count Percentage Total population 9,519,338 Workers 16 years and over 3,858,750 100.00% Means of transportation to work: Car, truck, or van 3,296,964 85.44% Drove alone 2,714,944 70.36% Carpooled 582,020 15.08% Means of transportation to work: Public transportation 254,091 6.58% Bus or trolley bus 234,662 6.08% Streetcar or trolley car 1,946 0.05% Subway or elevated 6,200 0.16% Railroad 7,660 0.20% Ferryboat 366 0.01% Taxicab 3,257 0.08% Means of transportation to work: Motorcycle 6,758 0.18% Means of transportation to work: Bicycle 24,015 0.62% Means of transportation to work: Walked 113,004 2.93% Means of transportation to work: Other means 29,275 0.76% Worked at home 134,643 3.49% 101 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 6.2 Los Angeles County's Metropolitan rails ridership during September 2003 Transportation Authority bus lines and Day of Week Bus Lines - MTA Rails Red Line Blue Line Green Line Average Weekday Boardings 1,157,643 112,021 74,406 35,847 Average Saturday Boardings 780,026 82,346 54,770 20,557 Average Sunday and Holiday Boardings 568,529 70,444 44,972 14,754 Total Calendar Month Boardings 30,273,256 3,034,049 2,006,464 908,787 Total Fiscal Year-to-Date Boardings 95,677,202 9,035,697 74,406 2,757,242 Table 6.3 Public transit ridership in Los Angeles County from 1999 to 2000, data from California State Controller System Ridership Vehicles in Operation at Peak Weekday Usage MTA 392,773,778 1,997 Foothill Transit 16,273,000 259 Long Beach Transit 26,255,487 151 Santa Monica's Big Blue Bus 22,057,734 134 MetroLink 6,978,588 133 LADOT 3,356,943 88 Santa Clarita Transit 2,321,035 48 Torrance Transit 4,509,300 43 Gardena Municipal Bus Lines 6,136,864 39 Antelope Valley Transit Authority 2,216,090 36 Culver City Transit 4,525,307 27 1 0 2 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Not only MTA daily riders suffered from the transit strike, but also motorists driving on highways, local residents and local businesses in Los Angeles County. According to Department of Motor Vehicles (DMV), more than 26 millions motor vehicles were registered in California. One quarter of them were registered in Los Angeles County. Only seven states have more registered cars than does Los Angeles County: California, Florida, Texas, New York, Ohio, Illinois, and Pennsylvania. Motorists driving on highways suffered from longer periods of rush hours and reduced speed. Travel behavior (Lee and McNally, 2003) changed during transit strike period. Local businesses suffered from a revenue drop during the transit strike. According to the Los Angeles Business, the strike costs the local economy more than $4 million per day. 6.2 Objectives One of the objectives of this chapter is to investigate the impact of the transit strike through analysis of highway sensor data, using both a before-and-after comparison, and a control group comparison. The other goal of this chapter is to examine the real-time travel time forecasting models during transit strike period. There is a limited literature on the impact of transit strikes. Freilich (1966) first depicted the importance of emergency planning for transit strike based on the New York transit strike in 1966. Marmo (1990) also addressed the issues and phenomena during the New York transit strike of 1966. The political milieu between 103 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. New York State governor, New York City mayor, Transport Workers Union (TWU), and New York City Transit Authority (TA) were widely discussed in this book. Pheley (1999) researched the effects on access to medical care and measured value of New York hospitals during a transit strike. It is commonly concluded by the above literature that business operated as usual, but the cost was high during the New York transit strike in 1966. This research focused on the New York City transit strike in 1966 because the transit system in New York City was very large and complex at that time. It operated twenty-four hours per day and carried more than 1,836 billion passengers per year during 1970s. 210 118 170 210 210 210 101 405 605 110 710 l a : 105 405 Figure 6.1 Los Angeles County highway network 104 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Figure 6.1 shows the Los Angeles County highway network. The purpose of this research is to identify the level of impact on highway transportation from transit strike and apply travel time forecasting model to heavy traffic conditions. Unlike New York City, the major transportation method in Los Angeles County is highway transportation. There are total 1,740.5 miles of 37 freeways in Los Angeles County. Therefore, the transit strike has significant effects on highway traffic. Traffic data acquiring from hardware sensors installed on highways was used to show the impact on highway transportation by the mass transit strike. We focused on the data from downtown Los Angeles areas as a case study. The traffic data from Orange County was also used in contrast with the traffic data Los Angeles County at the same time interval. 6.3 Reasons for Strike In the Los Angeles transit strike of 2003, union officials wanted the MTA to increase its monthly contributions to the union's health care funds. The MTA paid about $1.4 million per month into the fund for the medical coverage of 2,000 employees and retirees before the strike. The MTA hasn't increased its contribution to the fund in more than a decade and rising medical costs have forced the union to spend fund reserves to keep up. But the union claimed that rapidly rising health insurance premiums had pushed the cost to $1.9 million monthly. 105 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. On the other hand, the MTA thought the union has mismanaged the fund and workers should contribute more to make up the difference. The MTA had agreed to put more into the fund, but wanted control over how it is managed. The decision to proceed with a walkout was made after negotiations between the union and the MTA broke off without any progress despite intervention from a state mediator. The MTA proposed equal representation on the six-member board overseeing the nearly insolvent fund and agreed to make a one-time contribution of $4.7 million- an increase from a previous offer of $4 million. The MTA's monthly payments to the fund would be increased from $1.4 million to $1.9 million. According to the statement from MTA CEO Roger Snoble, union leaders basically ran the trust fund into the ground and now they want the taxpayers to bail them out. After 35 days on the picket lines, a tentative contract agreement between labor and management ended mass transit strike in Los Angeles and MTA resumed operations. The Amalgamated Transit Union (ATU) leadership ended the strike upon securing a 7 percent wage increase over three years from the MTA and an agreement to enter nonbinding arbitration to resolve all remaining issues. Commuters also benefited from this strike. The fare for riding MTA was reduced from 1.35 dollars to 1.25 dollars (single ride). Moreover, MTA introduced one-day pass to simply the transfer for bus to bus, and bus to rail service. 106 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 6.4 Methodology and Study Design One of the objectives of this chapter is to investigate the impact of the transit strike through analysis of highway sensor data. According to the MTA, the system map for Metro Bus and Rail is divided into six areas of service: (1) North LA County, (2) San Fernando Valley/Burbank/Glendale, (3) West/Central Los Angeles, (4) Downtown Los Angeles, (5) East Los Angeles/San Gabriel Valley, and (6) South Los Angeles/Long Beach. To evaluate the effects of the strike, we analyzed traffic conditions at a set of locations surrounding west/central Los Angeles. Our study focused on these highways: • 1-5 Golden State Freeway - principal north/south route through the region • US 101 Hollywood Freeway - one of the oldest highways in the region, connecting downtown to Hollywood and San Fernando Valley. • I-110 Harbor/Pasadena Freeway - connecting downtown to Pasadena in the north and the port in the south • I-10 Santa Monica Freeway - primary east/west route, connecting downtown to the Century City Area, Santa Monica and the beach. • 1-105 Freeway - major east/west route, connecting Los Angeles International Airport to points east. • 1-405 San Diego Freeway - major north/south route passing in vicinity of UCLA campus and Los Angeles International Airport The significance of the transit strike naturally depends on the level of transit 107 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. service and patronage in the vicinity of the highway segment being studied, along with baseline highway congestion. Transit service is particularly strong in the area to the west of the downtown, bounded by I-10 to the south, I-110 to the east, and SR- 101 to the north, and stretching about five miles to the west. In addition to a large concentration of heavily patronized bus lines, this area is served by the MTA Red Line, the region’s only heavy-rail subway system. Transit patronage is much smaller in the vicinity of 1-105, although a light rail line is located in the highway’s median. Loop detectors data were collected both before and during the strike. We calculated average traffic speed from 20 consecutive working days before the transit strike and 20 consecutive working days during the transit strike. We used traffic data from 1-5 in Orange County as a control group, to evaluate whether changes in delay could be attributed to factors other than the strike, such as weather patterns or seasonal traffic patterns. 6.5 Statistics and Finding The results are divided into three sub-sections, first examining a sample of individual highway locations, next examining entire highway segments, and last calculating confidence intervals and comparing a large sample of locations to a control group. The traffic data for a control group are selected from Orange County (District 12) to compare the impact mostly on Los Angeles area. 1 0 8 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 6.5.1 Impact on Single Locations First of all, we analyzed the impact on highway transportation by focusing on the single locations in the middle of highway segment. Total eight locations on highway segments are selected in the area of West/Central Los Angeles, one of the highly dense populations in Los Angeles County. Figure 6.2 shows the map of these locations. Loop detectors in these locations are exactly in the middle of highway segments and between two major highway intersections. We observed the data from 5:00 AM to 10:00 PM everyday. Rush hour period was measured by the time when average traffic speeds were less than 60 miles/hour. The purpose of the analysis is to show the impact at single point on highways for the whole day. The length of rush hours and average speed are calculated for these locations. Table 6.4 shows the results from these locations. Three of the eight locations had separate morning rush hour period and evening rush hour period clearly. Figure 6.3 to Figure 6.10 show average speed comparisons for these locations. Figure 6.11 shows average flow comparison on 1-5 at the same location. Every location in this area had impact from transit strike. For example, morning rush hour on 1-5 expanded from 270 minutes to 315 minutes, or a 16.67% increase. Evening rush hour on 1-5 expanded from 105 minutes to 325 minutes, or a 209.52% increase. All day average speed on 1-5 reduced from 58.09 miles/hour to 51.17 miles/hour, or an 11.91% drop. Evening rush hour period during transit strike was almost three times of normal evening rush hour period. However, average flow 109 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. did not change a lot during transit strike period. According to Figure 7, number of flow had similar values all day during transit strike period. 405 170 101 101 101 405 Olio 405 105 105 405 110 134 10 60 105 Figure 6.2 Single Locations from West/Central Los Angeles 1-5 Southbound (Between 1-10 and SR-134) 3 40 o o on 8 O n < n Time o f Day Before Strike • -During Strike | Figure 6.3 Average speed comparisons before strike and during strike on 1-5 southbound between I-10 and SR-134 110 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 6.4 Statistics analysis for the impact on single locations Highways Measures Before Strike During Strike Difference 1-5 S (1-10 & SR-134) Morning Rush Period 270 Minutes 315 Minutes +16.67% Evening Rush Period 105 Minutes 325 Minutes +209.52% All Day Average Speed 58.09 Miles/Hr 51.17 Miles/Hr -11.91% I-10E (1-110 & I- 405) Morning Rush Period 165 Minutes 195 Minutes +18.18% Evening Rush Period 345 Minutes 425 Minutes +23.19% All Day Average Speed 52.03 Miles/Hr 46.48 Miles/Hr -10.67% SR-101S (1-110 & SR-170) Morning Rush Period 260 Minutes 335 Minutes +28.85% Evening Rush Period 265 Minutes 375 Minutes +41.51% All Day Average Speed 54.45 Miles/Hr 43.57 Miles/Hr -19.98% SR-101S (SR-170 & 1-405) Combined Rush Period 780 Minutes 810 Minutes +3.85% All Day Average Speed 46.53 Miles/Hr 42.59 Miles/Hr -8.47% I-105W (1-110 & I- 405) Combined Rush Period 250 Minutes 305 Minutes +22.00% All Day Average Speed 60.66 Miles/Hr 58.77 Miles/Hr -3.12% I-110N (1-10 & I- 105) Combined Rush Period 805 Minutes 855 Minutes +6.21% All Day Average Speed 51.11 Miles/Hr 44.94 Miles/Hr -12.07 I-405S (SR-101 & I-10) Combined Rush Period 790 Minutes 1020 Minutes +29.11% All Day Average Speed 50.14 Miles/Hr 42.83 Miles/Hr -14.58 1-405S (1-10 & I- 105) Combined Rush Period 765 Minutes 770 Minutes +0.65% All Day Average Speed 47.56 Miles/Hr 44.80 Miles/Hr -5.80% R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 1-10 Eastbound (Between 1-110 and 1-405) o 8 © < T i ro © § 8 8 Time of Day | Before Strike During Strike | Figure 6.4 Average speed comparisons before strike and during strike on I-10 eastbound between I-110 and 1-405 SR-101 Southbound (Between I-110 and SR-170) Cl . 3 0 c /i © > r > cl in © * 3 * 8 Time of Day |........ Before Strike------- During Strike | Figure 6.5 Average speed comparisons before strike and during strike on SR-101 southbound between 1-110 and SR-170 112 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. SR-101 Southbound (Between SR-170 and 1-405) o. 3 0 o v i o > / i o m o ^ (N O d o 0 \ o \ o o Time of Day | Before Strike During Strike j Figure 6.6 Average speed comparisons before strike and during strike on SR-101 southbound between SR-170 and 1-405 1-110 Northbound (Between 1-10 and 1-105) V " ) O I V } O 1 / 1 o 7! f ! C l 9 7! t-4 oo c s o o Time of Day p* • • Before Strike-------During Strike [ Figure 6.7 Average speed comparisons before strike and during strike on I-110 northbound between I-10 and 1-105 113 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 1-405 Southbound (Between SR-101 and 1-10) 70 -r "S 30 O vh O O < « ■ > — I o o > n o > / ■ > o " 7 f1 'n 9 7 Time of Day • Before Strike During Strike | Figure 6.8 Average speed comparisons before strike and during strike on 1-405 southbound between SR-101 and I-10 1-405 Southbound (Between I-10 and 1-105) S 50 o o v ) o » n o T f c s m m o rr s s s s s s s Time of Day Before Strike ■ During Strike] Figure 6.9 Average speed comparisons before strike and during strike on 1-405 southbound between I-10 and 1-105 114 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 1-105 Westbound (Between I-110 and 1-405) 80 70 60 ? 50 o 5 I 4 0 -o 6 30 o o J U 20 10 0 Figure 6.10 Average speed comparisons before strike and during strike on 1-105 westbound between I-110 and 1-405 8 8 n in n Time of Day I / O '< 0 V O ■ Before Strike • -During Strike | N N n N 1-5 Southbound (Between I-10 and SR-134) 700 -r 600 500 -- 400 -- 200 100 o s Time of Day Before Strike During Strike Figure 6.11 Average flow comparisons before strike and during strike on 1-5 southbound 115 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 6.5.2 Impact along Routes In this section, we investigate the impact on traveling continuous routes on a highway; that is, segments of highways, with average speed comparison with MTA ridership. MTA ridership data can be found in Table 6.2. Three indexes are defined by the following equations, one hour average speed before strike, one hour average speed during strike, and speed difference: One hour Average Speed Before Strike (ASB) = Average Speed from Sep. 15 to Oct. 10 weekdays traffic speed from 7 - 8 AM. One hour Average Speed During Strike (ASD) = Average Speed from Oct. 20 to Nov. 14 weekdays traffic speed from 7 - 8 AM. Speed Difference (SD): Average SpeedB e fo re S tr ik e - Average Speed A fte r S tr ik e x} Q Q % Average SpeedB e f o r e S tr ik e MTA Ridership data acquired from MTA website (http://www.mta.net/). M«rtl IWtywood SR-101 Red Line Downtown im Angeles Figure 6.12 MTA rail: red line and SR-101 116 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Impact along MTA Red Line One of the most important rail lines in Los Angeles County is the MTA red line, which connects downtown Los Angeles from Union Station to Hollywood. MTA red line serves 17.4 miles and is parallel to the SR-101 highway. Figure 6.12 shows the map for MTA rail red line and SR-101 highway. Table 6.5 and Figure 6.13 show the average speeds comparison (ASB and ASD) on I-101 southbound. SD data are also shown in table 6.5. Abs Post Mile is the location for loop detectors that measures from one of the ends. In table 6.5, loop detectors that close to downtown area have bigger number of Abs Post Mile. From Table 6.5, the impact of transit strike had applied to every point along this route. As much as 37% of average speed reduction can be found along this route. Average Speed for SR-101 70.00 60.00 - 50.00 • - 5 40.00 ■ g 30.00 20.00 10.00 134 110 170 405 0.00 3.43 3.91 4.14 5.08 5.55 6.13 6.44 6.83 7.25 7.45 7.71 8.34 9.46 10.7 11.2 11.4 12.5 14.1 15.1 16 17.1 Post Mile 1 — •— One Hour Average Speed Before Strike -*~One Hour Average Speed During Strike] Figure 6.13 Average speed comparisons on SR-101 Southbound 117 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 6.5 Average speed comparison on I-101 southbound, ASB data from September 15 to October 10, 2003 and ASD data from October 20 to November 14, 2003 Abs Post Mile ASB (Miles/Hour) ASD (Miles/Hour) SD 3.428 45.31 41.70 7.98% 3.908 36.95 36.07 2.37% 4.138 36.92 33.04 10.49% 5.078 26.08 22.62 13.25% 5.548 28.51 19.22 32.61% 6.128 21.32 18.26 14.34% 6.438 21.94 18.81 14.27% 6.828 22.41 20.34 9.20% 7.248 26.86 20.79 22.59% 7.448 28.36 20.06 29.29% 7.708 35.98 22.48 37.52% 8.338 53.65 39.03 27.25% 9.458 58.36 41.54 28.82% 10.658 44.59 35.92 19.46% 11.178 43.81 36.12 17.56% 11.388 43.91 30.65 30.20% 12.518 35.49 25.42 28.38% 14.583 43.85 30.64 30.12% 15.633 50.00 33.52 32.96% 16.533 54.42 39.72 27.02% 17.643 51.83 41.86 19.23% Impact along MTA Blue Line Another rail line in Los Angeles County, which connects downtown Los Angeles to Long Beach, is the MTA blue line. MTA blue line serves 22 miles and 118 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. parallels the I-110 highway and SR-710.1-110 is also served by a busway along with a large number of surface street bus routes. Therefore, transit patronage is also high in this corridor, though not as high as the 101 corridor. Figure 6.14 shows the map for MTA blue line and I-110 highway. Table 6.6 and Figure 6.15 show the average speeds comparison on I-110 northbound between ASB and ASD. SD data is also shown in Table 6.6. According to the data from Table 6.6, the impact of transit strike had almost applied to every point along this route. As much as 41% of average speed reduction can be found along this route. Similar to the 101 results, speeds declined the most toward the tail of ordinary queueing for traffic approaching the downtown, between mileposts 13 and 16 - effectively pushing major congestion back about 3 miles on the highway. By contrast, traffic speeds did not change appreciably in close vicinity to the downtown, as this section already experienced significant queueing during the 7-8:00 AM. D c 1-710 Long Beach Figure 6.14 MTA rail: blue line and 1-110 119 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 6.6 Average speed comparison on 1-110 northbound, ASB data from September 15 to October 10, 2003 and ASD data from October 20 to November 14, 2003 Abs Post Mile ASB (Miles/Hour) ASD (Miles/Hour) SD 1.2 65.38 66.06 -1.03% 1.58 72.23 74.35 -2.94% 2.77 71.00 69.33 2.36% 5.31 46.44 40.52 12.75% 5.53 42.84 37.42 12.66% 6.77 45.26 39.49 12.74% 7.91 55.36 51.16 7.58% 9.14 61.24 57.60 5.95% 9.61 65.95 59.81 9.31% 10.64 62.40 57.62 7.66% 11.15 59.25 53.06 10.45% 11.9 65.45 64.41 1.59% 12.79 65.50 63.58 2.93% 13.06 66.72 65.75 1.45% 13.74 65.87 61.87 6.08% 14.22 45.86 29.37 35.96% 14.43 42.67 29.69 30.41% 15.03 32.05 29.27 8.67% 15.29 35.71 31.27 12.44% 15.81 46.19 27.19 41.14% 15.95 65.93 47.20 28.40% 16.51 60.23 40.06 33.49% 17.06 65.51 53.07 18.99% 17.61 67.99 59.70 12.20% 17.9 65.99 52.66 20.21% 18.57 22.03 22.04 -0.02% 19.09 23.72 22.10 6.83% 19.4 24.88 22.47 9.70% 19.93 30.72 25.71 16.30% 20.53 20.16 19.66 2.48% 21.29 29.42 28.42 3.39% 22.98 36.36 33.32 8.36% 24.39 69.16 69.16 0.00% R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Average Speed for 1-110 80.00 70.00 - - 60.00 S' 50.00 - £■ 30.00 ----- 20.00 10.00 405 105 0.00 (N 00 ^ 4 vo Post Mile | — One hour Average Speed Before Strike One hour Average Speed During Strike | Figure 6.15 Average speed comparison on I-110 northbound Impact along MTA Green Line Finally, the MTA green line serves 20 miles and parallels the 1-105 highway. It connects to the vicinity of the Los Angeles International Airport (LAX). Figure 6.16 shows the map for MTA green and 1-105 highway. Table 6.7 and Figure 6.17 show the average speeds comparison on 1-105 eastbound between ASB and ASD. SD data is also shown in Table 6.7. In the figure and table, smaller post miles represent locations that are close to Los Angeles International Airport. From Table 6.7, the influence of transit strike is not complete to the whole highway. The segment that is far from LAX area, between 1-710 and 1-605, had better traffic speed even during 121 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Speed (Miles/Hour) strike period. However, speed declines by as much as 19% of the segment that is closest to the LAX area. LAX Green Line 1-105 1-110 Figure 6.16 MTA rail: green line and 1-105 Average Speed Comparsion on I-105 80.00 70.00 60.00 50.00 40.00 - ~ 30.00 - 20.00 10.00 405 1 1 0 710 605 0.00 Postmile One hour Average Speed Before Strike ■ One hour Average Speed During Strike Figure 6.17 Average speed comparisons on 1-105 Eastbound 122 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 6.7 Average speed comparison on 1-105 eastbound, ASB data from September 15 to October 10, 2003 and ASD data from October 20 to November 14, 2003 Abs Post Mile ASB (Miles/Hour) ASD (Miles/Hour) SD 0.6 74.58 73.96 0.84% 0.9 74.36 72.97 1.87% 1.8 71.23 64.53 9.40% 3.1 70.92 61.46 13.35% 3.6 70.98 59.27 16.51% 4.2 68.38 56.48 17.41% 4.6 66.58 59.45 10.70% 4.9 66.77 62.77 5.98% 5.5 66.26 64.49 2.66% 6 67.07 66.43 0.96% 6.6 67.59 67.41 0.27% 7.56 68.40 67.19 1.77% 7.8 71.90 58.84 18.16% 8.2 69.65 57.70 17.16% 8.4 68.99 55.90 18.98% 9 67.79 55.46 18.20% 9.7 65.67 58.05 11.60% 10.5 61.57 54.49 11.49% 10.9 63.62 52.43 17.59% 11.7 61.16 54.25 11.30% 11.9 59.64 51.38 13.85% 12.6 66.62 58.61 12.03% 13.2 69.67 70.55 -1.26% 13.8 68.97 70.92 -2.83% 14.4 56.49 56.03 0.81% 14.8 52.79 50.85 3.68% 15.3 59.55 59.23 0.54% 15.6 61.76 60.34 2.30% 15.9 65.26 66.04 -1.19% 16.3 66.31 67.62 -1.97% 16.8 59.17 61.25 -3.51% 17.3 36.55 45.47 -24.40% 18.13 58.16 59.32 -1.99% 123 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 6.5.3 Comparison to Control Group In this section, we compare changes in speed in Los Angeles County (District 7) to those observed on 1-5 within Orange County (District 12). Our comparison is again based on average traffic speed on 20 consecutive working days before the transit strike and 20 consecutive working days during the transit strike everyday from 7 AM to 8 AM. For each segment in LA County, 5 to 18 sites were included, and confidence intervals were derived by 1300 to 4680 sample data. A total of 142 sites were included for the segment on 1-5 southbound in Orange County, and confidence intervals were derived from 36920 sample data points. Table 6.8 also includes another index, Average Flow Ratio (AFR). The one-hour average flow ratio is calculated by the following equation: ™ One-Hour Average Flow During Transit Strike Average Flow Ratio (AFR) = ---------------------- ----------------- ------------------- One - Hour Average Flow Before Transit Strike If the average flow during transit strike is smaller than the average flow before strike, the value of AFR is smaller than 1. It should be noted that many locations experienced a reduction in flow while simultaneously experiencing a reduction in speed. While such an outcome is not implausible, it is surprising to see this as a fairly widespread result. Figure 6.18 shows average speed comparison on 1-5 southbound in Orange County. According to these data, the average speeds during the strike period are slightly smaller (1.08%) than speeds before the strike in Orange County. While this difference is indeed statistically significant, it is quite small compared to the speed 124 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. differences observed in several locations within LA County - especially those covering the tails of queues on approach routes toward the downtown (SR-101 and I- 110 in particular). It should be noted that not all locations in LA County experienced statistically significant reductions in speeds, though none experienced a significantly significant increase in speed. Table 6.8 95% Confidence interval for three highways along three MTA rail routes and compare with highway in Orange County at the same time interval Highways Segments ASB (Miles/Hour) ASD (Miles/Hour) AFR SD SR-101 I-110& SR-170 SR-170 & 1-405 (29.74, 30.38) (46.00,48.23) (24.51,25.20) (32.65, 36.91) 0.8986 0.8547 17.33% 37.36% 1-110 SR-47 & 1-405 1-405 & 1-105 1-105 & I-10 (58.37, 58.98) (63.74, 63.83) (34.12, 34.27) (55.16, 56.26) (60.05, 60.47) (27.94, 28.94) 0.9778 0.9350 0.9628 5.06% 5.53% 18.64% 1-105 1-405 & I-110 I-110& 1-710 1-710 & 1-605 (69.32, 69.72) (65.76, 65.92) (59.86, 60.36) (64.31,64.64) (56.22, 56.92) (59.34,61.69) 1.0180 0.9372 0.9127 7.26% 14.08% -0.68% 1-10 1-405 & I-110 I-110 & 1-5 1-5 & 1-710 (48.29, 49.74) (57.90, 60.85) (60.73, 60.87) (42.39, 43.96) (58.85,61.66) (60.41, 60.79) 0.9502 1.0516 0.9294 11.93% -1.48% -0.33% 1-5 Orange County (62.96, 63.23) (62.26, 62.54) 0.9780 1.08% 125 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 80 Interstate Highway 5 in Orange County •= 40 q. 30 ■ 10 0 I I I I 1 1 I 1 I I ......... I I I I 1............I................................. I I I I I I........HIM ..........I................I............m m ..................................................... I i— c \ i c \ i ^ t 0 3 0 ) ' ^ c o c o u r 5 ^ t o > i o m m r t - r « . c o o c \ j c o T t L n i n < o r * . r ,»«cx>c no >o cMO JU> r* »o > r- r- C O C O C O C D 0 ) G ) O O ) o o o o o P o st Mile ASB —— a s d | Figure 6.18 Average speed comparisons on 1-5 southbound in Orange County 6.6 Real-Time Forecasting Model during Transit Strike The other goal of this chapter is to examine the real-time travel time forecasting models during a transit strike. In Chapter 4, we investigated the performance of real-time forecasting models under various traffic situations, including time of day, day of week, and incident conditions. One of the non-recurrent traffic conditions that we did not test in Chapter 4 is travel time during a transit strike. Therefore, we examine the performance of the forecasting models during a transit strike in this section. The traffic data from October 20 to October 24, 2003, the 126 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. second week of the transit strike, were collected and tested. All loop detectors on I- 10 westbound between 1-405 and I-110 were examined as in the experiments in Section 4.1. Because of the expanded rush period, each experiment in this section contains a four-hour testing period that includes 49 measured traffic speeds from 49 5-minute data sets. Again, three measured traffic speeds were needed to initiate the forecasting models. Therefore, a total of 46 values were forecasted. That is, n=46 in the MSE calculation. The experimental results for the Fuzzy Model and the WMA Model are shown in Table 6.9 and Table 6.10, respectively. The total MSE value from the Fuzzy Model is 2481.67, which is lower than the value of 3970.14 from the WMA Model. Compared to the results from the experiments in Section 4.2.1, the forecasting errors were relatively small because overall MSE in this experiment contains a four-hour testing period from five days instead of a three-hour testing period from four days. This is because, during the strikes, traffic speeds tend to stay low for a longer period of time. The changes in speeds are relatively small in comparison with normal traffic. Hence, the forecasting error declined during the strikes. Figure 6.19 shows the comparison graph from VDS ID=716063, which is the same location as the experiment in Section 4.2.1, on October 23, where the MSE from the Fuzzy Model is 13.05 and the MSE from the WMA Model is 27.49. As shown in the figure, traffic speeds increase from close to 40 miles/hour at 6:45 AM to close to 70 miles/hour after 7:00 AM at this location. The traffic condition around 127 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 7:00 AM in the morning is better then any other weekdays. Heavier traffic flow disappeared after 7:00 AM and the average traffic speed close to 70 miles/hour afterward on Friday in contrast with heavier traffic flow disappeared after 7:05 AM and the average traffic speed close to 65 miles/hour afterward on other weekdays. A possible traffic accident occurred at/close to this location after 9:10 AM because of traffic speed decline rapidly afterward. Again, larger forecasting errors occurred during the period of dramatic speed changed. Experiments During Transit Strike Period 80 60 -- 3 40 - & 3 0 20 C N O W - i o o in m Time of Day — Fuzzy Model ~ “ ®" WMA Model — a— Measured Speeds Figure 6.19 Experiments during a Transit Strike 128 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 6.9 Experiments during transit strike. Test data acquired from 6:00 AM to 10:00 AM in the morning on 1-10 westbound between 1-405 and 1-110. Fuzzy Model was applied to predict traffic speed Post Mile VDSID Fuzzy Model 20-0ct-03 21-Oct-03 22-Oct-03 23-Oct-03 24-Oct-03 Total MSE 4.305 763325 14.23 14.23 8.65 35.21 16.81 89.12 4.575 716032 20.33 13.36 0.07 20.21 7.39 61.37 5.065 763341 22.15 13.08 3.99 14.44 6.28 59.94 5.655 718099 28.98 26.13 17.23 39.15 30.84 142.33 6.575 717015 27.98 22.65 19.75 21.32 57.62 149.32 7.055 717019 21.26 14.80 21.36 15.45 13.62 86.50 7.645 718414 12.69 15.36 10.48 19.86 17.18 75.57 8.145 764244 13.47 15.45 18.40 14.78 13.94 76.03 8.375 717026 12.71 12.52 7.62 12.22 12.24 57.31 8.905 717031 22.08 17.52 21.79 20.41 23.71 105.51 9.045 718103 12.63 13.80 15.62 9.87 12.88 64.79 9.375 717033 38.78 28.61 27.44 18.18 27.57 140.59 10.075 763330 14.75 8.38 11.29 7.90 16.39 58.72 10.445 763743 24.64 15.87 30.28 13.38 35.97 120.15 10.795 717040 26.30 15.92 39.17 9.65 31.93 122.96 11.055 717041 20.16 18.46 28.50 7.24 42.81 117.16 11.375 716063 40.96 58.56 101.76 13.05 57.48 271.81 11.505 717043 80.84 85.56 49.35 28.83 65.76 310.33 11.965 717045 27.39 103.63 57.37 154.98 28.79 372.16 Sum of Total MSE 482.33 513.89 490.13 476.12 519.21 2481.67 129 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table 6.10 Experiments during transit strike. Test data acquired from 6:00 AM to 10:00 AM in the morning on 1-10 westbound between 1-405 and 1-110. Weighted Moving Average Model was applied to predict traffic speed Post Mile VDSID Weighted Moving Average Model 20-0ct-03 21-Oct-03 22-Oct-03 23-Oct-03 24-Oct-03 Total MSE 4.305 763325 19.81 42.06 7.29 77.45 24.45 171.05 4.575 716032 23.30 19.87 0.18 33.55 11.44 88.34 5.065 763341 27.19 18.06 2.98 18.24 9.31 75.79 5.655 718099 58.66 38.07 27.91 35.90 46.63 207.16 6.575 717015 32.81 27.77 22.10 26.89 86.18 195.75 7.055 717019 31.91 31.74 30.17 27.95 28.87 150.64 7.645 718414 27.77 22.93 24.96 28.86 29.97 134.50 8.145 764244 24.07 25.02 24.84 31.48 31.97 137.39 8.375 717026 28.96 29.27 25.26 27.38 32.51 143.39 8.905 717031 32.36 35.04 27.28 31.89 39.04 165.61 9.045 718103 35.15 37.95 30.18 29.46 35.86 168.61 9.375 717033 51.67 38.19 32.36 26.98 40.46 189.66 10.075 763330 39.75 32.26 25.64 27.31 36.87 161.84 10.445 763743 46.57 37.43 35.97 19.34 64.38 203.69 10.795 717040 57.97 37.13 48.59 20.34 73.98 238.00 11.055 717041 60.79 39.16 66.07 25.67 68.70 260.39 11.375 716063 57.06 109.22 170.25 27.49 74.65 438.67 11.505 717043 80.12 128.93 74.00 46.46 85.85 415.36 11.965 717045 27.60 138.08 63.47 166.40 28.77 424.33 Sum of Total MSE 763.52 888.20 739.50 729.03 849.88 3970.14 130 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 6.7 Summary The transit strike jammed freeways, creating gridlock on roads and freeways, and creating headaches for drivers as commuters who normally use public transportation took their own cars to work and school. Officials with commuter rail lines and bus services operated by individual cities scrambled to add extra trips and buses to accommodate some of the stranded travelers. We found that average traffic speeds on highways during the transit strike declined by as much as 20%, and the average length of the rush period on highways during the transit strike expanded by as much as 200%. The travel time forecasting models performed well during the transit strike. Average errors declined due to the lack of fluctuation traffic speeds. The forecasting errors were relatively small during the transit strike. Under the conditions that average travel experience from the past (previous months or years) without the strike does not apply to forecast current travel time (real-time travel time) under the strike, the proposed Fuzzy Model is able to generate close-to-measured prediction values. 131 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. 7 Conclusions Travel time forecasting has attracted researchers’ attention due to increasing traffic congestion in major cities, and the need to create accurate forecasts in many applications. Based on current traffic information and forecasting techniques, fuzzy methods were created in this thesis to predict highway travel time to support decisions for travelers and transportation industries in real-time. In this section, we conclude the dissertation and point out directions for future researches in this chapter. 7.1 Summary of Results Traffic data from loop detectors are the major data source for a typical Traveler Information System. Loop detector data that we used throughout this thesis are also the primary source to estimate real-time speeds at the locations of loop detectors. As wireless technology becomes more mature and handheld devices become less expensive, it will be easier to retrieve real-time information for travelers and transportation industries anytime and anywhere in the world. Based on current traffic data, historical traffic data, and forecasting techniques, a Fuzzy Reasoning Model was created to predict highway travel time in real-time and support decisions for travelers and transportation industries. The Fuzzy Model combines time and geographic factors into mathematical equations in order to increase accuracy. The method starts from analyzing real-time data provided by 132 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. single loop detectors and ultimately generates real-time travel time predictions for whole trips. Our modeling work is validated by comparing the experimental results with the measured traffic data from loop detectors. We examined travel time forecasting models for real traffic data under various traffic conditions, including time of day, day of week and incident conditions. The time series model, the proposed Fuzzy model, and the measured data for the experiments were compared in Chapter 4. The Fuzzy Model is superior to the Weighted Moving Average Model in many respects. The Fuzzy Model has much smaller mean squared errors than the WMA Model for the experiments on the single locations and for the whole routes. Also, the Fuzzy Model can rapidly estimate travel time under any traffic situation, such as traveling under incident conditions. The strong resemblance of estimated values between the Fuzzy Model and the measured data shows that our Fuzzy Model is capable of predicting travel time under many traffic conditions. A web-based decision support tool with real-time travel time forecasting, which provides access to a range of information sources and analyzes truck arrival patterns at the airport terminal, was implemented for trucking companies. The tool demonstrates the possibilities for incorporating real-time traffic measurements in truck scheduling. Outbound aircraft from express transportation companies can depart on schedule with the accurate scheduling from the web service. Unlike personal travel, trucking companies are concerned with the effect of traffic delays on 133 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. entire fleets. The web-based decision support tool predicts the completion time of sorting operations, which determines the earliest departure time for aircraft. 7.2 Future Research The current research presented in this thesis is a starting phase for the establishment of a travel time forecasting model that can be implemented in real-time. Although the Fuzzy Model performed better than the WMA Model for the experiments in the thesis, it was not perfect all the time. Dramatic speed changes, either increasing or decreasing, will generate larger forecast errors. It is inevitable to have errors for these situations. As we point out in Chapter 4, a possible improvement for these situations is to include more reference points from down stream speeds and up stream speeds. However, involving more reference points in the decision may reduce the ability to predict under normal traffic conditions. Hence, an individual Incident Enhanced Model was needed to solve this problem. Figure 7.1 shows the alternative design of the future forecasting models. This integrated model includes several specially designed models, which can be triggered under different traffic conditions determined by the central controller, the “Screener.” The accuracy of predictions can be improved if the central controller can detect traffic conditions rapidly and correctly. 134 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Input Output Screener Incident Enhanced Model Time Series Model Fuzzy Reason Model Figure 7.1 The integrated structure for future travel time forecasting model 135 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. References Abdelfatah, A. S. and Mahmassani H. S., 1998. 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Recursive Prediction of Traffic Conditions with Neural Network Models, Journal of Transportation Engineering, 472-481. 140 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Appendix A The Creation of Fuzzy Inference Rules In the Appendix A, we list the tables and figures that create fuzzy inference rules from Chapter 3. Each graph shows a collection of successful prediction points (circle sign for positive prediction and plus sign for negative prediction) and failed prediction point (cross sign) by speed difference sdt from a sample data set in a 3- dimension graph. The sample data set was collected from TMCs on October 21, 2002. In a three-hour interval, from 6:30 AM to 9:30 AM, we got a total of 37 5-minute traffic data files. Three data points were used to initiate the forecasting method. Hence, a total of 34 data points are shown in the tables and figures. h = { d i , d 5, d j ] Circle: Positive Plus: Negative Cross: Failed d i 12 ---— --" IQ S ' _— — 6- ---------- 4- 2- _------ 0- ---- -— -2- _ — — — - -4 ---- —- -6 = - -20 -10 10 -15 -10 ' 5 d2 Figure A.l Sample data for l\={d2, d5 , r/7} with 11 worked, 2 failed, out of 34 points 141 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table A. 1 Sample data for \\={d 2, d$, d-j} with 11 worked, 2 failed, out of 34 points So(0 d2 d5 dj PO/NE so(/+l) Result 52.56 -1.55 -0.98 -3.58 NE 59.29 Fail 59.29 -7.71 -6.73 -3.23 NE 52.27 Success 53.13 -0.85 -0.09 -3.47 NE 50.37 Success 50.37 2.67 2.76 0.1 PO 46.7 Fail 46.7 6.43 3.67 2.41 PO 48.92 Success 37.21 9.49 11.71 8.84 PO 38.17 Success 53.27 -15.1 -6.94 -1.51 NE 43.26 Success 43.26 3.07 10.01 11.69 PO 55.50 Success 55.50 -2.23 -12.24 -0.25 NE 49.72 Success 48.85 6.65 0.87 5.98 PO 59.49 Success 59.49 -9.77 -10.64 -4.02 NE 58.40 Success 61.16 -2.76 -3.34 -4.81 NE 58.33 Success 56.67 -1.53 -2.84 -0.94 NE 55.72 Success Circle: Positive Plus: Negative Cross: Failed - 3 5 - 1 5 -10 Figure A.2 Sample data for h={d2, d5 , d»} with 8 worked, 2 failed, out of 34 points. R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table A .2 Sample data for \2={d2, d$, d%} with 8 worked, 2 failed, out of 34 points S o (t) d 2 d $ d % PO/NE .S'o(H-l) Result 52.56 -1.55 -0.98 -0.26 NE 59.29 Fail 59.29 -7.71 -6.73 -7.55 NE 52.27 Success 53.13 -0.85 -0.09 -19.12 NE 50.37 Success 46.33 -9.12 -8.16 -20.46 NE 53.27 Fail 53.27 -15.1 -6.94 -27.48 NE 43.26 Success 55.50 -2.23 -12.24 -36.49 NE 49.72 Success 59.49 -9.77 -10.64 -29.28 NE 58.40 Success 61.16 -2.76 -3.34 -18.64 NE 58.33 Success 54.99 1.28 0.76 1.31 PO 55.29 Success 53.83 1.46 1.31 0.92 PO 56.67 Success ^ —{ds, d 7, d%} Circle: Positive Plus: Negative Cross: Failed -k. -10 6 -15 d7 0 Figure A.3 Sample data for l3={ds, d7 , d8} with 8 worked, 3 failed, out of 34 points 143 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table A.3 Sample data for l3={^5, dy, dg) with 8 worked, 3 failed, out of total 34 points ■ S o (f) ds dy dg PO/NE 5o(f+l) Result 51.58 -0.57 -2.33 -7.94 NE 52.56 Fail 52.56 -0.98 -3.58 -0.26 NE 59.29 Fail 59.29 -6.73 -3.23 -7.55 NE 52.28 Success 53.04 -0.76 -1.43 -11 NE 53.13 Fail 53.13 -0.09 -3.47 -19.12 NE 50.37 Success 48.92 -2.22 -1.75 -23.91 NE 37.21 Success 53.27 -6.94 -1.51 -27.48 NE 43.26 Success 59.49 -10.64 -4.02 -29.28 NE 58.4 Success 61.16 -3.34 -4.81 -18.64 NE 58.33 Success 56.27 -1.25 -1.47 -8.87 NE 55.75 Success 56.67 -2.84 -0.94 -0.93 NE 55.72 Success I4 — { tf? 4 , d5, dy} Circle: Positive Plus: Negative Cross: Failed '7 20 -10 -20 -10 -15 d4 10 Figure A.4 Sample data for Lj={d4 , d$, dy} with 10 worked, 4 failed, out of 34 points 144 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table A.4 Sample data for L*= {d^., d5, dj} with 10 worked, 4 failed, out of 34 points So(t) d<\ d 5 di PO/NE ,so(f+l) Result 51.58 -2.94 -0.57 -2.33 NE 52.56 Fail 52.56 -3.31 -0.98 -3.58 NE 59.29 Fail 59.29 -10.31 -6.73 -3.23 NE 52.28 Success 53.04 -5.93 -0.76 -1.43 NE 53.13 Fail 53.13 -1.52 -0.09 -3.47 NE 50.37 Success 46.7 3.77 3.67 2.41 PO 48.92 Success 37.21 9.96 11.71 8.84 PO 38.17 Success 43.26 8.5 10.01 11.69 PO 55.50 Success 49.72 5.53 5.78 5.83 PO 48.85 Fail 48.85 6.7 0.87 5.98 PO 59.49 Success 59.49 -4.66 -10.64 -4.02 NE 58.40 Success 61.16 -8.05 -3.34 -4.81 NE 58.33 Success 56.27 -5.71 -1.25 -1.47 NE 55.75 Success 56.67 -6.39 -2.84 -0.94 NE 55.72 Success Circle: Positive Plus: Negative Cross: Failed 10-1 0 - d $ - 10- -20 -30- -407 -14 Figure A.5 Sample data for h={d5, d§, ds} with 12 worked, 5 failed, out of 34 points 145 I5—1“ 5; “ 6> “ 8J -20 -40 -12 -10 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table A.5 Sample data for 15= { < ^ 5, d$, d%] with 12 worked, 5 failed, out of 34 points So(t) d 5 df, ds PO/NE .s'o(H-l) Result 51.58 -0.57 -5.53 -7.94 NE 52.56 Failed 52.56 -0.98 -8.92 -0.26 NE 59.29 Failed 59.29 -6.73 -6.99 -7.55 NE 52.28 Succeed 53.04 -0.76 -2.09 -11 NE 53.13 Failed 53.13 -0.09 -11.09 -19.12 NE 50.37 Succeed 48.92 -2.22 -21.34 -23.91 NE 37.21 Succeed 38.17 -0.96 -16.37 -13.73 NE 46.33 Failed 46.33 -8.16 -21.89 -20.46 NE 53.27 Failed 53.27 -6.94 -27.4 -27.48 NE 43.26 Succeed 55.5 -12.24 -24.73 -37.49 NE 49.72 Succeed 59.49 -10.64 -32.7 -29.28 NE 58.4 Succeed 61.16 -3.34 -30.85 -18.64 NE 58.33 Succeed 56.27 -1.25 -1.43 -8.87 NE 55.75 Succeed 54.99 0.76 0.47 1.31 PO 55.29 Succeed 53.83 1.31 2.73 0.92 PO 56.67 Succeed 56.67 -2.84 -1.92 -0.93 NE 55.72 Succeed 55.72 0.95 0.02 1.05 PO 57.38 Succeed R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Appendix B Reports for Experimental Results In the Appendix B, we list detail experimental results from Section 4.1. The experiments are designed to test traffic speed forecasting at a single location. Traffic data from May, 2003, were collected and tested in the experiment. All loop detectors on I-10 westbound between 1-405 and I-110 were examined throughout this section (Figure 4.1). Each experiment contains a three-hour testing period and includes 37 measured traffic speeds from 37 5-minute data sets. Because three measured traffic speeds were needed to initiate the forecasting models, a total of 34 forecasting values were made. Mean Square Error (MSE) is used to measure the accuracy of the models and is defined as follows: MSE= ;=i n where A f,- is the measured speed (miles/hour), Ft is the forecasted speed (miles/hour), and n is the number of data points, which is 34 in this section. Table B.l and Table B.2 show the experiment results on {Monday, Tuesday, Wednesday, and Thursday}. Table B.3 and Table B.4 show the experiment results on {Friday}. Table B.5 and Table B.6 show the experiment results on {Saturday, Sunday and holiday}. Also, Table B.7 and Table B.8 show the experiment results on {Noon: 11:00 AM - 2:00 PM}. Table B.9 and Table B.10 show the experiment results on {Evening: 5:00 PM - 8:00 PM}. 147 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table B.l Experiments on Monday, Tuesday, Wednesday and Thursday. Test data acquired from 6:30 AM to 9:30 AM on 1-10 westbound between 1-405 and 1-110. Fuzzy Model was applied to predict traffic speed, MSE values are the sum of 34 data points each day Post Mile VDS E D Fuzzy Model 12-May-03 13-May-03 14-May-03 15-May-03 Total MSE 4.305 763325 56.49 78.90 33.10 4.24 172.73 4.575 716032 63.07 84.85 37.71 5.36 190.99 5.655 718099 60.46 110.00 93.36 96.24 360.06 6.205 717012 26.26 28.29 32.61 28.49 115.65 6.575 717015 58.50 34.97 54.32 39.12 186.91 7.055 717019 39.19 51.75 64.71 54.91 210.56 8.145 764244 32.41 34.47 46.10 33.61 146.59 8.375 717026 23.39 30.81 44.31 27.49 126.00 8.545 717029 16.33 29.75 43.92 13.35 103.35 8.905 717031 12.94 42.86 34.91 23.50 114.21 9.045 718103 17.77 26.04 26.22 28.25 98.28 9.375 717033 12.75 22.62 13.21 38.04 86.62 10.075 763330 44.89 50.59 37.50 95.94 228.92 10.425 717036 115.11 97.93 71.04 185.98 470.06 10.445 763743 61.14 92.19 54.16 11.03 218.52 10.795 717040 82.26 58.22 97.44 5.94 243.86 11.055 717041 42.93 44.64 73.11 5.71 166.39 11.375 716063 55.06 56.83 46.66 5.77 164.32 11.505 717043 36.32 52.27 20.82 3.33 112.74 11.965 717045 46.75 13.20 34.25 1.77 95.97 Sum of Total MSE 904.02 1041.18 959.46 708.07 3612.73 148 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table B.2 Experiments on Monday, Tuesday, Wednesday and Thursday. Test data acquired from 6:30 AM to 9:30 AM on 1-10 westbound between 1-405 and I-110. WMA Model was applied to predict traffic speed, MSE values are the sum of 34 data points each day Post Mile VDS ID Weighted Moving Average Model 12-May-03 13-May-03 14-May-03 15-May-03 Total MSE 4.305 763325 93.28 145.63 72.57 4.11 315.59 4.575 716032 79.93 115.26 58.60 3.75 257.54 5.655 718099 61.89 121.31 102.68 94.17 380.05 6.205 717012 38.35 36.37 32.39 33.77 140.88 6.575 717015 68.18 32.43 58.14 66.48 225.23 7.055 717019 79.64 50.96 83.38 89.14 303.12 8.145 764244 61.20 55.12 77.51 65.79 259.62 8.375 717026 27.13 30.96 36.08 32.43 126.60 8.545 717029 20.81 32.18 41.36 26.25 120.60 8.905 717031 18.96 35.47 36.73 26.05 117.21 9.045 718103 29.19 30.86 34.49 42.30 136.84 9.375 717033 21.54 21.10 13.33 34.45 90.42 10.075 763330 51.66 56.37 38.37 127.76 274.16 10.425 717036 115.42 74.13 81.21 202.76 473.52 10.445 763743 81.70 77.86 106.37 9.12 275.05 10.795 717040 116.21 75.48 162.71 4.55 358.95 11.055 717041 71.98 69.40 81.94 4.84 228.16 11.375 716063 99.49 117.90 72.87 5.66 295.92 11.505 717043 63.81 67.09 39.02 3.12 173.04 11.965 717045 37.87 11.85 36.88 1.26 87.86 Sum of Total MSE 1238.24 1257.73 1266.63 877.76 4640.36 149 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table B.3 Experiments on Friday. Test data acquired from 6:30 AM to 9:30 AM on I- 10 westbound between 1-405 and I-110. Fuzzy Model was applied to predict traffic speed, MSE values are the sum of 34 data points each day Post Mile VDS ID Fuzzy Model 9-May-04 16-May-04 23-May-04 30-May-04 Total MSE 4.305 763325 124.80 126.40 1.19 7.96 260.35 4.575 716032 75.83 175.15 1.56 2.19 254.73 5.655 718099 74.52 101.99 38.34 82.07 296.92 6.205 717012 22.85 44.95 21.91 28.21 117.92 6.575 717015 26.33 55.21 42.95 22.69 147.18 7.055 717019 20.29 78.08 93.73 17.06 209.16 8.145 764244 36.29 40.88 66.56 16.83 160.56 8.375 717026 34.17 28.95 35.82 15.50 114.44 8.545 717029 15.40 12.53 50.04 9.97 87.94 8.905 717031 18.63 21.16 32.24 12.68 84.71 9.045 718103 22.91 24.88 69.10 16.19 133.08 9.375 717033 16.77 26.70 58.56 12.68 114.71 10.075 763330 25.27 45.94 28.26 44.64 144.11 10.425 717036 98.29 187.68 27.83 44.56 358.36 10.445 763743 111.18 115.16 8.21 36.49 271.04 10.795 717040 146.18 186.40 4.66 15.87 353.11 11.055 717041 76.28 187.21 2.63 4.89 271.01 11.375 716063 53.91 103.72 2.69 3.40 163.72 11.505 717043 54.32 127.95 1.64 5.57 189.48 11.965 717045 1.41 1.12 5.98 5.29 13.80 Sum of Total MSE 1055.63 1692.06 593.90 404.74 3746.33 150 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table B.4 Experiments on Friday. Test data acquired from 6:30 AM to 9:30 AM on I- 10 westbound between 1-405 and I-110. W M A Model was applied to predict traffic speed, MSE values are the sum of 34 data points each day Post Mile VDS ID Weighted Moving Average Model 9-May-04 16-May-04 23-May-04 30-May-04 Total MSE 4.305 763325 170.72 220.96 1.15 15.35 408.18 4.575 716032 62.29 179.26 1.45 2.31 245.31 5.655 718099 69.67 151.29 34.58 96.96 352.50 6.205 717012 30.52 78.28 27.49 33.97 170.26 6.575 717015 39.59 88.34 66.22 23.96 218.11 7.055 717019 34.56 105.79 128.54 38.12 307.01 8.145 764244 52.21 82.69 88.25 26.72 249.87 8.375 717026 30.75 31.44 65.32 16.67 144.18 8.545 717029 30.02 24.77 73.23 22.44 150.46 8.905 717031 24.04 25.81 85.14 22.45 157.44 9.045 718103 30.05 33.78 115.28 36.30 215.41 9.375 717033 14.88 22.08 84.81 28.67 150.44 10.075 763330 21.88 54.40 39.70 60.81 176.79 10.425 717036 115.35 198.15 34.79 59.00 407.29 10.445 763743 120.93 232.85 7.97 52.59 414.34 10.795 717040 146.64 223.02 5.70 16.09 391.45 11.055 717041 80.45 184.34 2.50 4.82 272.11 11.375 716063 122.40 208.93 2.93 2.97 337.23 11.505 717043 63.48 128.81 1.69 4.68 198.66 11.965 717045 0.92 0.87 4.32 3.47 9.58 Sum of Total MSE 1261.35 2275.86 871.06 568.35 4976.62 151 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table B.5 Experiments on Saturday, Sunday and holiday. Test data acquired from 6:30 AM to 9:30 AM on I-10 westbound between 1-405 and 1-110. Fuzzy Model was applied to predict traffic speed, MSE values are the sum of 34 data points each day Post Mile VDS ID Fuzzy Model 17-May-03 18-May-04 24-May-04 25-May-04 Total MSE 4.305 763325 2.72 4.168 5.81 3.31 16.01 4.575 716032 2.47 0.009 0.56 0.58 3.62 5.655 718099 2.48 0.142 2.74 4.21 9.57 6.205 717012 3.13 0.009 5.15 3.49 11.78 6.575 717015 4.19 1.753 4.21 4.42 14.57 7.055 717019 1.31 0.308 3.27 6.43 11.32 8.145 764244 3.67 0.990 4.53 7.66 16.85 8.375 717026 2.39 6.022 1.62 4.26 14.29 8.545 717029 2.65 0.011 2.20 2.67 7.53 8.905 717031 0.12 0.247 1.49 2.12 3.98 9.045 718103 0.92 0.711 3.48 3.93 9.04 9.375 717033 1.17 1.552 1.82 2.06 6.60 10.075 763330 2.12 0.941 3.27 4.80 11.13 10.425 717036 1.46 0.013 7.35 8.00 16.82 10.445 763743 4.69 2.013 12.44 5.98 25.12 10.795 717040 3.79 0.051 10.85 5.63 20.32 11.055 717041 2.69 2.305 4.61 3.58 13.19 11.375 716063 6.31 2.001 3.29 0.76 12.36 11.505 717043 7.69 0.028 1.96 1.65 11.33 11.965 717045 8.16 0.288 6.63 10.60 25.68 Sum of Total MSE 64.13 23.56 87.28 86.14 261.11 152 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table B.6 Experiments on Saturday, Sunday and holiday. Test data acquired from 6:30 AM to 9:30 AM on I-10 westbound between 1-405 and 1-110. WMA Model was applied to predict traffic speed, MSE values are the sum of 34 data points each day Post Mile VDS ID Weighted Moving Average Model 17-May-03 18-May-04 24-May-04 25-May-04 Total MSE 4.305 763325 2.92 2.797 4.32 4.67 14.71 4.575 716032 3.03 0.011 0.57 0.55 4.16 5.655 718099 1.54 0.168 3.23 4.59 9.53 6.205 717012 3.05 0.011 3.95 3.18 10.19 6.575 717015 3.84 2.023 2.62 4.39 12.87 7.055 717019 1.51 0.324 5.78 8.02 15.63 8.145 764244 4.68 0.951 4.60 9.70 19.93 8.375 717026 1.62 6.425 0.91 2.78 11.74 8.545 717029 2.02 0.011 2.15 1.83 6.01 8.905 717031 0.10 0.240 0.94 2.02 3.30 9.045 718103 0.82 0.597 5.89 6.44 13.75 9.375 717033 1.66 1.360 2.44 2.15 7.61 10.075 763330 1.75 0.676 4.57 4.00 11.00 10.425 717036 1.09 0.011 8.91 7.24 17.25 10.445 763743 4.58 1.810 11.51 5.81 23.71 10.795 717040 4.09 0.054 9.47 5.89 19.50 11.055 717041 2.83 2.216 2.93 3.57 11.55 11.375 716063 7.64 1.930 3.27 0.67 13.51 11.505 717043 5.07 0.034 2.33 0.90 8.33 11.965 717045 6.48 0.267 5.53 6.18 18.46 Sum of Total MSE 60.32 21.92 85.92 84.58 252.74 153 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table B.7 Experiments at noon. Test data acquired from 11:00 AM to 2:00 PM on I- 10 westbound between 1-405 and I-110. Fuzzy Model was applied to predict traffic speed, M SE values are the sum of 34 data points each day Post Mile VDS ID Fuzzy Model 12-May-03 13-May-03 14-May-03 15-May-03 Total MSE 4.305 763325 92.92 11.30 4.02 140.67 248.91 4.575 716032 84.12 4.11 3.82 153.54 245.59 5.655 718099 162.64 23.06 8.38 96.49 290.57 6.205 717012 63.63 22.81 34.60 52.51 173.55 6.575 717015 180.97 89.39 127.04 63.58 460.98 7.055 717019 395.76 89.94 162.21 199.00 846.91 8.145 764244 49.21 54.27 120.27 166.88 390.63 8.375 717026 10.52 30.62 103.45 116.34 260.93 8.545 717029 30.46 95.78 84.46 125.24 335.94 8.905 717031 45.72 95.85 38.43 160.16 340.16 9.045 718103 15.66 88.11 17.75 121.13 242.65 9.375 717033 37.65 190.83 5.68 132.71 366.87 10.075 763330 358.13 157.93 5.77 207.26 729.08 10.425 717036 2.32 34.56 6.82 85.28 128.98 10.445 763743 2.51 41.37 27.96 154.42 226.26 10.795 717040 4.92 78.91 6.90 156.08 246.81 11.055 717041 2.75 127.06 20.94 142.89 293.64 11.375 716063 3.01 31.66 59.78 129.98 224.43 11.505 717043 1.47 23.25 32.88 86.62 144.22 11.965 717045 3.45 74.16 4.25 1.15 83.01 Sum of Total MSE 1547.82 1364.97 875.41 2491.94 6280.13 154 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table B.8 Experiments at noon. Test data acquired from 11:00 AM to 2:00 PM on I- 10 westbound between 1-405 and I-110. W M A Model was applied to predict traffic speed, MSE values are the sum of 34 data points each day Post Mile VDS ID Weighted Moving Average Model 12-May-03 13-May-03 14-May-03 15-May-03 Total MSE 4.305 763325 141.31 17.74 4.05 237.38 400.48 4.575 716032 127.40 3.76 3.30 158.87 293.33 5.655 718099 175.90 31.38 9.62 183.62 400.52 6.205 717012 71.07 28.48 42.80 72.65 215.00 6.575 717015 236.48 101.43 175.50 62.49 575.90 7.055 717019 459.81 134.56 203.39 257.10 1054.86 8.145 764244 66.90 56.44 127.19 181.80 432.33 8.375 717026 48.91 44.56 155.09 117.05 365.61 8.545 717029 28.41 97.80 75.54 141.91 343.66 8.905 717031 47.86 117.78 66.04 168.04 399.72 9.045 718103 18.06 104.27 34.94 151.80 309.07 9.375 717033 43.28 289.39 6.64 197.25 536.56 10.075 763330 331.77 157.35 5.05 172.51 666.68 10.425 717036 1.71 125.33 7.50 116.96 251.50 10.445 763743 2.73 53.99 22.03 230.42 309.17 10.795 717040 3.44 71.50 4.29 253.30 332.53 11.055 717041 2.56 177.24 21.04 234.19 435.03 11.375 716063 2.01 67.96 72.76 255.77 398.50 11.505 717043 0.94 45.07 25.37 150.82 222.20 11.965 717045 3.00 120.90 3.14 0.88 127.92 Sum of Total MSE 1813.55 1846.93 1065.28 3344.80 8070.56 155 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table B.9 Experiments in the evening. Test data acquired from 5:00 PM to 8:00 PM on 1-10 westbound between 1-405 and 1-110. Fuzzy Model was applied to predict traffic speed, MSE values are the sum of 34 data points each day Post Mile VDS ID Fuzzy Model 19-May-03 20-May-03 21-May-03 22-May-03 Total MSE 4.305 763325 4.05 25.60 2.48 5.56 37.68 4.575 716032 1.91 36.08 12.62 3.94 54.55 5.655 718099 45.44 34.67 91.24 60.25 231.60 6.205 717012 21.86 22.87 38.13 30.13 112.99 6.575 717015 46.20 36.72 55.96 40.22 179.10 7.055 717019 46.15 61.02 66.83 61.84 235.84 8.145 764244 49.82 31.77 44.32 130.94 256.85 8.375 717026 26.30 23.77 21.65 51.40 123.11 8.545 717029 49.31 49.86 45.73 64.94 209.84 8.905 717031 46.87 47.61 32.09 44.17 170.74 9.045 718103 70.78 50.84 37.17 71.58 230.38 9.375 717033 61.02 46.21 28.09 79.83 215.15 10.075 763330 43.04 30.57 44.40 44.00 162.01 10.425 717036 28.88 19.30 32.11 81.50 161.78 10.445 763743 39.34 32.82 34.93 57.49 164.58 10.795 717040 46.43 31.66 44.92 58.63 181.64 11.055 717041 49.09 25.93 32.25 48.27 155.53 11.375 716063 38.27 24.88 34.51 66.29 163.95 11.505 717043 30.84 17.75 24.65 45.00 118.25 11.965 717045 112.63 11.65 60.13 122.89 307.30 Sum of Total MSE 858.24 661.58 784.21 1168.87 3472.90 156 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission. Table B.10 Experiments in the evening. Test data acquired from 5:00 PM to 8:00 PM on I-10 westbound between 1-405 and I-110. W M A Model was applied to predict traffic speed. M SE values are the sum of 34 data points each day Post Mile VDS ID Weighted Moving Average Model 19-May-03 20-May-03 21-May-03 22-May-03 Total MSE 4.305 763325 2.70 51.57 3.03 4.41 61.71 4.575 716032 2.51 38.94 27.22 4.42 73.09 5.655 718099 61.84 50.22 145.54 88.96 346.56 6.205 717012 43.07 33.03 53.99 41.36 171.45 6.575 717015 78.33 56.13 74.17 64.83 273.46 7.055 717019 75.24 82.49 77.70 63.56 298.99 8.145 764244 61.11 39.95 53.04 150.50 304.61 8.375 717026 37.46 42.95 34.62 78.55 193.58 8.545 717029 57.26 60.29 48.76 86.67 252.98 8.905 717031 77.32 92.75 63.05 84.01 317.13 9.045 718103 91.29 86.18 69.58 117.47 364.52 9.375 717033 104.37 90.61 75.17 117.59 387.75 10.075 763330 56.12 28.25 55.41 46.28 186.06 10.425 717036 50.04 23.74 51.75 104.85 230.38 10.445 763743 71.91 55.38 60.42 114.73 302.43 10.795 717040 88.04 58.35 65.52 126.79 338.71 11.055 717041 96.93 43.52 62.67 119.74 322.86 11.375 716063 85.97 47.12 47.61 119.20 299.90 11.505 717043 50.22 25.46 32.78 78.78 187.24 11.965 717045 152.02 10.42 120.39 200.27 483.11 Sum of Total MSE 1343.75 1017.35 1222.44 1812.99 5396.53 157 R eproduced with perm ission of the copyright owner. Further reproduction prohibited without perm ission.

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Asset Metadata

Creator Lo, Shih-Che (author)

Core Title Integrated model for highway -based travel time forecasting with application to truck transportation

School Graduate School

Degree Doctor of Philosophy

Degree Program Industrial and Systems Engineering

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag engineering, industrial,Engineering, System Science,OAI-PMH Harvest,transportation

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Hall, Randolph W. (committee chair), McBride, Richard (committee member), Moore, James E. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-407444

Unique identifier UC11340206

Identifier 3145237.pdf (filename),usctheses-c16-407444 (legacy record id)

Legacy Identifier 3145237.pdf

Dmrecord 407444

Document Type Dissertation

Rights Lo, Shih-Che

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA