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University of Southern California Dissertations and Theses
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Reliable and power efficient protocols for space communication and wireless ad-hoc networks
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Reliable and power efficient protocols for space communication and wireless ad-hoc networks
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RELIABLE AND POWER EFFICIENT PROTOCOLS FOR SPACE COMMUNICATION AND WIRELESS AD-HOC NETWORKS by Wonseok Baek 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 (ELECTRICAL ENGINEERING) December 2006 Copyright 2006 Wonseok Baek Dedication It was a long journey. Without deep and endless trust, support, and love, I would never complete my journey. At the end of this long journey, I dedicate this dis- sertation to my parents, my wife Hye-Yong, my daughter Kaitlyn, and my son Lynden. ii Table Of Contents Dedication ii List Of Tables vi List Of Figures vii Abstract x Chapter1:Introduction 1 1.1 Significance of the Research . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Error control with ARQ . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Power efficiency in wireless ad-hoc networks . . . . . . . . . 4 1.2 Review of Previous Work . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.1 ARQ schemes . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.2 Power saving in wireless ad-hoc networks . . . . . . . . . . . 7 1.3 Contribution of the Research . . . . . . . . . . . . . . . . . . . . . . 10 1.3.1 Analysis of ARQ schemes in IPN . . . . . . . . . . . . . . . 10 1.3.2 Power-aware topology control and CSMA/CA MAC protocol 12 1.4 Organization of Thesis . . . . . . . . . . . . . . . . . . . . . . . . . 13 Chapter2:Background Review 15 2.1 IPN, DTN, CCSDS and CFDP . . . . . . . . . . . . . . . . . . . . 15 2.2 Description of CFDP’s ARQ Schemes . . . . . . . . . . . . . . . . . 17 2.2.1 Deferred NAK mode . . . . . . . . . . . . . . . . . . . . . . 19 2.2.2 Immediate NAK mode . . . . . . . . . . . . . . . . . . . . . 20 Chapter3:Analysis of Deferred NAK Mode 24 3.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.2 Timer Setting Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.3 Expected Value of EOF Delivery Time . . . . . . . . . . . . . . . . 28 3.4 Expected File Delivery Time . . . . . . . . . . . . . . . . . . . . . . 29 3.5 Numerical Presentation . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 iii Chapter4:Analysis of Immediate NAK Mode 43 4.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.2 Timer Setting Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.2.1 Rule to determine the NAK EOF timer value . . . . . . . . . 47 4.2.2 Mathematical description of timer setting rule . . . . . . . . 50 4.3 Analysis of Immediate NAK Mode . . . . . . . . . . . . . . . . . . 53 4.3.1 Bounds on the expected value of T def . . . . . . . . . . . . . 54 4.3.2 Bounds on the expected value of T inc . . . . . . . . . . . . . 61 4.3.2.1 Case (1): N ≥k+2 (Short propagation delay rela- tive to file transmission time) . . . . . . . . . . . . 65 4.3.2.2 Case (2): N <k+2 (Long propagation delay rela- tive to file transmission time) . . . . . . . . . . . . 70 4.3.3 Bounds on the expected file delivery time of the Immediate NAK mode . . . . . . . . . . . . . . . . . . . 78 4.4 Numerical Presentation . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.4.1 Numerical results for the Immediate NAK mode . . . . . . . 80 4.4.2 Performance comparison of the Immediate and Deferred NAK mode . . . . . . . . . . . . . . . . . . . . 82 4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Chapter5:Power-Aware Topology Control for Wireless Ad-Hoc Networks 89 5.1 Proposed Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 90 5.1.1 Weighted link cost . . . . . . . . . . . . . . . . . . . . . . . 91 5.1.2 Topology construction through power-aware node classification . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 5.1.2.1 Core node connectivity . . . . . . . . . . . . . . . . 93 5.1.2.2 Non-core node connectivity . . . . . . . . . . . . . 94 5.1.2.3 Active node connectivity . . . . . . . . . . . . . . . 94 5.1.2.4 Passive node connectivity . . . . . . . . . . . . . . 96 5.2 Performance Evaluation . . . . . . . . . . . . . . . . . . . . . . . . 97 5.2.1 Proof for global connectivity . . . . . . . . . . . . . . . . . . 97 5.2.2 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . 99 5.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 Chapter6:CSMA/CA MAC Protocol Design for Topology Controlled Ad-Hoc Networks: A Cross Layer Approach 107 6.1 RTS-CTS Range for Topology Controlled Wireless Ad-Hoc Networks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 6.1.1 Hidden node problem due to asymmetric RTS-CTS ranges . 108 6.1.2 Algorithmforresolutionofhiddennodeproblemduetoasym- metric RTS-CTS ranges . . . . . . . . . . . . . . . . . . . . 111 6.1.3 Performance comparison by simulation . . . . . . . . . . . . 112 iv 6.2 Transmission Power Adjustment for RTS-CTS Range . . . . . . . . 114 6.2.1 Hidden node problem due to carrier sensing . . . . . . . . . 116 6.2.2 Algorithm for resolution of hidden node problem due to car- rier sensing . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 6.2.3 Performance comparison by simulation . . . . . . . . . . . . 118 6.3 Approximate Throughput Analysis . . . . . . . . . . . . . . . . . . 118 6.3.1 System model and assumption . . . . . . . . . . . . . . . . . 121 6.3.2 Approximate analysis . . . . . . . . . . . . . . . . . . . . . . 122 6.3.3 Numerical results . . . . . . . . . . . . . . . . . . . . . . . . 128 6.4 Throughput, Fairness, and Energy Efficiency . . . . . . . . . . . . . 128 6.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 Chapter7:Conclusion and Future Work 133 7.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 7.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 References 137 v List Of Tables 3.1 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 5.1 Performance comparisons for LMST-based case . . . . . . . . . . . 104 5.2 Performance comparisons for SPT-based case . . . . . . . . . . . . 104 6.1 System parameters used in simulation . . . . . . . . . . . . . . . . . 114 vi List Of Figures 2.1 The illustration of the Deferred NAK mode. . . . . . . . . . . . . . 20 2.2 The illustration of the Immediate NAK mode. . . . . . . . . . . . . 22 3.1 Effect of timeout values on CFDP performance. . . . . . . . . . . . 27 3.2 Upper bound of R s ∗. . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.3 Expected file delivery time vs. P ef . . . . . . . . . . . . . . . . . . . 38 3.4 Expected file delivery time vs. number of PDUs. . . . . . . . . . . . 39 3.5 Expected file delivery time vs. number of PDUs. . . . . . . . . . . . 40 3.6 Deferred NAK: Analytic and simulation results. Expected file deliv- ery time of Deferred NAK Mode vs. BER. File size = 1MB, trans- mission rate = 20Kbps in both directions, and propagation delay = 480s. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.1 TimersettingproblemfortheNAKgeneratedonsuccessfulreception of the EOF PDU . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.2 Illustration of W inc n . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.3 Incremental procedure of Immediate NAK mode . . . . . . . . . . . 63 4.4 Example of incremental procedure . . . . . . . . . . . . . . . . . . . 73 4.5 Immediate NAK: Analytic vs. simulation results. ExpectedfiledeliverytimeofImmediateNAKmodewithBERvari- ation. File size = 1 Mbyte, transmission rate = 1 Mbps in both directions, and propagation delay = 40 ms. . . . . . . . . . . . . . . 81 vii 4.6 Immediate NAK: Analytic vs. simulation results. ExpectedfiledeliverytimeofImmediateNAKmodewithBERvari- ation. File size = 1 Mbyte, transmission rate = 2 Kbps in both directions, and propagation delay = 480 s. . . . . . . . . . . . . . . 82 4.7 Immediate NAK: Analytic vs. simulation results. ExpectedfiledeliverytimeofImmediateNAKmodewithBERvari- ation. File size = 1 Mbyte, transmission rate = 20 Kbps in both directions, and propagation delay = 480 s. . . . . . . . . . . . . . . 83 4.8 Immediate NAK: Analytic vs. simulation results. ExpectedfiledeliverytimeofImmediateNAKmodewithBERvari- ation. File size = 1 Mbyte, Transmission rate = 20 Kbps in both directions, and propagation delay = 4,800 s. . . . . . . . . . . . . . 84 4.9 Simulation results. Expected file delivery time of Deferred and Immediate NAK modes with BER variation. File size = 1 Mbyte, transmission rate = 1 Mbps in both directions, and propagation delay = 40 ms. . . . . . . 85 4.10 Simulation results. Expected file delivery time of the Deferred and Immediate NAK modes with BER variation. File size = 1 Mbyte, transmission rate = 2 Kbps in both directions, and propagation delay = 480 s. . . . . 86 4.11 Simulation results. Expected file delivery time of the Deferred and Immediate NAK modes with BER variation. File size = 1 Mbyte, transmission rate = 20 Kbps in both directions, and propagation delay = 480 s. . . . 87 4.12 Simulation results. Expected file delivery time of the Deferred and Immediate NAK modes with BER variation. File size = 1 Mbyte, transmission rate = 20 Kbps in both directions, and propagation delay = 4,800 s. . . 88 5.1 Mean and standard deviation of network lifetime. . . . . . . . . . . 101 5.2 Mean and standard deviation of network partition time . . . . . . . 101 5.3 Mean and standard deviation of network lifetime. . . . . . . . . . . 102 5.4 Mean and standard deviation of network partition time . . . . . . . 102 5.5 Mean network lifetime and network partition time with different topologyupdateintervalforLMST-basedpower-awaretopologycon- trol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 viii 5.6 Mean network lifetime and network partition time with different topology update interval for SPT-based power-aware topology con- trol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 6.1 Hidden node problem in topology controlled wireless Ad-Hoc net- works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 6.2 Test topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 6.3 PerformancecomparisonbetweenvariableRTS-CTSrangeandmax- imum RTS-CTS range . . . . . . . . . . . . . . . . . . . . . . . . . 115 6.4 Performance comparison among node 1, 3, 4, and 5 with CSMA/CA MAC protocol with variable RTS-CTS range but without carrier sensing power adjustment . . . . . . . . . . . . . . . . . . . . . . . 119 6.5 Performance comparison among node 1, 3, 4, and 5 with CSMA/CA MACprotocolwithvariableRTS-CTSrangeandwithcarriersensing power adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 6.6 Imbedded Markov Chain . . . . . . . . . . . . . . . . . . . . . . . . 123 6.7 Numerical results from analysis . . . . . . . . . . . . . . . . . . . . 132 ix Abstract The central theme of this thesis is the design and analysis of reliable and power efficient networking protocols under various application scenarios. The work con- sists of two major parts. The first part focuses on networking issues for reliable data transfer in the context of space communication. The second part investigates power efficient topology control for wireless ad-hoc networks. In the first part of research, we consider reliable space communication. In many cases, space networking faces extremely long propagation delays, intermittent link connectivity,limitedbandwidth,andlimitedpowerbudgets. Ourmaincontribution ismathematicalmodellingandanalysisoftwoARQschemesofCFDP,theDeferred NAKmodeandtheImmediateNAKmode,inthesingle-hopfiletransferoperation. We propose an ARQ timer-setting rule that minimizes the expected file delivery time under the constraint that the throughput efficiency is maximized. Then, we derive a closed-form expression for the expected file delivery time of the Deferred NAKmodeofCFDPaswellasupperandlowerboundsexpressionfortheexpected file delivery time of the Immediate NAK mode of CFDP, respectively. In the second part of research, we study power-efficient communication in wire- less ad-hoc networks to provide end-to-end connectivity. Although power-efficient topology control can reduce the total power consumption of a network as a whole, a power-aware solution that allows power consumption to be evenly distributed among network nodes so as to prolong the network lifetime is highly desirable. Our x main contribution is the development of a power-aware topology control algorithm and its associated CSMA/CA based MAC protocol. The proposed power-aware topology control algorithm at a given node only demands the residual energy lev- els and the location information of its reachable neighboring nodes. Besides, an algorithm to set up the RTS-CTS range in CSMA/CA-based MAC protocol is pro- posed to alleviate the hidden node problem, to avoid throughput degradation and to resolve the fairness problem. Finally, an analytical model that provides useful information to upper layer protocols to achieve better performance of the network is presented. xi Chapter 1 Introduction 1.1 Significance of the Research Recently, interests in the architectural and protocol design principles arise from the need to provide interoperable communications with and among extreme and performance-challenged environments, where continuous end-to-end connectivity cannotbeassumed. Examplesofsuchenvironmentsincludespacecraft,military/tac- tical, and some forms of ad-hoc sensor/actuator networks. Among the challenges to be addressed are large delay for transmissions resulting from either physical link properties or extended periods of network partitioning, high per-link error rates making end-to-end reliability difficult, and heterogeneous underlying network tech- nologies (including non-IP-based Internets). Thesubjectofefficientandreliabledatatransportisoneofthemostfundamen- tal problems in networking research. Furthermore, the problem of implementing efficient and reliable data transport protocol occurs not onlyat the transport layer, but also at the link layer and the application layer as well. We are concerned with networking techniques for data transfer under stringent conditions due to various special application contexts in this research. More specifically, we are concerned 1 with error control schemes in harsh environments and concerned with the power efficiency in general wireless ad-hoc networks. 1.1.1 Error control with ARQ Error control is a key factor in the design of reliable data transport schemes. It is often accomplished by a technique called the Automatic Repeat reQuest (ARQ) error control scheme. In most cases, the objective of ARQ scheme is to deliver a sequence of protocol data units (PDU) in the order of arrival with neither repeti- tions nor errors through an unreliable virtual channel provided by the underlying protocol layer. To achieve this objective, the basic operations required for an ARQ scheme are PDU error detection and retransmission request for erroneous PDU. It seems to be simple, but not as easy as it appears since the ARQ scheme is a distributed algorithm, and the reverse direction of data transmission is also subject to unreliability [6]. In addition to that, there exist a number of versions of ARQ schemes based on the actions at the sender and the receiver. The receiver may acknowledge each correctlyreceivedPDUbyaspecialacknowledgement(ACK)PDU,ortheacknowl- edgement may be embedded as a control field in PDUs if there are PDUs flowing in the reverse direction. Negative acknowledgement (NAK) may also be used for erroneous PDU. In either case (ACK alone or the ACK/NAK case), a timer must be used to avoid deadlock situations. The sender, not receiving a reply (ACK or NAK) within a specified time interval after transmission, repeats transmission of the PDU in question. If this procedure was not built in the ARQ scheme, the sender would wait forever for an ACK/NAK that had itself been lost or in error and discarded. There are a number of ways for responding to ACK/NAKs at the 2 sender. Based on the response to ACK/NAKs at the sender, ARQ schemes are divided into two categories: Stop-and-Wait (SW) ARQ scheme and sliding window ARQ scheme. Furthermore, there are two types of sliding window ARQ depend- ing on the receiver’s action after detection of the PDU error; namely, Go-back-N (GBN) ARQ and Selective Repeat (SR) ARQ schemes. Analysis of ARQ schemes has two aspects: correctness and performance. The correctness is related to the distributed nature of ARQ for unreliable message ex- change such that it questions each PDU delivered to the receiver is released to the upper layer once and only once without error. The performance of ARQ deals with throughput and delay, and depends on the actions at the sender/receiver. Since slight modification of the actions at the sender/receiver may lead to a whole dif- ferent ARQ scheme even though it looks similar, there exists a variety of different ARQ schemes. Furthermore, a specific ARQ scheme may have quite different per- formanceaccordingtoitsoperationalenvironment,e.g.,link-delayforthelinklayer ARQscheme, end-to-enddelayforthetransportlayerARQscheme, thePDUerror rate, and PDU error statistics, etc. . All these factors mentioned above make the analysisofARQschemesquitechallengingandmeaningful. Analyticalresultsshow thedependencyofaspecificARQschemeonenvironmentalvariablesandthensug- gest a way for adjustment to achieve better performance. Also, it provides us a clearideaaboutwhichARQschemetousetomeetcertainrequirementsofaspecific environment and how to design a new ARQ scheme for a specific application. Inthefirstpartofthisresearch,weanalyzethespecificARQschemedesignedto work in the InterPlanetary Network (IPN). The operational environment of IPN is quitedifferentfromthatoftheconventionalARQscheme. Thepropagationdelayis extremely long such that the sender cannot expect the response (ACK/NAK) from the receiver in short time. Also, the power constraint is very strict, the bandwidth 3 is low, the bit error rate is high, and the link connectivity is intermittent. As a result, the ARQ scheme designed to work in the IPN environment has different aspects as compared with the conventional ARQ schemes, and its analysis is also quite different. 1.1.2 Power efficiency in wireless ad-hoc networks Power efficiency is a major concern in wireless ad-hoc networks, since their nodes arewithlimitedenergysupplyinmostcases. Duetothelackofaphysicalbackbone infrastructure in such networks, end-to-end connectivity among nodes is achieved via wireless multi-hop communications and new complexity is added to protocol design and operation to maintain connectivity among nodes. Specifically, there is a great need of topology control to provide end-to-end connectivity in a power- efficient way. As a result, power-efficient topology control has attracted a lot of attention in recent years in this field. Although power-efficient topology control can reduce the total power consump- tion of a network as a whole, it cannot guarantee that power saving is evenly dis- tributedamongallnetworknodeswithrespecttoaroutingprotocol. Duetouneven power consumption, a few nodes can be depleted individually, which may in turn break network connectivity and paralyze some portion or even the entire network. A power-aware solution that allows power consumption to be evenly distributed among network nodes so as to prolong the network lifetime is highly desirable. Most topology control algorithms proposed so far use variable transmission power yet without taking the effect of the underlying Medium Access Control (MAC)protocolintoaccount. Ontheotherhand,powersavingcanalsobeachieved by adjusting the transmission power at the MAC layer but without considering the 4 impact of topology control. When topology control with variable transmission power is implemented in wireless ad-hoc networks, several issues arise and the un- derlyingMACprotocoldesignisaffectedaccordingly. Theseissuesincludethrough- put degradation, fairness and the hidden node problem that affect the underlying MAC protocol design. In the second part of this research, a power-aware topology control scheme that allows power consumption to be evenly distributed among network nodes, and thereby prolongs the network lifetime, is proposed. Besides, an algorithm to set up the Ready-To-Send (RTS)/Clear-To-Send (CTS) range in the Carrier Sense Multiple Access with Collision Avoidance (CSMA/CA) based MAC protocol is proposed to alleviate the hidden node problem, to avoid throughput degradation and to resolve the fairness problem. Finally, an analytical model that provides useful information to upper layer protocols to achieve better performance of the network as a whole is presented. 1.2 Review of Previous Work 1.2.1 ARQ schemes The history of research in the ARQ scheme goes back to early 1960s [31]. Much of the research effort has been devoted to the analysis of ARQ performance in the link layer and the transport layer. However, the main issues in link layer ARQ and transport layer ARQ are somehow different. This is mainly due to the fact that the transport layer ARQ deals with end-to-end error control, which is closely related to congestion control as well. In contrast, the link layer ARQ mainly deals with point-to-point error control [6,39,41]. 5 In the early stage of ARQ research, the performance of ARQ schemes was in- vestigated and improvement of ARQ schemes was suggested by assuming an inde- pendent and identically distributed (i.i.d.) PDU error process and the availability of a reliable feedback channel (no errors in ACK/NAK) [31]. Later on, some analy- sis started to consider the Markov PDU error process (e.g., the Markov forward channel model). A review of nonindependent errors was given by Kanal and Sas- try in [25]. Towsley [44] considered a Markov forward channel model and focused on the queueing performance analysis. Leung et al. [28] examined a Go-back-N ARQ scheme in a Markov channel. Lu and Chang [32] extended the study to chan- nels modelled by the k-th-order Markov and to other two classic ARQ schemes; namely, the stop-and-wait and selective-repeat ARQ schemes. All above results were obtained assuming the availability of a reliable feedback channel. Kim and Un [26] made a pioneering effort in studying the effect of an unreliable feedback channel. They analyzed Go-back-N and selective repeat ARQ schemes by taking into account both Markov forward and feedback channels so as to understand the effects of dependent errors and unreliable feedback. Zorzi and Rao [53] extended the analysis of ARQ schemes for Markov forward and feedback channels using re- newal theory. Nevertheless, the accuracy of Markov channel approximation and estimation of Markov chain parameters were not discussed, and the cause of the Markov error process was not explained. With the rapid growth and popularity of wireless communications, the perfor- mance of ARQ schemes over wireless channels has received much attention. The most distinct factor affects the ARQ performance in wireless communication is the multipathfadingeffectofwirelesschannels. Muchresearcheffortwasdevotedtothe modelling of fading channels using the Markov chain and statistics of bit/symbol errors from the Markov chain model of the fading channel. In a multipath fading 6 environment, it was shown that bit/symbol errors are bursty and can be modelled by a finite state Markov chain [47]. The famous Gilbert-Elliott model is a special two-state Markov chain model [54]. Zorzi and Rao [54] extended the bit/symbol level Markov chain model to the PDU level Markov model. It was shown that the two-state Markov chain approximation of the PDU error process is adequate for slow fading channels, and the PDU error process degenerates into an i.i.d. process for sufficiently fast fading channels. It was also shown that the parameters of a PDU error process can be derived in terms of parameters of the bit/symbol er- ror process. In other words, the Markov chain parameters can be estimated using fading channel simulation. These results can be applied to the analysis of ARQ schemes. More recent research on the ARQ scheme analysis was done using the Hidden Markov Model (HMM). Turin [45] showed that previous research results on the Markov PDU error process is a special case of the Hidden Markov Model. The strengthofHMMisthatitprovidesanunifiedapproach. Thatis,onceabit/symbol levelHMMisconstructed,thePDUlevelHMMcanbederivedfromthebit/symbol level HMM. In [45], Turin explained how to derive the PDU level HMM from the bit/symbol level HMM and analyzed the GBN ARQ scheme using HMM. The most recent work by Turin and Zorzi [46] focused the queueing performance (the queuelengthandthePDUdelayprobabilitydistribution)undertheRayleighfading channel using the HMM of the PDU error process. 1.2.2 Power saving in wireless ad-hoc networks Power-efficient topology control has attracted a lot of attention in wireless ad-hoc networks. Therelayregionandenclosureconceptwasfirstintroducedin[38],andit 7 wasshownthatthetopologyconstructedaccordinglyisaminimumpowertopology thatpreservestheminimumenergypathbetweeneverypairofnodes. Later,Liand Halpen[29]proposedanimprovedversionof[38]oflowercomplexity. Acentralized algorithm that minimizes the total power consumption while maintaining global connectivity was studied in [13]. Two centralized algorithms that minimize the maximum power per node and two corresponding distributed heuristic algorithms were presented in [37]. Recentworkonpower-efficienttopologycontrolincludesthelocalizedminimum- spanning-tree (LMST) algorithm proposed by Li et al. [30] and the shortest-path- tree (SPT) algorithm proposed by Wang et al. [48]. In the LMST topology control algorithm, each node first collects the location information of nodes within its maximum transmission range and then constructs a local MST and takes one-hop away nodes as its neighbors. It is proved that the resulting topology maintains global connectivity and the node degree is bounded by 6. In the SPT topology control algorithm, each node gathers the location information of nodes within its maximum transmission range, constructs a local SPT, and takes one-hop away nodes as its neighbors. The resulting topology maintains global connectivity and contains only bidirectional links. The SPT scheme preserves the minimum-energy path between each node pair while the MST scheme does not. Singh et al. [40] considered a power-aware routing scheme and argued that the remainingbatterycapacityshouldbeconsideredbytheroutingprotocoltoprolong the network lifetime. Even though the total transmission power can be a metric to measure the performance of a routing algorithm, it does not truely reflect the lifetime of the network. This is because that the minimum total power route may overuseaspecificnodeanddepletesitsenergyrapidly. Thus, theMin-MaxBattery Cost Routing (MMBCR) was proposed in [40] to address this problem, where the 8 routing cost is defined as the maximum of the inverse of the remaining battery capacity of nodes in the route. The desired route is selected among all viable routes such that the selected route has the minimum cost value. Toh [43] proposed another power-aware routing protocol, which is called the Conditional Min-Max Battery Capacity Routing (CMMBCR). The main idea is to combine the Minimum Total Transmission Power Routing (MTPR) and the Min- Max Battery Cost Routing (MMBCR) using the residual battery energy of each node. If intermediate nodes between source and destination nodes have sufficient residual battery energy, it chooses MTPR. However, if all routes have at least one intermediate node that has the residual battery energy below a threshold, it chooses MMBCR. The optimal maximum lifetime routing problem can be solved by the linear programming technique. Two heuristic routing algorithms were given in [12]. However, power-aware routing algorithms have their limitations. They typically demand the exact traffic flow information and the residual energy level of each node, which is not very practical. Besides, their complexity is high. Generally speaking,theyaredifficulttoimplementwhenthetrafficflowischangingfrequently. Power saving with variable transmission power has also been considered in the design of MAC protocols [21,24,34,36,51]. The busy tone method was used for MAC protocol design in [34,51]. With a separate control channel for busy tone transmission, each node can estimate the required transmission power to reach a peer node of reception. The estimation of transmission power of DATA and ACK to a receive node can be achieved by RTS-CTS transmission with the maximum power [21,24,36]. On one hand, the RTS-CTS transmission technique can be used to reduce the collision probability caused by asymmetric links due to variable transmission power. On the other hand, it may result in a severe collision problem and degrade the throughput performance [19]. It was pointed out in [20,22] that 9 the maximum RTS-CTS transmission power is not suitable for the capacity of the entire network. Wang and Kar [49] analyzed the throughput performance of the CSMA/CA MAC protocol using the local topology information and explained the fairness issue rigorously. However, symmetric links were assumed and no power control was used in the MAC protocol in their analysis. 1.3 Contribution of the Research 1.3.1 Analysis of ARQ schemes in IPN In recent years, the Consultative Committee for Space Data Systems (CCSDS) has madeconsiderableeffortstoprovideflexibleandefficienttransferofvarioustypesof data in a wide variety of mission configurations, from relatively low Earth-orbiting spacecraft to complex arrangements of deep-space orbiters and landers supported by multiple transmission links. In many mission scenarios, space networking faces extremely long propagation delays, intermittent link connectivity, limited band- width, and limited power budgets [4,42,52]. In response to these challenges and the need to automate the communication among spacecraft, the CCSDS File De- livery Protocol (CFDP) has been developed [9–11,14–16,27]. TheaforementionedmissionenvironmentsmaketheconventionalARQschemes impractical [7]. Under the extremely long propagation delay of the IPN environ- ment, the conventional ACK based ARQ schemes do not work properly. Thus, the most salient feature of ARQ schemes used in the CFDP, in comparison with con- ventional ARQ schemes, is that an acknowledgement (ACK) is not issued for most protocol data units (PDUs). For those PDUs, only negative acknowledgements (NAKs) are issued, which happens if the receiver perceives an anomaly in PDU 10 delivery. ACKs are only used for ancillary data PDUs such as EOF (End-Of-File) and FIN (FINished) PDUs, which are used for closing the file transfer operation. Another distinct difference is that the ARQ schemes of CFDP deal with the finite number of PDUs rather than streams of PDUs. Thus, the performance measure is different from that of conventional link layer ARQ schemes. In terms of perfor- mance measures, we are mainly concerned with the time taken to transfer a file (i.e., the expected file delivery time) and throughput efficiency resulting from the protocol specification. In this research, we model and analyze two ARQ schemes of CFDP (i.e. the Deferred NAK mode and the Immediate NAK mode) in a single-hop file transfer operation. Due to the NAK based ARQ schemes and the finite number of PDUs, the mathematical analysis of CFDP is quite challenging. Furthermore, the two different NAK mechanisms of the Immediate NAK mode of CFDP make the math- ematical derivation of the expected file delivery time even more difficult. To meet these challenges, we use an elaborately designed strategy of derivation. For ex- ample, breaking the file delivery time into two parts based on two different NAK mechanisms is used to facilitate the derivation. The main contribution of this research is to provide a closed-form expression in evaluating performance metrics. We address the problem of timer setting and propose a new timer-setting rule under the objective of maximizing throughput efficiency. Using the proposed timer-setting rule, we derive the expression for the expected file delivery time of the Deferred NAK mode of CFDP and upper and lower bounds for the expected file delivery time of the Immediate NAK mode of CFDP, respectively. 11 1.3.2 Power-aware topology control and CSMA/CA MAC protocol A power-aware approach in the context of topology control that allows the power consumption to be evenly distributed among network nodes, and thereby prolongs thenetworklifetime,isproposedinthisresearch. Whenanodeismakingadecision on whether a wireless link between itself and a reachable neighboring node should be preserved in the topology being constructed, the decision is made based on not only the distance from its neighboring nodes but also the residual energy levels of itself and its neighboring nodes. Also, the topology is restructured from time to time based on the residual energy level of each node. We also point out that most topology control algorithms proposed so far are mainly for the power savings using variable transmission powers taking no account of the effect from the underlying MAC protocol. Meanwhile, power saving by adjusting transmission power directly at the MAC layer is also considered in the design of some MAC protocols, but the effect from the topology control was not considered either. We presentCSMA/CA based MAC protocol that transmit RTS- CTS with variable power, as well as DATA and ACK, when a topology is given by thetopologycontrolalgorithm. Inourproposedalgorithm,eachnodedeterminesits transmissionpowerforRTS-CTSaswellasforDATA-ACKfromthegiventopology. We observe that asymmetric RTS-CTS ranges due to variable transmission power causes the hidden node problem and the fairness problem when RTS-CTS range is determined without considering the location of the neighboring nodes. In our proposed algorithm, each node starts with minimal RTS-CTS range and increases RTS-CTS range until symmetric RTS-CTS range is achieved. Then, it also adjust the transmission power for DATA-ACK. 12 The main contribution of the second part of research is to propose an power- aware topology control algorithm and to propose a CSMA/CA based MAC proto- col for topology controlled wireless ad-hoc networks. Unlike power-aware routing schemes,whereexacttrafficflowandresidualenergylevelofeachnodearerequired, our power-aware topology control algorithm only requires the residual energy lev- els and location information of the reachable neighboring nodes. We also propose an algorithm to set up RTS-CTS range in CSMA/CA based MAC protocol that can alleviate the hidden node problem, avoid the degradation of the throughput performance of MAC protocol, and resolve the fairness problem when a topology is given by the topology control algorithm. We developed an analytical model that canprovideusefulinformationfortheupperlayerprotocols,includingthetopology control,aswellasfortheMACitselfforappropriatelyadjustingcontrolparameters to achieve higher performance of the network as a whole. 1.4 Organization of Thesis The rest of thesis is organized as follows. The first part of this thesis consists of Chapters 2-4. First, we introduce the concept of IPN and the role of CFDP in IPN in Chapter 2. The operational description of ARQ schemes of CFDP is also presented. Then, the basic operation oftheCSMA/CAMACprotocolisexplained. InChapter3,wediscusstheDeferred NAKmodeofCFDP.Weproposethetimer-settingrulethatminimizestheexpected file delivery time under the objective of maximizing throughput efficiency. Then, based on the proposed timer-setting rule, we derive the expression for the expected file delivery time and discuss how to compute it numerically. In Chapter 4, we discusstheImmediateNAKmodeofCFDP,andproposeatimer-settingruleforthe 13 Immediate NAK mode of CFDP. Furthermore, we derive upper and lower bounds for the expected file delivery time. On the basis of our derivation, we show how the optimal expected file delivery time varies with parameters such as the channel quality, PDU size, file size, etc. . The second part of this thesis consists of Chapters 5 and 6. In Chapter 5, we present the power-aware topology control algorithm for wireless ad-hoc networks. Itisshownthattheproposedpower-awareschemecanbeappliedtoexistingpower- efficient topology control algorithms. We demonstrate the performance improve- ment of the proposed power-aware scheme over existing power-efficient topology control algorithms. In Chapter 6, we discuss issues of the CSMA/CA MAC proto- col when topology control is employed for wireless ad-hoc networks. We describe a CSMA/CA-based MAC protocol that transmits RTS-CTS, DATA and ACK with variable power for a given topology obtained by the proposed topology control algorithm. Then, an analytical model for the proposed CSMA/CA-based MAC protocol is developed. Concluding remarks and future research directions are given in Chapter 7. 14 Chapter 2 Background Review 2.1 IPN, DTN, CCSDS and CFDP In 60’s and 70’s, space system technologies were rapidly developed and imple- mented. However, due to the lack of compatibility among existing and new tech- nologies, efficient management of space systems became more challenging. Fur- thermore, interests in cooperative space operations were growing among interna- tional space agencies. Thus, the Consultative Committee for Space Data Systems (CCSDS) [1] was established in 1982 to provide standard communication and data handlingtechniquestosupportspacescienceapplicationsconductedexclusivelyfor peaceful purposes. Since its establishment, CCSDS has been incrementally devel- oping a basic set of standardized space communication techniques that are widely used in the space community today. In 90’s, developments in space technologies have enabled numerous deep space scientific missions such as Mars exploration. These missions produce a significant amount of data to be transferred to the Earth. For successful transfer of scientific data via reliable communications, NASA outlined significant challenges in develop- ing next generation space network architectures and initiated a project called the 15 InterPlaNetary Internet (IPN). As part of the “Next Generation Internet” initia- tive, theUSDefenseAdvanceResearchProjectAgecy(DARPA)supportedasmall groupattheJetPropulsionLaboratory(JPL)tostudythetechnicalarchitectureof IPN. Later on, researchers from NASA, JPL, MITRE Corporation, SPARTA, and GlobalScience&TechnologyformedtheIPNSpecialInterestsGroup(IPNSIG)[2] under the sponsorship of the Internet Research Task Force (IRTF). One objective of IPN was to blend ongoing CCSDS work in standardized space communication capabilities with the state-of-the-art technique developed in the terrestrial Internet community so as to allow data transfer of Internet users on the Earth with other remotely located Internet users on other planets or spacecrafts. The basic architectural concept is that users of the Internet on earth and users on flying spacecrafts and other planets are interconnected via a long delay deep space backbone network. However, there are significant challenges posed by the deep space networking paradigm that need to be addressed. They include: • Extremely long and variable propagation delays. • Asymmetrical and low bandwidth. • High link error rate. • Intermittent link connectivity. • Lack of fixed communication infrastructure. • Power constraint. Inresponsetothesechallengesandtheneedforreliablefiletransferandmanage- ment, the CCSDS File Delivery Protocol (CFDP) was developed [9–11,14–16,27]. 16 The most distinct characteristics of CFDP are the unique retransmission mech- anism (NAK based ARQ) and the store-and-forward operation. The store-and- forward operation, also known as custody transfer, is a key concept in IPN. Once a file is reliably transferred from the source point to the relay point, its custody is also transferred such that the source point can remove the file from its memory and use the freed memory for other operation. The store-and-forward operation is required in deep space networking since the end-to-end connectivity may be impos- sible due to the time-disjoint links and extremely long propagation delay. Even the end-to-end connectivity is possible, the source point has to hold up the file for a verylongdurationoftimeifittriestotransferafilethroughend-to-endcontinuous transmission and retransmissions reliably. The unique features of ARQ schemes of CFDP will be introduced in the next section. Since non-interactive asynchronous store-and-forward services, which are able to operate over diverse types of networks, would be useful for several networks currentlyinuseorbeingcontemplated,theDelayTolerantNetworkResearchGroup (DTNRG) [3] was formed in 2002. The architecture of CFDP provided by IRTF’s IPNSIG became a basis for generalization to networks other than those operating in deep space. Even though IPNSIG has been moved to the historical status within IRTF, it remains active as part of CCSDS and functions as a standards group concerned with protocols operating in deep space. 2.2 Description of CFDP’s ARQ Schemes InCFDP,eachfiletransferoperationiscalleda“transaction”andthesenderassigns a transaction ID to each transaction. The transaction ID, along with the source ID and other information, is contained in the header of each PDU. The sender informs 17 the receiver of the start of the file transfer by transmitting the meta data PDU, which contains information such as the source and destination IDs, the file name, the file size, etc. Like most PDUs in CFDP, there is no ACK for the meta data PDU, and the sender is allowed to transmit file data PDUs that carry the actual content of the file after transmitting the meta data PDU. In other words, there is no handshaking needed to initiate a “transaction”. The receiver detects the failure of delivering the file data PDU or the meta data PDUbynoticingmissingelementsinthesequenceofPDUscorrectlyreceived. Each file data PDU has a field that specifies the starting byte number and ending byte number of the file data carried by the PDU. Thus, the receiver can detect missing PDUs by observing the starting and ending byte numbers of correctly received PDUs. If the meta data PDU is lost in the first trial, the receiver can detect its loss since the transaction ID in the header of the newly received file data PDU will indicate the start of a new transaction. The receiver reacts to missing PDUs by sending NAK messages. Each NAK message contains a list of PDUs requested by the receiver for retransmission. Upon receiving a NAK, the sender retransmits the requested PDUs. When the sender completes the sending of all file data PDUs of a transaction, it sends an EOF PDU, indicating the end of the transferred file. AfterreceivingtheEOFPDU,thereceiveracknowledgesitwithanACK(EOF) and waits until the meta data PDU and all remaining file data PDUs are received before it closes the transaction. All data are eventually received because of the NAK mechanisms, and the receiver can notice the reception of all data from the filesizeinformationcontainedinthemetadataPDUandtheEOFPDU.Then, the receiver sends a FIN PDU. After receiving the FIN PDU, the sender acknowledges it with an ACK(FIN) and closes the transaction. When the ACK(FIN) is success- fully delivered back to the receiver, the receiver also closes the transaction. Then, 18 the transaction is closed at both entities. According to CFDP, the sender and the receiver must both transmit an ACK message in response to each EOF/FIN PDU evenafterclosingthetransactiontopreventpossibleanomaliesinclosingthetrans- action (e.g., the one described in [5]). Since there are ACKs and retransmission timer mechanisms for EOF and FIN PDUs, their exchange is reliable. Depending upon the mission requirements and the transmission capability, four selectable ARQ schemes are offered by CFDP. The four ARQ schemes (Immedi- ate NAK, Deferred NAK, Asynchronous NAK, and Prompt NAK modes) share a common mechanism in initiating and closing the file transfer operation, but they differ in their time of issuing NAK messages and lists of PDUs requested for re- transmission. In this research, we consider only the Deferred NAK mode and the Immediate NAK mode. They are described below. 2.2.1 Deferred NAK mode In the Deferred NAK mode, the receiver defers issuance of NAKs until it correctly receivestheEOFPDUfromthesender. Thereceiverkeepstherecordofallmissing PDUs until the EOF PDU is successfully delivered. After receiving the EOF PDU, thereceiverissuesanACK(EOF)andissuesaNAKthatrequestsretransmissionof all missing PDUs, if any. Upon receiving a NAK, the sender immediately retrans- mits all PDUs that the NAK requests. At the end of each transmission of a NAK, the receiver sets a NAK timer, and when the NAK timer expires the receiver again examines the record of missing PDUs. If missing PDUs still remain, the receiver issues another NAK and again starts a NAK timer. This process continues until the receiver receives all necessary PDUs, that contain the whole file content and the meta data PDU. After receiving all necessary PDUs, the receiver issues a FIN 19 EOF Delivery Time File Delivery Time M FD(last) ACK (EOF) Sender Receiver Last missing PDU NAK NAK RT 1 NAK Timer value 2T prop FIN NAK RT 2 EOF Timer value EOF EOF ACK (FIN) Figure 2.1: The illustration of the Deferred NAK mode. PDU. Upon receiving the FIN PDU, the sender issues an ACK(FIN) and closes the transaction. The delivery of the FIN PDU is guaranteed in the same way as the EOF PDU. The receiver closes the transaction when the ACK(FIN) is successfully delivered to the receiver. An illustration of the operation of the Deferred NAK mode is shown in Fig. 2.1. In this figure, M stands for the meta data PDU, and FD(k) the k th file data PDU. Theprotocoldefinitionin[11]specifiesthemeaningandtheformatofthesePDUsin detail. Furthermore, T prop is the one-way propagation delay, and RT k the duration of the k th retransmission spurt, which means consecutive transmission of PDUs back to back. File delivery time and EOF delivery time will be mathematically defined in Section 3.1. 2.2.2 Immediate NAK mode IntheImmediateNAKmode,thereceivergeneratesNAKsformissingPDUsbefore receiving the EOF PDU. The operation of the Immediate NAK mode is chrono- logically divided into two procedures: an “incremental lost segment detection pro- cedure” followed by a “deferred lost segment detection procedure” [11]. In the 20 following, we will call the incremental lost segment detection procedure the “in- cremental procedure” and the deferred lost segment detection procedure the “de- ferred procedure”. The incremental procedure starts at the sender’s transmission of the meta data PDU initiating the transaction and ends after the EOF reception at the receiver’s end. The incremental procedure ends at the end of ACK(EOF) transmission or at the end of NAK transmission immediately following ACK(EOF) transmission. If the last file data PDU is successfully received prior to the EOF reception, the incremental procedure ends upon the transmission of ACK(EOF). If the reception of EOF finds the last file data PDU missing (possibly with other PDUs), then the incremental procedure ends upon the transmission of the NAK. The deferred procedure starts at the end of the incremental procedure and ends when the meta data PDU and all file data PDUs are successfully received by the receiver. Themajordifferencebetweentheoperationsoftheincrementalprocedure and the deferred procedure is in their NAK mechanism. During the incremental procedure of the Immediate NAK mode, the receiver generates NAK whenever there is a missing PDU followed by a successful PDU. This NAK only requests the newly found missing PDUs, and the NAK timer is not required during the incremental procedure. Upon receiving a NAK, the sender immediatelyretransmitsallPDUsthattheNAKrequests. NotethatcertainPDUs might remain still missing even after the incremental procedure due to the loss and/or error of NAK or retransmitted PDUs. The receiver requests those missing PDUs during the deferred procedure. Immediately after the EOF reception, the receiver acknowledges it with an ACK(EOF) (and transmits a NAK if necessary) and starts a NAK timer if there still exist any missing PDUs. Then, the deferred procedure starts. 21 Duration of incremental procedure Duration of deferred procedure File Delivery Time Sender Receiver NAK NAK RT 1 NAK-Timer value 2T prop FIN NAK RT 2 EOF NAK-Timer value EOF delivery time NAK ACK (EOF) T inc T def M ACK (FIN) ( T inc - Interval ) ( T def - Interval ) Figure 2.2: The illustration of the Immediate NAK mode. Upon the expiration of the NAK timer, the receiver examines the record of missing PDUs. If missing PDUs exist, the receiver requests them all and sets a NAK timer upon transmission of NAK. Again, upon the expiration of the NAK timer, the receiver examines the record of missing PDUs. If some missing PDUs still remain, the receiver generates another NAK and starts a NAK timer. This process continues until the receiver receives all necessary PDUs, which constitute the entire file content and the meta data PDU. Note that the receiver can request retransmission of a missing PDU before receiving EOF. However, the receiver does not request retransmission of the same PDU more than once before receiving the EOF. According to [11], the receiver always starts the NAK timer upon the EOF reception if there is still a missing PDU. This is done even if it does not generate a new NAK in response to the EOF reception. Note that a NAK is generated in response to the EOF reception if and only if the first transmission of the very last file data PDU is unsuccessful. After receiving all necessary PDUs, the receiver 22 generates a FIN PDU. Upon receiving the FIN PDU, the sender acknowledges it with an ACK(FIN) and closes the transaction. The delivery of the FIN PDU is guaranteed in the same way as the EOF PDU through acknowledgement. The receiver closes the transaction when the ACK(FIN) is successfully received. In Fig. 2.2, we show the operation of the Immediate NAK mode, where M de- notesthemetadataPDU,andFD(k)thek th filedataPDU.Theprotocoldefinition in [11] defines the meaning and the format of these PDUs in detail. Again, T prop is the one-way propagation delay, and RT k the duration of the k th retransmission spurt in T def . The terms T inc –interval, T inc , T def –interval, and T def will be defined in Section 4.1. 23 Chapter 3 Analysis of Deferred NAK Mode 3.1 Preliminaries In this chapter, we present modelling and analysis of the Deferred NAK mode of CFDP. We consider the single-hop file transfer operation. With regard to perfor- mance measures, this research is mainly concerned with the time taken to transfer a file (expected file delivery time) and throughput efficiency resulting from the protocol specification. We define throughput efficiency as the average ratio of the total information data amount delivered to the amount of data transmitted. The more likely the retransmission of the same PDU are, the less the throughput efficiency is. This definition of throughput efficiency is directly related to the transmission power efficiency, which is extremely important in space communication. We define the “file delivery time” precisely as the time from the beginning of the transmission (first bit of the meta data PDU) until the first instant when all file data, meta data, and the EOF PDU have been successfully received by the receiver. Similarly, “EOF delivery time” is defined as the time from the beginning of transmission of the EOF PDU until the first instant when the EOF PDU has 24 beensuccessfullyreceivedandanACK(EOF)hasbeentransmittedbythereceiver. As illustrated in Fig. 2.1, the file delivery time consists of a number of transmission spurts (initial transmission of a file and several retransmission spurts after success- ful transmission of the EOF PDU), EOF delivery time, and time gaps between transmission spurts. “Transmission spurt” refers to consecutive transmissions of PDUs back to back. Note that our definition of file delivery time does not include the time for the FIN-ACK(FIN) procedure. The reason that we define file delivery time in this way is that the whole file is obtained by the receiver as soon as all file data, meta data, and the EOF PDU have been successfully received by the receiver. If one is interested in the duration of the entire transaction, the time to delivertheACK(EOF)andtheFIN-ACK(FIN)musttobeincludedalongwiththe file delivery time. For the simplicity of analysis, we make the following assumption. • The meta data PDU and all file data PDUs have identical lengths, identical transmission times, and identical probabilities of failed delivery (PDU error or loss). The meta data PDU is usually shorter than a data PDU and thus has lower probability of failed delivery. However, the length of the meta data is so small in comparison with the length of the file data that the assumption ofequallengthshasrelativelyanegligibleeffectonthetotalfiledeliverytime. • All NAKs have identical lengths and identical probabilities of failed delivery. (The length of a NAK depends on the number of PDUs that it requests. However, the differences are small, and the lengths of NAKs are all small, so this assumption should not significantly affect the performance measure.) • PDUerroreventsinforwardandbackwardlinksarestatisticallyindependent. Notations we use are specified in Table 3.1. 25 Table 3.1: Notations Symbol Definition P ef Prob. of PDU error in forward link P ef(EOF) Prob. of error in delivering EOF PDU P er Prob. of error in delivering NAK T prop One-way propagation delay T PDU Transmission time of meta data or file data PDU T NAK Transmission time of NAK PDU T EOF Transmission time of EOF PDU T ACK(EOF) Transmission time of ACK(EOF) PDU 3.2 Timer Setting Rule As can be deduced from the protocol description in the Introduction, the expected file delivery time depends upon certain parameter values that an implementer can freely choose; for example, the time-out value of the EOF timer and the time-out value of the NAK timer. In this research, we assume that the parameter values are set to minimize the expected file delivery time under the constraint that the throughput efficiency is maximized. Note that there is a trade-off between the throughput efficiency and file delivery time. For example, if the sender retransmits PDUs requested for retransmission multiple times in a row, the expected number of retransmission spurts will decrease, and so will the expected file delivery time. However, such a practice will result in decrease of the throughput efficiency and thus require more power consumption. In this research, we place high priority on the throughput efficiency because power is extremely limited in space networks. In this section, we address the timer setting problem related to throughput efficiency and propose a timer setting rule that does not compromise throughput efficiency while minimizing the file delivery time. Under the environment of the long propagation delay, the throughput efficiency can be compromised in the form of unnecessary duplicate retransmission of an 26 EOF ACK (EOF) EOF Time-out-EOF is too short. Unnecessary duplicate retransmission of EOF PDU (a) EOF timer NAK Unnecessary duplicate retransmission of PDU k Time-out for NAK is too short NAK i j k k (b) NAK timer Figure 3.1: Effect of timeout values on CFDP performance. identical PDU. For example, if the timeout value of the EOF timer, which we refer to as timeout EOF, is set too small, the sender retransmits the EOF PDU before receiving the ACK(EOF) because of timer expiration, even in the case in which the first EOF PDU and the ACK(EOF) are successfully delivered. Unnecessary duplicate retransmission of the file data PDU can occur if the timeout value of the NAK timer is set too small, as illustrated in Fig. 3.1. For such parameter values, we suggest the following and use them for our mathematica derivation: • ThetimeoutvalueoftheEOFtimer,timeout EOF,shouldbe2T prop +T ACK(EOF) , where T prop denotes the one-way propagation delay between the sender and 27 the receiver. (In a real implementation, the value of 2T prop should be esti- mated or computed by the sender. Also, the time–out value should include some delays such as node processing delay, etc. To take into account the delaysandestimationerrorintime–outvalue, wecanaddslacktoatime–out value. This is discussed later in detail.) • T k timer(NAK) , denoting the time–out value of the NAK timer set upon issuance of the NAK that causes the k th retransmission spurt, should be 2T prop + RT k , whereRT k denotes the transmission time of the PDUs requested by the receiver for the k th retransmission spurt. It can be intuitively argued that this timer setting does not compromise the throughput efficiency while minimizing the file delivery time. 3.3 Expected Value of EOF Delivery Time Denoting by G EOF the geometrically distributed random variable that counts the numberofEOFPDUtransmissionsuptoandincludingthefirstsuccessfuldelivery, we can express the EOF delivery time as (G EOF −1)(T EOF +timeout EOF)+(T prop +T EOF ), and its expected value as E[(G EOF −1)](T EOF +timeout EOF)+T prop +T EOF = P ef(EOF) 1−P ef(EOF) (T EOF +timeout EOF)+T prop +T EOF . (3.1) For timeout EOF = 2T prop +T ACK(EOF) , the expected EOF delivery time is 28 P ef(EOF) 2T prop +T EOF +T ACK(EOF) 1−P ef(EOF) +T prop +T EOF . (3.2) 3.4 Expected File Delivery Time We first define and analyze the random variable representing the number of trans- mission spurts in the transaction. We define random variable K i to represent the numberoftransmissionsofthei th PDUuptoandincludingitsfirstsuccessfultrans- mission. Then, underourchannelassumption,K i hasageometricdistribution. We denote by N the total number of PDUs carrying the file data plus 1 (counting the meta data). The transmission spurts will re-occur until all PDUs are delivered to the receiver, so the number of transmission spurts is max(K 1 ,K 2 ,...,K N ). We define random variable M N as M N = max(K 1 ,K 2 ,...,K N ) and note that M N −1 is the number of retransmission spurts. NowweconsiderthetimeintervalbetweentheissuanceofaNAKandtherecep- tion of the corresponding retransmissions. Once EOF PDU has been successfully received,thereceiverissuesthefirstNAKandsetstheNAKtimer. Inthisanalysis, we assume that the timeout value of the NAK timer is set at the two times prop- agation delay plus retransmission time. Since the receiver knows the amount of missing data and the transmission rate of the link, the receiver can simply compute the transmission time of those missing PDUs. Let us first consider the expected time between issuance of the first NAK and “nominal reception of the last bit of the first retransmission spurt”, by which we mean the time that the last bit of the firstretransmissionspurtistransmittedplusT prop . InthecasethatallofthePDUs 29 of that retransmission spurt are lost, there is no actual reception. Note that the timeout value of the NAK timer is set as T k timer(NAK) = 2T prop +RT k , k = 1,2,... (3.3) Taking into account the case that a NAK is lost (with the result that the NAK timer expires), the expected time between issuance of the first NAK and nominal reception of the last bit of the first retransmission spurt is given as ∞ X i=1 i T NAK +T 1 timer(NAK) P i−1 er (1−P er ) = T NAK +T 1 timer(NAK) 1−P er = T NAK +2T prop +RT 1 1−P er . (3.4) Similar expressions follow for the time between issuance of the first NAK after the nominal reception of then th retransmission spurt and the nominal reception of last bit of the (n+1) th retransmission spurt. Thus, the expected time interval between the issuance of the first NAK and reception of last bit of last retransmission spurt can be obtained as E M N −1 X k=1 2T prop +T NAK +RT k 1−P er ! = [E(M N )−1](2T prop +T NAK ) 1−P er + E P M N −1 k=1 RT k 1−P er . (3.5) Note that E P M N −1 k=1 RT k is the expected total time taken for transmission of meta and file data PDUs until all of them have been successfully delivered minus the time taken to transmit them for their first trials. Thus, 30 E M N −1 X k=1 RT k ! = N X i=1 E(K i −1)·T PDU = (N ·T PDU ) 1 1−P ef −1 . (3.6) Note that in Deferred NAK mode, the receiver sends NAK only after receiving EOF PDU. Therefore, expected file delivery time of a transaction, which includes the expected EOF delivery time, is given as T prop +N ·T PDU + [E(M N )−1](2T prop +T NAK ) 1−P er + (N ·T PDU ) P ef 1−P ef 1−P er + " P ef(EOF) 2T prop +T EOF +T ACK(EOF) 1−P ef(EOF) +T EOF # = T prop + [E(M N )−1](2T prop +T NAK ) 1−P er +N ·T PDU 1+ P ef (1−P er )(1−P ef ) + " P ef(EOF) 2T prop +T EOF +T ACK(EOF) 1−P ef(EOF) +T EOF # . (3.7) To complete the analysis, we need to obtain E(M N ). We first provide the following proposition, which is somewhat illuminating. 1 Proposition 1 P N k=1 1/k −ln(P ef ) ≤E(M N )< P N k=1 1/k −ln(P ef ) +1 Proof: 1 We derived these bounds with simple engineering mathematics. Other mathematically inter- esting properties of M N can be found in [35]. 31 K i for each i has geometric distribution P(K i =k) =P k−1 ef (1−P ef ), k = 1,2,3,... (3.8) We take the approach of approximating M N ≡ max(K 1 ,K 2 ,...,K N ) by max(X 1 ,X 2 ,...,X N ), where X i for each i has exponential distribution f X (x) =λexp(−λx), x≥ 0 . (3.9) • max(X 1 ,X 2 ,...,X N ) Recall that the expected time until any arrival amongn independent Poisson processes, each with arrival rate λ, is 1/(nλ) [18]. Consider N independent Poisson processes each of which terminates after the first arrival. Then, the timeuntiltheN th arrival(thelastarrival)ismax(X 1 ,X 2 ,...,X N ). Therefore, we see that E[max(X 1 ,X 2 ,...,X N )] = 1 Nλ + 1 (N −1)λ +···+ 1 2λ + 1 λ = 1 λ N X k=1 1 k . (3.10) • M N ≡ max(K 1 ,K 2 ,...,K N ) Consider mapping d, d(x)≡ λx −lnP ef , (3.11) where we denote ⌈y⌉≡ min{n∈Z | y ≤n}. Then, random variables d(X 1 ),d(X 2 ),...,d(X N ) are statistically independent and have a geometric 32 distribution identical to that of random variable K i . Moreover, for each real- ization of random variables X 1 ,X 2 ,...,X N we have max{d(X 1 ),d(X 2 ),...,d(X N )} =d(max(X 1 ,X 2 ,...,X N )). (3.12) Therefore, we have E(M N ) =E[max(K 1 ,K 2 ,...,K N )] =E[max{d(X 1 ),d(X 2 ),...,d(X N )}] =E[d(max(X 1 ,X 2 ,...,X N ))]. (3.13) From (3.11), we have d(max(X 1 ,X 2 ,...,X N )) ≥ λmax(X 1 ,X 2 ,...,X N ) −lnP ef (3.14) and d(max(X 1 ,X 2 ,...,X N )) < λmax(X 1 ,X 2 ,...,X N ) −lnP ef +1. (3.15) Therefore, from(3.10), (3.13), (3.14), and (3.15) we have P N k=1 1/k −lnP ef ≤E(M N )< P N k=1 1/k −lnP ef +1 . (3.16) Proposition 1 indicates thatE(M N ) increases in logarithmic order withN. The expected file delivery time in (3.7) has a term that increases linearly with N and a termthathasthefactorE(M N ). Forverylongpropagationdelay,themultiplicative factorE(M N )ismuchlargerthanthatofthetermlinearofN,whichisontheorder of the PDU transmission time. In such an environment, as the number of PDUs in 33 the file (N) increases, the expected file delivery time is initially dominated by the term logarithmically growing withN, and the order of growth later becomes linear with a small multiplicative factor for large values of N. For a small propagation delay (relative to the PDU transmission time, T PDU ), the order of growth is always dominated by the term linear of N. Proposition 1 provides a good idea of the expected file delivery time’s order of growth with N, but the difference between the bounds in Proposition 1 is 1.0. This can be considered loose, especially for applicationtothecaseofalongpropagationdelay. Thus,wenowdiscussnumerical evaluation ofE(M N ). We have E(M N ) = ∞ X m=1 P(M N ≥m) = ∞ X m=1 [1−P(M N <m)] = 1+ ∞ X m=2 [1−P(M N <m)] = 1+ ∞ X m=2 " 1− N Y i=1 P(K i <m) # = 1+ ∞ X m=2 h 1− 1−P m−1 ef N i = 1+ ∞ X m=1 h 1− 1−P m ef N i . (3.17) Note thatE(M N ) can be expressed as a finite summation as follows: E(M N ) = 1+ N X k=1 N k P k ef 1−P k ef (−1) k+1 . (3.18) Thus, in theory we can compute the exact value of E(M N ) in a finite number of computational operations. However, we face difficulties in numerical evaluation 34 for a large value of N. Term N k P k ef 1−P k ef (−1) k+1 of summation in (3.18) can have a very large factor N k and a very small P k ef . Thus, the evaluation of a term can be numerically difficult. Truncating the summation by omitting the terms that are difficult to compute does not give a good idea of how accurate such an approximation is. In addition, the terms in the summation could be both positive and negative, so such truncation does not give an upper or lower bound either. In fact, from (3.17) we can use finite summation 1+ P s ∗ m=1 [1−(1−P m ef ) N ] as both an approximation and a lower bound. As we increase the number of additions, s ∗ , the evaluation becomes more accurate. The numerical inaccuracy (the remainder) can be expressed as follows: R s ∗, ∞ X m=s ∗ +1 h 1− 1−P m ef N i = ∞ X m=s ∗ +1 P m ef n 1+ 1−P m ef + 1−P m ef 2 +···+ 1−P m ef N−1 o .(3.19) We can guarantee the error percentage of numerical evaluation 1+ P s ∗ m=1 [1− (1−P m ef ) N ]byobtaininganupperboundonR s ∗. ByusingageneralizedBernoulli’s inequality [33, p69], term (1−P m ef ) n , n = 1,2,...,N −1 in (3.19) can be bounded above by 1−P m ef 1+(n−1)P m ef . Thus, we can obtain the following upper bound of R s ∗: R s ∗ ≤ ∞ X m=s ∗ +1 P m ef ( 1+ 1−P m ef + 1−P m ef 1+P m ef + 1−P m ef 1+2P m ef +···+ 1−P m ef 1+(N −2)P m ef ) . (3.20) 35 Individual terms in the right-hand side of (3.20) can be bounded above by using the following relations: ∞ X m=s ∗ +1 P m ef 1+nP m ef ≤ Z ∞ s ∗ +1 P x ef 1+nP x ef dx+ P s ∗ +1 ef 1+nP s ∗ +1 ef , (3.21) ∞ X m=s ∗ +1 P 2m ef 1+nP m ef ≥ Z ∞ s ∗ +1 P 2x ef 1+nP x ef dx . (3.22) Let y = 1+nP x ef , then we have Z ∞ s ∗ +1 P x ef 1+nP x ef dx = Z 1 1+nP s ∗ +1 ef 1 (nlnP ef )y dy = −ln 1+nP s ∗ +1 ef nlnP ef , (3.23) Z ∞ s ∗ +1 P 2x ef 1+nP x ef dx = Z 1 1+nP s ∗ +1 ef y−1 (n 2 lnP ef )y dy =− P s ∗ +1 ef nlnP ef + ln 1+nP s ∗ +1 ef n 2 lnP ef . (3.24) From (3.20)–(3.24), we have R s ∗ ≤ ∞ X m=s ∗ +1 2P m ef −P 2m ef + N−2 X n=1 ∞ X m=s ∗ +1 P m ef 1+nP m ef − N−2 X n=1 ∞ X m=s ∗ +1 P 2m ef 1+nP m ef ≤ 2P s ∗ +1 ef 1−P ef − P 2(s ∗ +1) ef 1−P 2 ef + N−2 X n=1 " −ln 1+nP s ∗ +1 ef nlnP ef + P s ∗ +1 ef 1+nP s ∗ +1 ef # + N−2 X n=1 " P s ∗ +1 ef nlnP ef − ln 1+nP s ∗ +1 ef n 2 lnP ef # . (3.25) For a desired level of accuracy, one can use (3.25) to determine an appropriate value of s ∗ for computingE(M N ). Fig. 3.2 indicates that this upper bound decays very rapidly as we increase s ∗ . Thus, one can numerically compute E(M N ) with a fairly small number of additions and guarantee a small error percentage. In order to further simplify the decision of a proper value of s ∗ for numerical computation, 36 0 5 10 15 0 5 10 15 20 25 30 35 40 45 50 Upper bound of remainder term steps done in summation (s*) Number of PDU = 100000 P ef = 0.32 P ef = 0.16 P ef = 0.08 P ef = 0.04 P ef = 0.02 Figure 3.2: Upper bound of R s ∗. one can obtain an upper bound of the right-hand side of (3.25). For example, using the well-known inequality ln(1+x)≤x, we derive R s ∗ ≤ 2P s ∗ +1 ef 1−P ef − P 2(s ∗ +1) ef 1−P 2 ef +(N −2) 1− 1 lnP ef P s ∗ +1 ef . (3.26) The upper bound in (3.26), in addition, explicitly shows that the error term decays at least exponentially fast as s ∗ increases. 3.5 Numerical Presentation The mathematical expression derived in previous sections for the expected file de- livery time in Deferred NAK Mode is numerically presented in Fig. 3.3–3.6. Note that the astronomical unit (a.u., 1 a.u. = 480 s) is used. Fig. 3.3–3.6 illustrate how the expected file delivery time in Deferred NAK Mode is affected by variables such as the PDU error rate, the number of PDUs in the file, the PDU transmission 37 10 -2 10 -1 10 0 0 10 20 30 40 50 60 Expected File Delivery Time (in a.u.) P ef T prop = 1.0 a.u., T PDU = 0.8 sec 10 -2 10 -1 10 0 0 10 20 30 40 50 60 Expected File Delivery Time (in a.u.) P ef Number of PDU = 1000, T prop = 1.0 a.u. T PDU = 0.08 sec T PDU = 0.8 T PDU = 8 N = 100 N = 1000 N = 10000 Figure 3.3: Expected file delivery time vs. P ef . time, etc. In these figures, we assumed that T NAK , T EOF , and T ACK(EOF) are two orders of magnitude less than T PDU because of the small sizes of the NAK, EOF, and ACK(EOF) PDUs. We also assumed that P ef(EOF) and P er are two orders of magnitude less than P ef for the same reason. In Fig. 3.6, we compare the numerical evaluation of expression (3.7) and the results of random simulation. In this figure, we set s ∗ = 20 to compute E(M N ) numerically. The figure illustrates how the expected file delivery time is affected by the bit error rate (BER) of the link. The considered region of BER without forward error correction (FEC) is between 10 −5 and 10 −7 because achievable BERs without FEC range between 10 −5 and 10 −7 in typical space communications. The simulation results and the mathematically derived results closely match, as can be observed from the figure. However, the random simulation took much more computational time and required much more programming efforts. 38 0 2000 4000 6000 8000 10000 0 5 10 15 20 25 30 35 40 Expected File Delivery Time (in a.u.) Number of PDUs P ef = 10 -3 , T prop = 2 a.u. 0 2000 4000 6000 8000 10000 10 20 30 40 50 60 70 Expected File Delivery Time (in a.u.) Number of PDUs P ef = 10 -3 , T prop = 10 a.u. T PDU = 0.08 T PDU = 0.8 T PDU = 8 T PDU = 0.08 T PDU = 0.8 T PDU = 8 Figure 3.4: Expected file delivery time vs. number of PDUs. 3.6 Conclusion WederivedtheexpressionfortheminimumexpectedfiledeliverytimeoftheCFDP Deferred NAK Mode under the constraint that the throughput efficiency is maxi- mized in the sense that there is no unnecessary duplicate retransmission. For the purpose of gaining simple performance intuition, in determining the NAK timer- setting rule we assumed that the sender can start retransmission immediately after receiving a NAK PDU. (Recall that we set the timeout value of the NAK timer for the k th retransmission spurt as T k timer(NAK) = 2T prop +RT k in Section 3.2.) In real operations, the sender may not be able to start retransmission of the PDUs requested by the NAK. For example, if the sender is performing multiple outgoing transactions concurrently (multiplexed transactions), the sender may have to de- lay the requested retransmissions in a particular transaction because of previously queued outbound data belonging to another transaction that must be transmitted beforethenewlyrequestedPDUsareretransmitted. Thisqueueingdelayisdifficult 39 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 0 5 10 15 20 25 30 35 Expected File Delivery Time (in a.u.) Number of PDUs P ef = 10 -3 , T PDU = 0.8 sec T prop = 10 -2 a.u. T prop = 1.0 T prop = 5.0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 x 10 4 0 2 4 6 8 10 12 14 Expected File Delivery Time (in a.u.) Number of PDUs T prop = 1.0 a.u., T PDU = 0.08 sec P ef = 10 -2 P ef = 10 -2.5 P ef = 10 -3 P ef = 10 -4 Figure 3.5: Expected file delivery time vs. number of PDUs. to estimate. However, a simple way of improving throughput efficiency in such an operational environment is to add a constant valuez to the NAK timer–namely, to use T k timer(NAK) = 2T prop +RT k +z, k = 1,2,... (3.27) The actual value of z to be used depends upon the level of throughput efficiency desired and the PDU scheduling scheme of the sender. (The scheduling scheme at the sender is specific to the implementation and beyond this paper’s scope.) If the timeout value of NAK timer (3.27) is used in place of the timeout value of 40 10 -7 10 -6 10 -5 3.5 4 4.5 5 5.5 6 6.5 7 7.5 Expected File Delivery Time (in a.u.) BER PDU Length = 1.5 Kbytes 10 -7 10 -6 10 -5 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 Expected File Delivery Time (in a.u.) BER PDU Length = 2 Kbytes Def. NAK (analysis) Def. NAK (simulation) Figure 3.6: Deferred NAK: Analytic and simulation results. Expected file delivery timeofDeferredNAKModevs. BER.Filesize=1MB,transmissionrate=20Kbps in both directions, and propagation delay = 480s. NAK timer (3.3), the expected time between the issuance of the first NAK and the nominal reception of the last bit of the last transmission spurt in (3.5) is replaced by E M N −1 X k=1 2T prop +T NAK +RT k +z 1−P er ! = [E(M N )−1](2T prop +T NAK +z) 1−P er + E P M N −1 k=1 RT k 1−P er , (3.28) and thus the expected file delivery time is T prop + [E(M N )−1](2T prop +T NAK +z) 1−P er +N ·T PDU 1+ P ef (1−P er )(1−P ef ) + " T EOF + P ef(EOF) 2T prop +T EOF +T ACK(EOF) 1−P ef(EOF) # . (3.29) 41 Note that the expected file delivery time depends upon several variables–e.g., filesize,PDUsize,thepropagationdelay,etc. Withtheresultsofourmathematical derivation in (3.7) and(3.29) wecan generate numericalvaluesfor theexpected file delivery time quickly, without computationally intensive random simulation, for a range of different environmental and design variables. Finally, we note that the CFDP or its variant may be useful beyond space applications, althoughtheCFDPhasbeenstandardizedbyCCSDSforuseinspace networking. For example, the feature of no ACK message for the file data PDUs (i.e.,NAKonly)mayalsobeusefulforsecurecommunicationinwhichthereceiver’s emission should be small in order to hide its presence or location. 42 Chapter 4 Analysis of Immediate NAK Mode 4.1 Preliminaries In this chapter, We consider the single-hop file transfer operation of Immediate NAK mode of CFDP, and present modelling and analysis of the Immediate NAK mode of CFDP. The file delivery time and EOF delivery time are defined in the same way as in Deferred NAK mode. However, the two different NAK mechanisms oftheImmediateNAKmodemakethemathematicalderivationoftheexpectedfile delivery time quite challenging, and we will use an elaborately designed strategy of derivation to meet this challenge. For the convenience of mathematical derivation, wefirstdefineT inc -intervaltobetheintervalfromthebeginningofthetransmission (the first bit of the meta data PDU) until the NAK timer set upon the first error- free EOF reception is expired, as illustrated in Fig. 2.2. We denote by T inc the length of the T inc -interval. Thus, in Immediate NAK mode T inc is the duration of the incremental procedure plus the time-out period of the NAK timer set on the first error-free EOF reception. The T def -interval is defined as the interval from the issuance of the first NAK that requests all missing PDUs until the first moment when all file data, meta data, and the EOF PDU have been successfully received 43 by the receiver, as illustrated in Fig. 2.2. We denote byT def the length of the T def - interval. (IfthereisnoNAKthatrequestsallmissingPDUs, thenT def = 0.) Thus, T def consists of the duration of the retransmission spurts and time gaps between retransmission spurts. (“Transmission spurt” refers to consecutive transmissions of PDUs back to back. See Fig. 2.2 for an illustration.) From the next sections, we derive the expected file delivery time for the Immediate NAK mode of CFDP by examining T inc and T def , respectively. Note that T inc (T def ) does not exactly coincide with the duration of the “incremental loss segment detection procedure” (“deferred loss segment detection procedure”). For the simplicity of analysis, we make an additional assumption in addition to the assumption made in Section 3.1. • Compared with the file data PDU, the size of NAK, ACK, and EOF PDUs is much smaller, so we ignore the transmission time of these PDUs. For performance analysis of Immediate NAK mode, we also have to specify the action of the sender at the instance of expiration of the EOF timer if a PDU to be retransmitted is waiting in the queue. Note that at the instance of expiration of the EOF timer, the sender may be retransmitting a PDU, and another PDU to be retransmitted may be waiting. We can consider two implementations of the sender’s action in such a case. 1 First, after finishing the transmission of the rest of the PDU being transmitted, the sender could pause retransmission of the PDUs that have been requested for retransmission. The purpose of this pause is “rapid response to the expiration” of the EOF timer. While pausing the retransmission of PDUs previously requested, the sender sends the EOF PDU again. Then, the 1 The protocol specification does not address this case, and the two implementation presented here are not found in existing literature. 44 sender resumes retransmission of the PDUs requested. (EOF retransmission is in- sertedbetweentheretransmissionoffiledataPDUspreviouslyrequested.) Second, the sender could complete retransmission of all PDUs previously requested before retransmitting the EOF PDU in response to the EOF timer expiration. In this paper, we assume the former implementation of CFDP. 2 4.2 Timer Setting Rule Basically, the same timer setting rules specified in Section 3.2 are applied to Imme- diate NAK mode. Thus, “time-out-EOF,” denoting the time-out value of the EOF timer, should be 2T prop . (Recall that we assume the transmission times of NAK, ACK, and EOF PDUs are negligible in the analysis of Immediate NAK mode as mentioned in Section 4.1.) Also, T k timer(NAK) , denoting the time–out value of the NAK timer set upon issuance of the NAK that causes the k th retransmission spurt in the T def –interval, should be 2T prop +RT k , where RT k denotes the transmission time of the PDUs requested by the receiver for the k th retransmission spurt in the T def –interval. In addition to the timers mentioned above, special attention should be paid to the value of the NAK timer that the receiver sets in response to receiving the EOF. Let us recall that in the Immediate NAK mode a NAK timer is set regardless of whether or not a NAK is generated in response to receiving the EOF. We will refer to this special NAK timer as the “NAK EOF timer.” Without proper setting of the time-outvalue of theNAK EOF timer, duplicateretransmissionsmay occur. In this section, we discuss the value to be set for the NAK EOF timer. Let us illustrate two cases of a duplicate retransmission that is caused by improper setting of the 2 Adifferentimplementationofthesender’sactioncanresultinadifferentexpectedfiledelivery time. 45 Time_out as proposed N-6 N-1 Time_out = 2T prop +T PDU Possibility of duplicated retransmission. NAK will request PDU N, N-2, and N-3 No possibility of duplicated retransmission N-5 N-4 N-3 N-2 N NAK requests 1 PDU (N) NAK requests 5 PDUs (N-6~N-2) N N-6 N-5 N-4 N-3 N-2 N-1 N-7 N-7 EOF EOF Figure 4.1: Timer setting problem for the NAK generated on successful reception of the EOF PDU time-out value of the NAK EOF timer. First, we consider the case in which the first transmission of PDU N (the last file data PDU in the file) from the sender is unsuccessful. In this scenario, the reception of the EOF by the receiver spawns an actual issuance of a NAK message, and the NAK EOF timer associated with the NAK message is set. We note that this NAK message requests retransmission of PDU N and possibly retransmission of other PDUs newly found missing, according to the protocol specification [11]. If the NAK EOF timer were set, like other NAK timers set during the T def –interval, to be two times the propagation delay plus the transmission time of PDUs requested by the NAK, then duplicate retransmissions could occur. Fig. 4.1 illustrates such duplicate retransmissions. Second, we consider the case in which the first transmission of PDU N by the senderissuccessful;thatis,thereceiverreceivesPDUN priortoreceivingtheEOF. In this case, the reception of EOF does not spawn a NAK generation. However, if thereisstillamissingPDUatthetimeofEOFreception,theNAK EOF timerisset inaccordancewiththespecification[11]. IftheNAK EOF timerissetattoosmalla 46 value,therecouldagainbeanunnecessaryduplicateretransmission. Indetermining the time–out value of the NAK EOF timer to be set upon EOF reception, there is a trade-off between the possibility of unnecessary duplicate retransmission and the delay in the file delivery time. Therefore, we propose a rule that chooses the time– out value of the NAK EOF timer to be as small as possible while guaranteeing that there will be no unnecessary duplicate retransmission. 4.2.1 Rule to determine the NAK EOF timer value We propose that a timer be set upon every generation of a NAK, including even theNAKsgeneratedpriortothereceptionofEOF(intheincrementalprocedure). 3 However, before successful EOF reception, the receiver does nothing at the instant of NAK timer expiration. The purpose of the receiver’s setting of NAK timers prior to receiving EOF is to have an account of the system’s pending retransmis- sion activities at the instant of EOF reception. From now on, we refer to those NAK timers used before successful EOF reception as NAK timer–inc for clarity of description. The following conceptual mechanism describes the rules determining the value of each NAK timer–inc: NAK timer–inc setting rule: (1) At the generation of the very first NAK, the time–out value of the NAK timer–inc is set to be two times the propagation delay plus transmission time of the requested PDUs. (2) At the generation of subsequent NAKs, the following rules are applied: 3 Even though a timer is set upon every generation of a NAK, the number of timers that the receiver maintains at the same time is at most two. More details are provided in the NAK timer- inc setting rule in this section. Also, a good tuning of system parameters should keep the packet error rate small, so the number of NAKs and the the NAK timer-inc setting events should be small. 47 – If there is no active NAK timer–inc, (remaining time–out = 0), the new NAK timer–inc value is again set to be two times the propagation delay plus transmission time of the requested PDUs. – If there is an active NAK timer–inc (remaining time–out > 0), the re- ceiver compares the remaining time–out value of this active timer with two times the propagation delay. ∗ If the remaining time–out value of the active timer is greater than two times the propagation delay, the receiver starts a new NAK timer–inc and sets its value to be the remaining time–out value of the active timer plus transmission time of the requested PDUs. The receiver stops the old timer. ∗ If the remaining time–out value of the active timer is less than two times the propagation delay, the receiver starts a new NAK timer– inc andsetsitstime-outvaluetobetwotimesthepropagationdelay plus the transmission time of requested PDUs. The receiver stops the old timer. UponthesuccessfulreceptionofEOF,thereceivertakesoneofthethreeactions stated below: a. If reception of EOF spawns a NAK, the NAK EOF timer is set as if it were a NAK timer–inc, in accordance with the NAK timer–inc setting rules 1 and 2 above. b. If the reception of EOF does not spawn a NAK and there is an active NAK timer–inc,thereceiverstartsaNAK EOF timerthetime–outvalueofwhichis 48 the remaining time–out value of the active NAK timer–inc, and the receiver stops the NAK timer–inc. c. If the reception of EOF does not spawn a NAK and there is no active NAK timer-inc, NAK EOF timer is set to be zero. If there are still missing PDUs at this time, the receiver starts deferred procedure by issuing a NAK that requests all missing PDUs. Otherwise, this implies that meta data, all file data PDUs, and EOF have been received successfully. The receiver transmits FIN PDU. Our proposal for the NAK EOF timer–setting rule, which relies on the NAK timer–inc setting rule, eliminates the ambiguity in how to determine the time–out value of the NAK EOF timer. (The specification [11] gives freedom on this value to implementers.) As previously explained, NAK EOF timer is set upon the first successful reception of EOF. However, an improper setting of the NAK EOF timer value can cause unnecessary duplicate retransmissions. (Refer to Fig. 4.1.) With- out proper consideration of potential retransmission activities at the sender, it is hard to determine the smallest time–out value of theNAK EOF timer that prevents any unnecessary duplicate retransmission. Our NAK EOF timer setting rule uses NAK timer–inc sothatthereceiver, uponreceivinganEOF,mayhaveaccuratees- timation of thesender’s potential retransmission activities. Section 4.2.2 rigorously showshowtheproposedNAK EOF timer–settingruleminimizestheNAK EOF timer while preventing unnecessary duplicate retransmissions. From now on, we assume implementationofourtimer–settingrulesandthe“rapidresponsetotheexpiration of EOF timer” that was explained in Section 4.1. 49 4.2.2 Mathematical description of timer setting rule Let us denote by R inc n the time–out value of the n th NAK timer–inc set during the T inc –interval. According to the timer–setting rule, the time–out value of any NAK timer–inc is greater than two times the propagation delay. That is, R inc n = 2T prop +W inc n , (4.1) where W inc n > 0. To define W inc n more rigorously, we define two more random variables as follows: • N inc n is the number of PDUs requested by the n th NAK in the T inc –interval. • T n is the inter–issuance time between the n th NAK and the (n−1) th NAK in the T inc –interval, where T 1 ≡ 0. For the first NAK timer-inc, we have W inc 1 =N inc 1 ·T PDU , (4.2) so R inc 1 = 2T prop +W inc 1 = 2T prop +N inc 1 ·T PDU . (4.3) Inotherwords, accordingtorule(1)inSection4.2, thetimerequiredinadditionto 2T prop in the time–out value of the 1 st NAK timer-inc is the time as that required to retransmit all the PDUs requested by the 1 st NAK for retransmission. For the n th NAK in the T inc –interval (n≥ 2), we have R inc n = R inc n−1 −T n +N inc n ·T PDU if R inc n−1 −T n ≥ 2T prop , 2T prop +N inc n ·T PDU if R inc n−1 −T n < 2T prop . (4.4) 50 Thisrelationmathematicallydescribesrule(2)inSection4.2. (NotethatR inc n−1 −T n is the remaining time–out value at the issuance of the n th NAK.) From (4.1), we can re-write (4.4) into R inc n = 2T prop +W inc n−1 −T n +N inc n ·T PDU if W inc n−1 ≥T n , 2T prop +N inc n ·T PDU if W inc n−1 <T n . (4.5) Therefore, the n th NAK timer-inc in (4.1) can be described by recursion of W inc n : W inc n = W inc n−1 +N inc n ·T PDU −T n if W inc n−1 ≥T n , N inc n ·T PDU if W inc n−1 <T n . (4.6) Now, we interpret W inc n , which is given to the n th NAK timer–inc in addition to two times the propagation delay in order to avoid unnecessary duplicate retrans- missions: W inc n isdefinedbasedonthereceiver’sestimation, underthehypothetical assumption that NAK delivery never fails, of the number of backlogged PDUs that the sender has at the time of its reception of the n th NAK. The physical meaning of W inc n is the duration the sender needs from its nominal reception time of the n th NAK issued by the receiver (the time at which the n th NAK is issued by the receiver plus the propagation delay) to finish retransmitting all of the backlogged PDUs at that time (assuming no failure in NAK delivery) plus the duration re- quired to retransmit all the PDUs requested in the n th NAK for retransmission. See Fig. 4.2 for an illustration ofW inc n . In Fig. 4.2 (a), when the receiver issues the n th NAK it estimates the number of backlogged PDUs as 3 at the time of arrival of the n th NAK. It is correct because the (n−1) th NAK is successfully delivered to the sender. However, the estimation would be incorrect if the (n−1) th NAK fails 51 2T prop k+1 k+6 k+2 k+3 k+4 k+5 k+7 n th NAK requests 1 PDU (k+7) (n-1) th NAK requests 5 PDUs (k+1~k+5) k+7 k+1 k+2 k+3 k+4 k+5 k+6 k k k+8 k+8 W n inc (a) 2T prop k+1 k+6 k+2 k+3 k+4 k+5 k+7 n th NAK requests 1 PDU (k+7) (n-1) th NAK requests 5 PDUs (k+1~k+5) k+7 k+1 k+2 k+3 k+4 k+5 k+6 k k k+8 k+8 W n inc k+7 (b) Figure 4.2: Illustration of W inc n . to be delivered to the sender. Fig. 4.2 (b) illustrates such a case; when the receiver issues the n th NAK it estimates the number of backlogged PDUs as 3 at the time of arrival of the n th NAK, but there are no backlogged PDUs at the sender at the time of arrival of the n th NAK because the (n−1) th NAK fails to be delivered to the sender. As a result, the time-out value of the n th NAK timer–inc might be set to be longer than what it is actually required. Let us denote by R the time–out value set for NAK EOF . Let L be the number of NAKs issued in the T inc –interval. We also define A to be the time from the 52 issuance of the last (L th ) NAK that is generated by the receiver in theT inc –interval until the reception of EOF. (See Fig. 4.5 for illustration ofA.) Then, we can write: R = R inc L −A + (4.7) where R inc n is the time–out value of the n th NAK timer-inc set during the T inc – interval (4.1). In the event that the reception of EOF spawns a NAK, this NAK is the last NAK in the T inc –interval and is, by the definition of L, the L th NAK in the T inc –interval, so we set A at zero. In such an event, (4.7) is reduced to: R =R inc L = 2T prop +W inc L (4.8) 4.3 Analysis of Immediate NAK Mode AsdescribedinSection4.1,thefiledeliverytimeofCFDPinImmediateNAKmode can be divided into two parts: T inc and T def . In the Immediate NAK operation, the receiver can request retransmission of a missing PDU before receiving EOF. However, the receiver does not request retransmission for the same PDU more than once before receiving the EOF. Thus, the Immediate NAK mode allows one retransmission for each PDU during the T inc –interval. Taking this property into account, we examine and derive the expected value of T inc and T def . We denote by PDU 1, PDU 2, ..., PDU N the consecutive PDUs in the original order of occurrence in the file to be delivered to the receiver. 53 4.3.1 Bounds on the expected value of T def Recall that the time-out value of NAK timer used in T def –interval for the k th re- transmission spurt is set to be T k timer(NAK) = 2T prop +RT k , where RT k denotes the duration of k th retransmission spurt. We denote by H N the number of retrans- mission spurts for N PDUs during the T def –interval in the Immediate NAK mode. Then,takingintoaccountthecasethatNAKmaybelost(andthustheNAKtimer expires), the expected value of T def is obtained as E(T def ) = E 2T prop +RT 1 1−P er + 2T prop +RT 2 1−P er +···+ 2T prop +RT H N 1−P er = E(H N )2T prop 1−P er + E(RT 1 +RT 2 +···+RT H N ) 1−P er . (4.9) In(4.9), RT 1 +RT 2 +...+RT H N is the time that the sender’s transmitter spends in retransmitting the PDUs in the T def –interval. E(RT 1 +RT 2 +...+RT H N ) is given as the following: Proposition 2 E(RT 1 +RT 2 +...+RT H N ) = N ·T PDU ·P ef 1−P ef −N ·P ef (1−P er )T PDU (4.10) Proof: The total time that the sender’s transmitter spends in transmitting meta data and file data PDUs (total N PDUs) until all of them are successfully delivered during the whole duration of the transaction can be expressed as, N ·T PDU +Z +RT 1 +RT 2 +···+RT H N , 54 where Z denotes the total time that the sender’s transmitter spends in retransmit- ting PDUs in the T inc –interval and RT 1 +RT 2 +···+RT H N is the time that the sender’s transmitter spends in retransmitting the PDUs in the T def –interval. (For an illustration, see Fig. 2.2.) We have a simple expression for the expected value of the total time that the sender’s transmitter spends in transmitting meta data and file data PDUs–namely, E[N ·T PDU +Z +RT 1 +RT 2 +···+RT H N ] = N ·T PDU 1−P ef . (4.11) Thus, we have E(RT 1 +RT 2 +···+RT H N ) = N ·T PDU 1−P ef −N ·T PDU −E(Z) = N ·T PDU ·P ef 1−P ef −E(Z) . (4.12) ToobtainE(Z),weobservethatPDUnisretransmittedduringtheT inc –interval if and only if (i) the first transmission of PDU n is unsuccessful, and (ii) the NAK requesting PDU n for retransmission is successfully delivered to the sender. Therefore, the probability that PDU n is retransmitted during the T inc –interval is P ef (1−P er ). BecausethereareN PDUsinthefile, theexpectedvalueofZ isgiven as E(Z) =N ·P ef (1−P er )T PDU . (4.13) From (4.12) and (4.13), we have E(RT 1 +RT 2 +···+RT H N ) = N ·T PDU ·P ef 1−P ef −N ·P ef (1−P er )T PDU . (4.14) 55 From (4.9) and Proposition 2, we have E(T def ) = E(H N )2T prop 1−P er + N ·T PDU ·P ef (1−P ef )(1−P er ) −N ·P ef ·T PDU (4.15) ForE(H N ), we have the following upper and lower bounds. Proposition 3 E(M N )−1− 1−(1−P ef ) N 1+P er ≤E(H N ) ≤E(M N )−1− h 1−(1−P ef ) N i (1−P er ) (N−1)P ef( 1−P ef) +P ef 1− ( 1−P ef) N , (4.16) Refer to Section 3.4 for more details ofE(M N ). Proof: The random variable M N is defined as max(K 1 ,K 2 ,...,K N ), where random variable K i represents the number of transmissions of the i th PDU up to and including its first successful reception. We again note that K 1 ,K 2 ,...,K N are I.I.D. and geometrically distributed random variables. We observe a certain relationship between M N and H N , the number of retransmission spurts during the T def –interval in the Immediate NAK mode. First, we note that if all N PDUs are successfully received by the receiver at their first transmission (i.e., M N = 1), then H N = 0; therefore, E(H N | M N = 1) = 0 . For event M N ≡ max(K 1 ,K 2 ,...,K N ) > 1, we consider the following two sub– events: 56 Event a: M N > 1 and ∃ PDU i such that K i = M N and such that PDU i is transmitted only once (no retransmission) during T inc –interval. (This event happens due to the error/loss of NAKs requesting such PDUs.) Event b: M N > 1 and ∀ PDU i such that K i = M N PDU i is transmitted twice during the T inc –interval. Event M N = 1, Event a, and Event b are mutually exclusive and collectively exhaustive. Thus, Pr[M N = 1]+Pr[Event a]+Pr[Event b] = 1 . Also, note that E(H N |M N = 1) = E(M N −1|M N = 1) = 0 E(H N |Eventa) = E(M N −1|Eventa) E(H N |Eventb) = E(M N −2|Eventb) . Therefore, the unconditional expectation of H N is given as E(H N ) = E(M N −1 | M N = 1)Pr[M N = 1] +E(M N −1 | Event a)Pr[Event a] +E(M N −2 | Event b)Pr[Event b] = E(M N )−1−Pr[Event b] . (4.17) As a result, we can have a simple relation betweenE(M N ) andE(H N ): E(M N )−2≤E(H N )≤E(M N )−1 . (4.18) 57 Note that using (4.18) to obtain the bounds on the expected value of T def will result in loose bounds if propagation delay is very long. Now, we make the bounds on E(H N ) tighter by finding the bounds on Pr[Event b]. First, we consider a set, Π M , of PDUs that are transmitted M N times in the transaction–i.e., these are the PDUs that prolong the file delivery time. (This set, Π M , is a random set because exactly which N PDUs will be in the set is random.) Then, we consider the NAKs thataregeneratedintheT inc –intervalandrequestaPDUbelongingtosetΠ M . We denotebyrandomvariableS thenumberofsuchNAKs. Then,wehavePr[S = 0] = (1−P ef ) N because S = 0 if and only if all N PDUs are successfully delivered to the receiver without retransmission. Thus, we have Pr[S > 0] = 1−(1−P ef ) N . We now express Pr[Event b] as: Pr[Event b] = Pr[Event b | S = 0]Pr[S = 0]+Pr[Event b | S > 0]Pr[S > 0] . WeobviouslyhavePr[Event b | S = 0] = 0becauseS = 0impliesthatallN PDUs are successfully delivered to the receiver without retransmission. Thus, we have Pr[Event b] = Pr[Event b | S > 0]Pr[S > 0] . For each s> 0, we have Pr[Event b | S =s] = (1−P er ) s (4.19) (Given that S takes a positive integer s, event b happens if and only if those s NAKs reach the sender successfully.) We observe that 58 Pr[Event b | S > 0] = X s>0 Pr[S =s | S > 0](1−P er ) s = E h (1−P er ) S | S > 0 i ≥ (1−P er ) E(S | S>0) . (4.20) (The last inequality follows from Jansen’s inequality [18].) From the fact that S is less than or equal to the total number of NAKs generated in the T inc –interval, we have E(L)≥E(S) =E(S | S > 0)Pr[S > 0] , (4.21) where random variable L denotes the total number of NAKs generated in the T inc –interval as defined in Section 4.2.2. Relations in (4.21) provide a bound on E(S | S > 0), E(S | S > 0)≤ E(L) Pr[S > 0] , (4.22) andE(L) can be simply derived. Lemma 1 E(L) = (N −1)P ef (1−P ef )+P ef . (4.23) Proof: For the reception of PDU i to generate a NAK, PDU i must be delivered successfully at the first transmission, and also the first transmission of PDU i−1 mustbeunsuccessful. Term(N −1)P ef (1−P ef )accountsfortheexpectednumber ofNAKsgeneratedinresponsetosuccessfulreceptionoffiledataPDUsintheT inc – interval. For the reception of EOF to generate a NAK, the first transmission of 59 PDUN mustbeunsuccessful. TermP ef accountsfortheexpectednumberofNAKs generated in response to the reception of EOF. Thus, from (4.20)-(4.23) we have Pr[Event b | S > 0] ≥ (1−P er ) E(S | S>0) ≥ (1−P er ) E(L) Pr[S>0] = (1−P er ) (N−1)P ef( 1−P ef) +P ef 1− ( 1−P ef) N .(4.24) Thus, from (4.24), we obtain the following lower bound of Pr[Event b]: Pr[Event b] = Pr[S > 0]Pr[Event b | S > 0] ≥ Pr[S > 0](1−P er ) E(L) Pr[S>0] = h 1−(1−P ef ) N i (1−P er ) (N−1)P ef( 1−P ef) +P ef 1− ( 1−P ef) N . (4.25) For an upper bound, we note (1−P er ) s ≤ 1 1+sPer ≤ 1 1+Per for s > 0 from Bernoulli’s inequality [33]. Thus, from (4.19) Pr[Event b | S > 0]≤ 1 1+P er . Therefore, we have Pr[Event b] = Pr[S > 0]Pr[Event b | S > 0]≤ Pr[S > 0] 1+P er = 1−(1−P ef ) N 1+P er . (4.26) 60 From (4.17), (4.25), and (4.26), the bounds onE(M N ) are given as: E(M N )−1− 1−(1−P ef ) N 1+P er ≤E(H N ) ≤E(M N )−1− h 1−(1−P ef ) N i (1−P er ) (N−1)P ef( 1−P ef) +P ef 1− ( 1−P ef) N . (4.27) From (4.15) and Proposition 3, the upper bound and lower bound on E(T def ) are obtained, respectively, as E(T def )≤[E(M N )−1] 2T prop 1−P er − h 1−(1−P ef ) N i (1−P er ) (N−1)P ef( 1−P ef) +P ef 1− ( 1−P ef) N 2T prop 1−P er + N ·T PDU ·P ef (1−P ef )(1−P er ) −N ·P ef ·T PDU , (4.28) and E(T def )≥[E(M N )−1] 2T prop 1−P er − " 1−(1−P ef ) N 1+P er # 2T prop 1−P er + N ·T PDU ·P ef (1−P ef )(1−P er ) −N ·P ef ·T PDU . (4.29) 4.3.2 Bounds on the expected value of T inc AccordingtoourdefinitionofT inc intheImmediateNAKmode,T inc istheduration of the incremental procedure plus the time–out period of the NAK EOF timer set upon the first error–free EOF reception (see Fig. 2.2). In this section, we focus on 61 E(T inc ). A major idea to utilize in deriving E(T inc ) is that the Immediate NAK mode allows no more than one retransmission of a PDU during the T inc –interval. It turns out that the form of E(T inc ) depends upon whether k ≡ 2Tprop T PDU is larger than N −2, where N is the number of PDUs in the file, including the meta data. Case k+2>N applies to the configuration in which the propagation delay is long relative to the time taken to transmit the file. The other case, k+2 ≤ N, applies to the configuration with short propagation delay relative to the transmission time of the entire file. The expected value of T inc is given as E(T inc ) = N ·T PDU +E(X)+E(EOF delivery time)+E(R) if N ≥k+2, N ·T PDU +E(EOF delivery time)+E(R) if N <k+2. (4.30) where the random variable X and R are defined as follows: 1. Random variable R denotes the time–out value of the NAK EOF timer, as defined in Section 4.2.2. 2. Random variable X denotes the time spent by the sender in retransmitting PDUs before the first EOF transmission. Fig. 4.3 (a) and (b) illustrate (4.30). From the assumption made in Section 4.1 and (3.1), the expected EOF delivery time in (4.30) is given as E(EOF delivery time) = 1+P ef(EOF) T prop 1−P ef(EOF) . (4.31) The exact expression of E(X) and E(R) in (4.30) seems difficult to derive, so we will obtain their bounds. In doing so, we consider bounds on their conditional 62 ! " # $ % & ’ ( ) ( * + , - . / 0 1 . 2 3 4 0 5 . ( 6 Sender Receiver R=R L inc N*T PDU + X NAK ACK (EOF) 7 EOF 8 9 : ; < = X EOF timer T prop 6 . 4 2 > ? @ 5 0 @ @ 0 A ? , 0 2 @ 4 4 2 > ? @ 5 0 @ @ 0 A ? W L inc (a) N ≥k+2. R L inc FD(last) Sender Receiver EOF R NAK ACK (EOF) B C D E F G H B I J K L M N O P Q R S T Q U V W S X Q L Y A M T prop Y Q W U Z [ \ X S \ \ S ] [ O S U \ W W U Z [ \ X S \ \ S ] [ W L inc (b) N <k+2. Figure 4.3: Incremental procedure of Immediate NAK mode expectedvaluesconditionedonthreemutuallyexclusiveandcollectivelyexhaustive events and take their properly weighted sum. (For the representation of R, the time–out value of the NAK EOF timer, let us recall the definition of W inc n and A in Section 4.2.2.) 63 Event 1: The first EOF reception spawns issuance of a NAK. For example, if the first transmission of PDU N fails to be delivered to the receiver, the receiver notices the failed delivery of PDU N upon receiving EOF and issues a NAK: R =R inc L = 2T prop +W inc L . Note that R inc n is the time–out value of then th NAK timer-inc set during the T inc –interval and L is the number of NAKs issued in the T inc –interval. Thus, E(R| event 1) = 2T prop +E W inc L | event 1 . (4.32) Event 2: The first EOF reception does not spawn issuance of a NAK, and the sender’s first transmission of EOF results in successful EOF delivery to the receiver: R = R inc L −A + = 2T prop +W inc L −A + . Thus, E(R | event 2) =E 2T prop +W inc L −A + | event 2 . (4.33) Note that A is the time from the issuance of the last (L th ) NAK that is generated by the receiver in the T inc –interval until the reception of EOF and A> 0 in Event 2. Event 3: The first EOF reception does not spawn issuance of a NAK and the sender’s first transmission of EOF fails to deliver EOF to the receiver: R = R inc L −A + = 2T prop +W inc L −A + . 64 Thus, E(R | event 3) =E 2T prop +W inc L −A + | event 3 . (4.34) Note that A > 2T prop in Event 3 because the sender’s first transmission of EOF fails to deliver EOF to the receiver. The probability of each event is as follows: 1. P(event 1) = P ef . Event 1 happens if and only if the first transmission of PDU N is unsuccessful. 2. P(event 2) = (1−P ef ) 1−P ef(EOF) . Note that the first EOF reception does not spawn a NAK if and only if the first transmission of PDU N is successful, the probability of which is (1−P ef ). 3. P(event 3) = (1−P ef )P ef(EOF) . Note that E(R+X) = P 3 i=1 P( event i)E(R+X | event i) where X denotes the time spent by the sender in retransmitting PDUs before the first EOFtransmission and R denotes the time–out value of the NAK EOF timer. 4.3.2.1 Case (1): N ≥ k + 2 (Short propagation delay relative to file transmission time) Upper bound of E(X +R) Event 1 From(4.32),wehaveE(X +R | event 1) =E(X | event 1)+E(W inc L | event 1)+ 2T prop where X denotes the time spent by the sender in retransmitting PDUs be- fore the first EOF transmission and R denotes the time–out value of the NAK EOF 65 timer. For the definition of W inc L , refer to (4.6). To obtain an upper bound on E(X | event 1)+E(W inc L | event 1), we observe that X +W inc L cannot exceed the total transmission time of PDUs whose transmission is unsuccessful on the first attempt. Therefore, E(X | event 1)+E W inc L | event 1 ≤E(Q N ·T PDU | event 1) , where Q N is the number of PDUs whose transmission is unsuccessful on the first attempt. Event 1 happens if and only if the first transmission of PDU N (the last file data PDU) fails to be delivered to the receiver. Therefore, we have E(Q N | event 1) = (N −1)P ef + 1, where the last term 1 accounts for the fact that the last file data PDU is unsuccessful in Event 1. Thus, we have E(X | event 1)+E W inc L | event 1 ≤ E(Q N | event 1)T PDU = [(N −1)P ef +1]T PDU . (4.35) As a result, E(X +R | event 1) = E(X | event 1)+E W inc L | event 1 +2T prop ≤ [(N −1)P ef +1]T PDU +2T prop . (4.36) Event 2 From (4.33), we have E(X +R | event 2) =E(X | event 2)+E 2T prop +W inc L −A + | event 2 . (4.37) 66 where A is the time from the issuance of the last (L th ) NAK that is generated by the receiver in the T inc –interval until the reception of EOF. From the fact that A> 0 in Event 2, E(X | event 2)+E 2T prop +W inc L −A + | event 2 <E(X | event 2)+E W inc L |event 2 +2T prop . (4.38) Also,notethatE(X | event 2)+E(W inc L | event 2)canbeboundedinawaysimilar to that in Section 4.3.2.1–namely, E(X | event 2)+E W inc L | event 2 ≤E(Q N | event 2)T PDU = (N −1)P ef ·T PDU . (4.39) (Note that event 2 implies that PDU N’s first transmission is successful.) Thus, we have E(X +R | event 2)< (N −1)P ef ·T PDU +2T prop . (4.40) Event 3 From (4.34), we have E(X +R | event 3) =E(X | event 3)+E 2T prop +W inc L −A + | event 3 . (4.41) From the fact that A> 2T prop in Event 3, E(X | event 3)+E 2T prop +W inc L −A + | event 3 <E(X | event 3)+E W inc L | event 3 . (4.42) 67 Note thatE(X | event 3)+E(W inc L | event 3) can be bounded in the same way as was done in Section 4.3.2.1. As a result, we have E(X +R | event 3)< (N −1)P ef ·T PDU . (4.43) Resulting upper bound of E(X +R) From the weighted sum of (4.36), (4.40), and (4.43) with the probability for each event specified in Section 4.3.2, the upper bound on the expected value of X +R is obtained as E(X +R)<N ·P ef ·T PDU + 1−(1−P ef )P ef(EOF) 2T prop . (4.44) Lower bound of E(X +R) Event 1 ToobtainalowerboundonE(X), theexpectedvalueofX thatdenotesthetime spent by the sender in retransmitting PDUs before the first EOF transmission, we observe the following. Let us denote by random variable L N−k the total number of NAKs spawned by receiving any of PDUs 1,2,...,(N − k) during the T inc – interval. Then, the expected number of those NAKs successfully delivered to the senderisE(L N−k )(1−P er ). EachoftheseNAKsrequestsretransmissionofatleast one PDU, so we have a lower bound E(X | event 1) ≥ E(L N−k )(1−P er )T PDU . RegardingE(L N−k ), we have E(L N−k ) = N−k X i=2 Pr(PDU i−1 fails)Pr(PDU i is successfully delivered) = (N −k−1)P ef (1−P ef ) . 68 Thus, we have E(X | event 1) ≥ E(L N−k )(1−P er )T PDU = (N −k−1)P ef (1−P ef )(1−P er )T PDU . (4.45) With regard to the random variable R, the time–out value of the NAK EOF timer, in Event 1 we observe that R = 2T prop +W inc L ≥ 2T prop +T PDU . (4.46) because at least the last file data PDU is unsuccessful in Event 1. As a result, E(X +R | event 1) =E(X | event 1)+E W inc L +2T prop ≥ [(N −k−1)P ef (1−P ef )(1−P er )+1]T PDU +2T prop . (4.47) Event 2 A lower bound onE(X) is obtained in the same way as in (4.45), so we have E(X +R | event 2)≥E(X | event 2)≥ (N −k−1)P ef (1−P ef )(1−P er )T PDU . (4.48) Event 3 A lower bound onE(X) is obtained in the same way as in (4.45), so we have E(X +R | event 2)≥E(X | event 2)≥ (N −k−1)P ef (1−P ef )(1−P er )T PDU . (4.49) 69 Resulting lower bound of E(X +R) From the weighted sum of (4.47), (4.48), and (4.49) with the probability for each event specified in Section 4.3.2, the lower bound on the expected value of X+R is obtained as E(X +R)≥ 2T prop ·P ef +[(N −k−1)P ef (1−P ef )(1−P er )+P ef ]T PDU (4.50) 4.3.2.2 Case (2): N < k + 2 (Long propagation delay relative to file transmission time) Upper bound of E(R) Note that X, the time spent by the sender in retrans- mitting PDUs before the first EOF transmission, is zero (X = 0) for N < k +2. Therefore, we obtain a bound on the expected value of R, the time–out value of the NAK EOF timer, in the following sections. Event 1 Note that in Event 1, W inc L is at most Q N ·T PDU , where Q N is the number of PDUs whose transmission is unsuccessful at on the first attempt. Event 1 happens if and only if the first transmission of PDU N (the last file data PDU) fails to be delivered to the receiver. Therefore, we have E(Q N |event 1) = (N −1)P ef + 1. Thus, E W inc L | event 1 ≤E(Q N | event 1)·T PDU = [(N −1)P ef +1]·T PDU . (4.51) As a result, E(R | event 1) = 2T prop +E W inc L | event 1 ≤ 2T prop +[(N −1)P ef +1]·T PDU . (4.52) 70 Event 2 FromthefactthatW inc L isatmostQ N ·T PDU andE(Q N | event 2) = (N −1)P ef , we have E W inc L | event 2 ≤E(Q N | event 2)·T PDU = [(N −1)P ef ]T PDU . (4.53) From (4.53) and the fact that A, the time from the issuance of the last (L th ) NAK that is generated by the receiver in the T inc –interval until the reception of EOF, is greater than zero (A> 0) in Event 2, E(R | event 2) = E 2T prop +W inc L −A + | event 2 < 2T prop +E W inc L | event 2 ≤ 2T prop +[(N −1)P ef ]T PDU . (4.54) Event 3 Note that if the second EOF trial is successful, the expectation of W inc L can be bounded the same as in (4.53), E(W inc L | event 3, success of second EOF Tx) ≤ [(N −1)P ef ]T PDU . Otherwise, E(W inc L | event 3, failure of second EOF Tx) = 0. ThisisduetothefactthatifanyNAKgeneratedintheT inc –intervalissuccessfully delivered to the sender, it is before the sender’s second EOF transmission. There- fore, any retransmission in response successful NAK receptions during the T inc – interval is completed before the sender’s third EOF transmission since N <k+2. As a result, we obtain E W inc L | event 3 ≤ (N −1)P ef 1−P ef(EOF) T PDU , (4.55) where1−P ef(EOF) istheprobabilityofthesuccessofthesecondEOFtransmission. 71 From (4.55) and the fact that A> 2T prop in Event 3, E(R | event 3) = E 2T prop +W inc L −A + | event 3 < E W inc L | event 3 ≤ (N −1)P ef 1−P ef(EOF) T PDU . (4.56) Resulting upper bound of E(R) From the weighted sum of (4.52), (4.54), and (4.56) with the probability for each event specified in Section 4.3.2, the upper bound on the expected value of R is obtained as E(R)<2T prop 1−(1−P ef )P ef(EOF) + (N −1)P ef 1−(1−P ef )P 2 ef(EOF) +P ef T PDU . (4.57) Lower bound of E(R) Event 1 (4.46) still holds. Thus, E(R | event 1) = 2T prop +E W inc L | event 1 ≥ 2T prop +T PDU . (4.58) where R denotes the time–out value of the NAK EOF timer. Event 2 If L, the number of NAKs generated during the T inc –interval, is 0, then R = 0. Now, let us consider case L> 0. The L th NAK requests retransmission of at least onePDUifL> 0,sowehaveW inc L ≥T PDU . Also,duetoN <k+2,wehaveA,the 72 Sender Receiver EOF R NAK ACK (EOF) A M N=7 ^ _ ‘ a b c d e f d d fg c h f a d ‘ ‘ a b c d e f dd fg c W L inc R L inc e+f+g=5 e=2 f=1 g=2 Figure 4.4: Example of incremental procedure timefromtheissuanceofthelast(L th )NAKthatisgeneratedbythereceiverinthe T inc –interval until the reception of EOF, is greater than two times the propagation delay (A< 2T prop ) in Event 2. Thus, E(R | event 2, L> 0) = E 2T prop +W inc L −A + | event 2, L> 0 = 2T prop −E(A | event 2, L> 0)+E W inc L | event 2, L> 0 ≥ 2T prop −E(A | event 2, L> 0)+T PDU . (4.59) Now, we derive an upper bound of E(A | event 2, L> 0). First, we observe that the receiver receives any retransmitted PDUs after the reception of EOF be- cause any NAK generated in the T inc –interval arrives at the sender (if successfully delivered to the sender) after the sender’s transmission of EOF. (This is due to the fact that N < k +2 and that EOF is successfully delivered to the receiver upon first trial in Event 2. See Fig. 4.4 for an illustration.) Thus,itcanbededucedthatthetimefromthebeginningofthereceptionofthe meta data PDU until the reception of EOF is exactly N ·T PDU . We also observe that the first transmission of each PDU results in one of the following three events: 73 1) Successful reception of the PDU and this does not spawn a NAK. 2) Successful reception of the PDU and this spawns a NAK. 3) Failed reception of the PDU. Now, suppose that theL th NAK (the last NAK in the T inc –interval) is spawned by the reception of J th PDU. (We are still assuming L > 0.) Let us denote by e, f, and g the number of received PDUs corresponding to events (1), (2), and (3), respectively, out of set PDU1,PDU2,...,PDUJ. Then, the time from the beginning of the reception of the meta data PDU until and including the reception of J th PDU is obtained as J ·T PDU = (e+f +g)T PDU ≥ (f +g)T PDU . Now, we note thatf =L andg =Q N whereL is the number of NAKs generated during the T inc –interval and Q N is the number of PDUs whose transmission is unsuccessful at on the first attempt. (Regarding g = Q N , from the definitions of L and Event 2 there is no NAK generated from the reception of the J th PDU until the reception of EOF, so the first transmissions of (J + 1) th ,(J + 2) th ,...,N th PDUs are all successful.) For example, in Fig. 4.4, J = e+f +g = 5, e = 2, f = L = 1, and g =Q N = 2. From the definition of A, we have A = (N −J)T PDU ≤ [N −(L+Q N )]T PDU . As a result, we have E(A | event 2, L> 0)≤{N −E(L+Q N | event 2, L> 0)}T PDU . (4.60) Inserting (4.60) into (4.59), we have E(R | event 2, L> 0)≥ 2T prop −(N −1)T PDU +E(L+Q N | event 2, L> 0)T PDU . (4.61) 74 Note that L = 0 implies that R and Q N are all zero, which means that we have E(R | event 2) =E(R | event 2, L> 0)Pr(L> 0 | event 2) +E(R | event 2, L = 0)Pr(L = 0 | event 2) =E(R | event 2, L> 0)Pr(L> 0 | event 2) , (4.62) E(L | event 2) =E(L | event 2, L> 0)Pr(L> 0 | event 2) +E(L | event 2, L = 0)Pr(L = 0 | event 2) =E(L | event 2, L> 0)Pr(L> 0 | event 2) , (4.63) E(Q N | event 2) =E(Q N | event 2, L> 0)Pr(L> 0 | event 2) +E(Q N | event 2, L = 0)Pr(L = 0 | event 2) =E(Q N | event 2, L> 0)Pr(L> 0 | event 2) . (4.64) From (4.61), (4.62), (4.63), and (4.64), we have E(R | event 2) ≥ [2T prop −(N −1)T PDU ]Pr(L> 0 | event 2) +[E(L | event 2)+E(Q N | event 2)]T PDU . (4.65) Now, with regard to Pr(L > 0 | event 2), E(L | event 2), and E(Q N | event 2), we have the following proposition: Proposition 4 a. Pr(L> 0 | event 2) = 1−(1−P ef ) N−1 . Proof: Event 2 implies that the first transmission of PDU N is successful. 75 Therefore, in event 2, L = 0 if and only if PDU 1,PDU 2,...,PDU N −1 are in addition successful on their first transmission. Thus, Pr(L = 0 | event 2) = (1−P ef ) N−1 . b. E(Q N | event 2) = (N −1)P ef . Proof: In event 2, the first transmission of PDU N is successful, so Q N is thenumberofPDUsinPDU 1,PDU 2,...,PDU N −1thatfailontheirfirst transmission. Therefore, E(Q N | event 2) = (N −1)P ef . c. E(L | event 2) = (N −2)P ef (1−P ef )+P ef . Proof: PDU i for spawns a NAK if and only if transmission of PDU i−1 is unsuccessful and the first transmission of PDU i is successful. Therefore, the expected number of NAKs spawned by PDU i for 2 ≤ i ≤ N − 1 is P ef (1−P ef ). In event 2, PDU N’s first transmission succeeds, so PDU N spawns a NAK if and only if PDU N − 1 fails to be delivered on its first transmission. Therefore, the expected number of NAKs spawned by PDU N is P ef . Thus, E(L | event 2) = (N −2)P ef (1−P ef )+P ef . 76 From proposition 4 and (4.65), we obtain E(R | event 2) ≥ [2T prop −(N −1)T PDU ] h 1−(1−P ef ) N−1 i +[N ·P ef (2−P ef )−2P ef (1−P ef )]T PDU . (4.66) Event 3 In this event, we use an obvious lower bound: E(R | event 3) =E 2T prop +W inc L −A + | event 3 ≥ 0 . (4.67) Resulting lower bound of E(R) From the weighted sum of (4.58), (4.66), and (4.67) with the probability for each event specified in Section 4.3.2, the lower bound on the expected value of R is obtained as E(R)≥ (2T prop +T PDU )P ef +[2T prop −(N −1)T PDU ] h 1−(1−P ef ) N−1 i (1−P ef ) 1−P ef(EOF) +[N ·P ef (2−P ef )−2P ef (1−P ef )]T PDU (1−P ef ) 1−P ef(EOF) . (4.68) The resulting bounds for both cases are summarized below. Case (1): N ≥k+2 E(R+X)<N ·P ef ·T PDU + 1−(1−P ef )P ef(EOF) 2T prop , (4.69) E(R+X)≥ 2T prop ·P ef +[(N −k−1)P ef (1−P ef )(1−P er )+P ef ]T PDU . (4.70) 77 Case (2): N <k+2 E(R)< 2T prop 1−(1−P ef )P ef(EOF) + (N −1)P ef 1−(1−P ef )P 2 ef(EOF) +P ef T PDU , (4.71) E(R)≥ (2T prop +T PDU )P ef +[2T prop −(N −1)T PDU ] h 1−(1−P ef ) N−1 i (1−P ef ) 1−P ef(EOF) +[N ·P ef (2−P ef )−2P ef (1−P ef )]T PDU (1−P ef ) 1−P ef(EOF) . (4.72) 4.3.3 Bounds on the expected file delivery time of the Immediate NAK mode Case (1): N ≥k+2 By inserting (4.69) and (4.31) into (4.30) and adding (4.28), the upper bound on the expected file delivery time of the Immediate NAK mode is obtained as Expected file delivery time ≡E(T inc +T def ) <N(1+P ef )T PDU + 1−(1−P ef )P ef(EOF) 2T prop + [E(M N )−1]− h 1−(1−P ef ) N i (1−P er ) (N−1)P ef( 1−P ef) +P ef 1− ( 1−P ef) N 2T prop 1−P er + N ·T PDU ·P ef (1−P ef )(1−P er ) −N ·P ef ·T PDU + 1+P ef(EOF) T prop 1−P ef(EOF) . (4.73) By inserting (4.70) and (4.31) into (4.30) and adding (4.29), the lower bound on the expected file delivery time of the Immediate NAK mode is obtained as 78 Expected file delivery time ≡E(T inc +T def ) ≥N ·T PDU +2T prop ·P ef +[(N −k−1)P ef (1−P ef )(1−P er )+P ef ]T PDU + ( [E(M N )−1]− " 1−(1−P ef ) N 1+P er #) 2T prop 1−P er + N ·T PDU ·P ef (1−P ef )(1−P er ) −N ·P ef ·T PDU + 1+P ef(EOF) T prop 1−P ef(EOF) . (4.74) Case (2): N <k+2 By inserting (4.71) and (4.31) into (4.30) and adding (4.28), the upper bound of the expected file delivery time of the Immediate NAK mode is obtained as Expected file delivery time ≡E(T inc +T def ) <N ·T PDU +2T prop 1−(1−P ef )P ef(EOF) + (N −1)P ef 1−(1−P ef )P 2 ef(EOF) +P ef T PDU + [E(M N )−1]− h 1−(1−P ef ) N i (1−P er ) (N−1)P ef( 1−P ef) +P ef 1− ( 1−P ef) N 2T prop 1−P er + N ·T PDU ·P ef (1−P ef )(1−P er ) −N ·P ef ·T PDU + 1+P ef(EOF) T prop 1−P ef(EOF) . (4.75) By inserting (4.72) and (4.31) into (4.30) and adding (4.29), the lower bound of the expected file delivery time of the Immediate NAK mode is obtained as 79 Expected file delivery time ≡E(T inc +T def ) ≥N ·T PDU +(2T prop +T PDU )P ef +[2T prop −(N −1)T PDU ] h 1−(1−P ef ) N−1 i (1−P ef ) 1−P ef(EOF) +[N ·P ef (2−P ef )−2P ef (1−P ef )]T PDU (1−P ef ) 1−P ef(EOF) + ( [E(M N )−1]− " 1−(1−P ef ) N 1+P er #) 2T prop 1−P er + N ·T PDU ·P ef (1−P ef )(1−P er ) −N ·P ef ·T PDU + 1+P ef(EOF) T prop 1−P ef(EOF) . (4.76) 4.4 Numerical Presentation 4.4.1 Numerical results for the Immediate NAK mode The mathematical expression derived in previous sections for the expected file de- livery time in the Immediate NAK mode is numerically presented in Fig. 4.5– 4.8. Notethattheboundsobtainedinthispaperinrelationtotheexpectedfiledelivery time become tighter as the transmission rate or propagation delay increases. This is predicted from the formulas (4.69)-(4.72). Note that the considered region of BER without FEC is between 10 −5 and 10 −7 since the achievable BER without FEC is between 10 −5 and 10 −7 in typical space communication. Also, note that the astronomical unit (a.u.) is used in case of long propagation delay (1 a.u. = 480 s). Fig. 4.5– 4.8 also show the average file delivery time obtained through random simulation. From the numerical results, we observe that the average file delivery timeobtainedthroughrandomsimulationnumericallyliesbetweentheupperbound 80 10 -7 10 -6 10 -5 8 8.5 9 9.5 Expected File Delivery Time (in sec) BER PDU Length = 1.5 Kbytes 10 -7 10 -6 10 -5 8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10 Expected File Delivery Time (in sec) BER PDU Length = 2 Kbytes Imm. NAK (up) Imm. NAK (low) Imm. NAK (simulation) Figure 4.5: Immediate NAK: Analytic vs. simulation results. Expected file delivery time of Immediate NAK mode with BER variation. File size = 1 Mbyte, transmission rate = 1 Mbps in both directions, and propagation delay = 40 ms. and the lower bound obtained from the mathematical derivation for most points. On a small number of occasions, we obtained results of random simulation outside the bounds. We must note that the results of random simulation are not fully accurate. The random simulation repeats and averages the computation results for different trials in which parameters are randomly generated. Therefore, the confidence level increases with the number of trials run. There can always be an anomaly for any finite number of trials. 81 10 -7 10 -6 10 -5 9 10 11 12 13 14 15 16 17 Expected File Delivery Time (in a.u.) BER PDU Length = 1.5 Kbytes 10 -7 10 -6 10 -5 9 10 11 12 13 14 15 16 17 18 Expected File Delivery Time (in a.u.) BER PDU Length = 2 Kbytes Imm. NAK (up) Imm. NAK (low) Imm. NAK (simulation) Figure 4.6: Immediate NAK: Analytic vs. simulation results. Expected file delivery time of Immediate NAK mode with BER variation. File size = 1 Mbyte, transmission rate = 2 Kbps in both directions, and propagation delay = 480 s. 4.4.2 Performance comparison of the Immediate and Deferred NAK mode In Fig. 4.9–4.12, the performance of the Immediate NAK mode is compared with that of the Deferred NAK mode. In Section 4.3.2, the analysis of the Immediate NAK mode is conducted differently for two cases. In case (1), the total number of PDUs, N, is greater than or equal to the number of PDUs that can be transmitted during two times the propagation delay, which we denote by num in 2prop, plus 2. In case (2), N < num in 2prop+2. In Fig. 4.9–4.12 we compare the performance of the Deferred NAK mode and the Immediate NAK mode for both cases of N ≥ num in 2prop+2 and N < num in 2prop+2. 82 10 -7 10 -6 10 -5 2 3 4 5 6 7 8 Expected File Delivery Time (in a.u.) BER PDU Length = 1.5 Kbytes 10 -7 10 -6 10 -5 2 3 4 5 6 7 8 9 Expected File Delivery Time (in a.u.) BER PDU Length = 2 Kbytes Imm. NAK (up) Imm. NAK (low) Imm. NAK (simulation) Figure 4.7: Immediate NAK: Analytic vs. simulation results. Expected file delivery time of Immediate NAK mode with BER variation. File size = 1 Mbyte, transmission rate = 20 Kbps in both directions, and propagation delay = 480 s. When the sender and receiver are very close to each other, such as between a lander and an orbiter or between a rover and a lander in space networks deployed on other planets, we face smaller propagation delay than the transmission time of a file (N ≥ num in 2prop+2). To compare the performance of the Deferred and Immediate NAK modes in such an environment, we used the scenario of transfer- ring a 1–Mbyte file through a full duplex link with link speed at 1 Mbps in both directions. We set the propagation delay at 40 ms. Numerical results for expected file delivery time of Deferred and Immediate NAK mode are shown in Figure 12. We also considered the case wherein N ≥ num in 2prop + 2 results from very low transmission rate. For example, the transmission rate in deep space networks might be a few Kbps. Suppose that the transmission rate is 2 Kbps and file size is 1 Mbyte, and that propagation delay is 1 a.u. (1 a.u. = 480 s). Consider the 83 10 -7 10 -6 10 -5 25 30 35 40 45 50 55 60 65 70 Expected File Delivery Time (in a.u.) BER PDU Length = 1.5 Kbytes 10 -7 10 -6 10 -5 20 30 40 50 60 70 80 Expected File Delivery Time (in a.u.) BER PDU Length = 2 Kbytes Imm. NAK (up) Imm. NAK (low) Imm. NAK (simulation) Figure 4.8: Immediate NAK: Analytic vs. simulation results. Expected file delivery time of Immediate NAK mode with BER variation. File size =1Mbyte, Transmissionrate=20Kbpsinbothdirections, andpropagationdelay = 4,800 s. example cases, N = 667 for PDU size 1.5 Kbytes and N = 500 for PDU size 2 Kbytes. In these cases, N is larger than num in 2prop+2. The numerical results are shown in Fig. 4.10 for such a case. To numerically compare the performance of the Deferred and Immediate NAK modes in N < num in 2prop+2 environment, we take an example of a full duplex link in which the link speed is 20 Kbps in both directions. We set the file size to be 1 Mbyte. We take two cases: (1) the propagation delay = 1 a.u., and (2) the propagation delay = 10 a.u.. For 1 a.u. of propagation delay, numerical results for expectedfiledeliverytimeoftheDeferredandImmediateNAKmodesareshownin Fig. 4.11. For the other scenario (10 a.u. propagation delay), numerical results for expected file delivery times of the Deferred and Immediate NAK modes are shown in Fig. 4.12. 84 10 -7 10 -6 10 -5 8 8.5 9 9.5 Expected File Delivery Time (in sec) BER PDU Length = 1.5 Kbytes 10 -7 10 -6 10 -5 8 8.2 8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10 Expected File Delivery Time (in sec) BER PDU Length = 2 Kbytes Def. NAK (simulation) Imm. NAK (simulation) Figure 4.9: Simulation results. Expected file delivery time of Deferred and Immediate NAK modes with BER variation. File size = 1 Mbyte, transmission rate = 1 Mbps in both directions, and propagation delay = 40 ms. From the numerical results (Fig. 4.9–4.12), we notice that no significant perfor- mance difference is observed comparing Immediate NAK mode to Deferred NAK mode. We observed some performance improvement by Immediate NAK mode in the case of the num in 2prop and low BER regions, but it is less than 10% im- provement. We can deduce that no significant performance difference is expected in the range of parameters considered. (For other range of parameters, again data can be generated either through random simulation or the performance bounds analytically derived in this paper to compare Deferred NAK and Immediate NAK modes. With performance bound derived in this paper, we can compute the upper boundontheperformancegainoftheImmediateNAKmode. Useoftheanalytical performanceboundhastheadvantagesoflowcomputationalloadandcertainty, al- though this approach many not indicate the exact gain for a parameter that makes 85 10 -7 10 -6 10 -5 10 11 12 13 14 15 16 Expected File Delivery Time (in a.u.) BER PDU Length = 1.5 Kbytes 10 -7 10 -6 10 -5 10 11 12 13 14 15 16 17 18 Expected File Delivery Time (in a.u.) BER PDU Length = 2 Kbytes Def. NAK (simulation) Imm. NAK (simulation) Figure 4.10: Simulation results. Expected file delivery time of the Deferred and Immediate NAK modes with BER variation. File size = 1 Mbyte, transmission rate = 2 Kbps in both directions, and propagation delay = 480 s. the numerical bound loose.) As a result, it might be favorable to operate CFDP in Deferred NAK mode, since many fewer NAKs are required in this mode. The power consumed to generate NAKs frequently may have to be a significant design consideration in the deep space environment where power is extremely limited. 4.5 Conclusion Inthischapter,wederivedperformanceboundsontheexpectedfiledeliverytimeof the CFDP Immediate NAK mode. We observe that the throughput efficiency can be compromised in the form of unnecessary duplicate retransmissions of an identi- cal PDU. Due to very limited power budget in the deep space networking, in our performance analysis we consider the operational constraint that the throughput 86 10 -7 10 -6 10 -5 3.5 4 4.5 5 5.5 6 6.5 7 7.5 Expected File Delivery Time (in a.u.) BER PDU Length = 1.5 Kbytes 10 -7 10 -6 10 -5 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 Expected File Delivery Time (in a.u.) BER PDU Length = 2 Kbytes Def. NAK (simulation) Imm. NAK (simulation) Figure 4.11: Simulation results. Expected file delivery time of the Deferred and Immediate NAK modes with BER variation. File size = 1 Mbyte, transmission rate = 20 Kbps in both directions, and propagation delay = 480 s. efficiency should not be compromised. To maximize the throughput efficiency (in other words, to avoid unnecessary duplicate retransmissions) and to minimize the expectedfiledeliverytimeatthesametime, weproposedatimercontrolschemeto be used in the Immediate NAK of CFDP. Based on our proposal for the timer con- trol scheme, we derived bounds on the expected number of retransmission spurts, whichisthemostcrucialpartindeterminingtheexpectedfiledeliverytime. Then, we further derived bounds on the expected file delivery time. We provided numer- ical evaluation of our performance bounds and results of random simulation for comparison. 87 10 -7 10 -6 10 -5 30 35 40 45 50 55 60 65 70 Expected File Delivery Time (in a.u.) BER PDU Length = 1.5 Kbytes 10 -7 10 -6 10 -5 30 35 40 45 50 55 60 65 70 75 Expected File Delivery Time (in a.u.) BER PDU Length = 2 Kbytes Def. NAK (simulation) Imm. NAK (simulation) Figure 4.12: Simulation results. Expected file delivery time of the Deferred and Immediate NAK modes with BER variation. File size = 1 Mbyte, transmission rate = 20 Kbps in both directions, and propagation delay = 4,800 s. 88 Chapter 5 Power-Aware Topology Control for Wireless Ad-Hoc Networks Our approach to the problem of prolonging the network lifetime is through power- awaretopologycontrol. Thereasonsforourapproacharemainlythreefolds. First, through the power-aware topology control, we can still adapt to the very simple routing protocol while prolonging the network lifetime. Second, it is expected that frequent changes in traffic flows (source-destination pairs) do not highly affect the energyconsumptionofeachnodeduetothelimitedconnectivityandthesparseness ofthenetworkresultingfromthetopologycontrol. Namely,unlikethepower-aware routing, we can only consider the residual energy level, not the changes in traffic flow. Third, the network may be still connected among those alive nodes after the first death of nodes. We argue that the network should keep working until the network is partitioned among the alive nodes. We are thus interested in how long the network can maintain its global connectivity excluding the dead nodes. Apower-awaretopologycontrolalgorithmthatonlyrequirestheresidualenergy levelsandlocationinformationofthereachableneighboringnodesisthusproposed. When a node is making a decision on whether a wireless link between itself and a reachable neighboring node should be preserved in the topology being constructed, 89 the decision is made based on not only the distance from its neighboring nodes but also the residual energy level of itself and its neighboring nodes. Also, the topology is restructured from time to time based on the residual energy level of each node. 5.1 Proposed Algorithm Note that we do not build a power-aware topology control algorithm from the scratch. Instead,westartfromaclassofpower-efficienttopologycontrolalgorithms that satisfy certain conditions. Then, we apply our power-aware scheme to the power-efficienttopologycontrolalgorithmsandshowtheperformanceimprovement through the simulation. Our power-aware features generally can be applied to a class of power-efficient algorithms that satisfy the following requirements. • It works in localized way. • Link cost is a function of Euclidean distance between two nodes, and the algorithm builds topology based on the link cost. • The resulting topology only consists of bi-directional links. • It guarantees global connectivity (assuming the given network is connected) such that if two nodes are within the maximum transmission range, there exists a path. Notethatthesecondrequirementrequiresthateachnodehastheabilitytomeasure itsexactlocation. Also,itisassumedthateachnodeadjustsitstransmissionpower just enough for the specific links. Now, we describe our power-aware algorithm in details and show how it works with the class of power-efficient topology control 90 algorithms that satisfy the above conditions. Our power-aware algorithm consists of two parts: topology control through weighted link cost and power-aware node classification. 5.1.1 Weighted link cost In typical power-efficienttopology controlalgorithms, therequiredpowerfor trans- mission between two nodes u and v is used for link cost. The link cost, l(u,v), is givenasα 1 ·d(u,v) β +α 2 ,whereα 1 andα 2 areconstants,d(u,v)isEuclideandistance betweennodeuandv,andβ isthepathlossexponent. Toaddpower-awarefeature, we propose the weighted link cost such that link cost is given as α 1 ·d(u,v) β +α 2 min(e(u),e(v)) where e(·) represents the residual energy level of a node. Note that link cost is weighted by the minimum of the residual energy level of two nodes. The reason for taking minimum value as the weighting function is as follows: Although the weighted link cost already have been used in power-aware routing schemes, however, link cost is weighted only by the residual energy level of transmitting node in power-aware routing. If the power-awareness is handled through the routing without topology control,itisfinetoweightthelinkcostonlybytheresidualenergyleveloftransmit- ting node in the context of routing. Since the routing directly deals with the traffic flow and there is no limitation in the connectivity within maximum transmission rangeofeachnode, bi-directionallinkconstraint, whichisvitalintopologycontrol, will not be a problem in routing if every node has the same maximum transmission range. However, topology control better meets bi-directional link constraint since it limits the connectivity of each node. Thus, if each node weights link cost only by its own residual energy level and runs topology control algorithm in localized way, it can fail to guarantee the global connectivity due to bi-directional link constraint. 91 It is thus crucial in topology control that the end nodes of a link use the same link cost for the link when the topology is being constructed or maintained. 5.1.2 Topology construction through power-aware node classification Weobservethatsomenodesareover-usedforrelayingpacketssuchthatthesenodes deplete their own energy much more quickly than others despite the fact that the topology is constructed by a power-efficient topology control algorithm. Thus, our main idea for the power-aware topology control is that the energy of the over-used nodes can be saved if those nodes are made free from routing job, and it can be achieved through topology control if we strictly limit the number of links of those nodes to be one. Our power-aware topology control algorithm tries to construct a topology using the nodes with the relatively higher residual energy level and at the same time limits the degree of the nodes with relatively lower residual energy level to be one. As a result, one main factor that affects a power-aware topology is how to determine the relative residual energy level and how to divide the nodes into two categories based on the relative residual energy levels. There can be many possible ways for that purpose, but our approach to the de- termination of the relativeness of the residual energy levels is a local and statistical way: To determine the relative residual energy level, each node locally broadcasts its residual energy level and location information through a beacon message. It is assumed that each node can accurately estimate its location through GPS or other methods. After gathering the information, it calculates the average and stan- dard deviation of the residual energy level of its own and the neighbors. Based 92 on the average, standard deviation, and its own residual energy level, each node is categorized into one of the following three sets. • Thecorenodeset. Ifitsresidualenergylevelisabovetheaveragevalueminus standard deviation, the node becomes a core node. • The non-core node set. If its residual energy level is below the average value minusstandarddeviation, thenodedeclaresitselfasanon-corenodethrough the second beacon message. After the second beacon message exchange, the non-core nodes are further categorized into one of the following two subsets. – The active node set. If its residual energy level is below the average value minus standard deviation and at least one core node is within its transmission range, the node becomes an active node. – The passive node set. If its residual energy level is below the average value minus standard deviation and no core node is within its transmis- sion range, the node declares itself as a passive node through the third beacon message. 5.1.2.1 Core node connectivity Thecorenodesformavirtualbackboneandplaytheroleofarouter. Eachcorenode performsapower-efficienttopologycontrolalgorithmthatsatisfiestherequirements mentionedearlierwiththeweightedlinkcosttobuildavirtualbackbone. Notethat the constructed virtual backbone consists of core nodes only. After constructing the virtual backbone, core nodes send the connectivity information (i.e. the one- hop away neighboring core node information) to the neighboring active nodes. It should be noted that the virtual backbone composed of core nodes may not be 93 connected, and indeed there is no need to have a connected virtual backbone in our algorithm. However, if the distance between any core node pair is less than the maximum transmission range, these two core nodes are connected through a path thatconsistsofbi-directionallink(s)accordingtothethirdandfourthrequirements for topology control algorithm. 5.1.2.2 Non-core node connectivity The non-core nodes also employ the same power-efficient topology control algo- rithm that satisfies the requirements mentioned earlier with the weighted link cost. Initially, the active nodes and the passive nodes only applies topology control algo- rithm to the active nodes and the passive nodes, respectively. After constructing a topology, each non-core node performs the following algorithm. 5.1.2.3 Active node connectivity a. Each active node applies the same power-efficient topology control algorithm that satisfies the requirements with the weighted link cost to core nodes only. In other words, it performs the topology control algorithm to construct a topology only with the core nodes excluding other active nodes and passive nodes. Note that connection between active nodes and core nodes are deter- mined solely by the active nodes. b. Activenodesexchangetheconnectivityinformationwithone-hopawayneigh- boring active nodes. The connectivity information contains the list of its one-hop away neighboring core nodes and the location information. 94 c. After gathering the connectivity information of its one-hop away neighboring active nodes, any active node that has more than one active node as its one- hop away neighboring node performs the following pruning procedure. (a) An active node compares the list of its one-hop away neighboring core nodes with that of its one-hop away neighboring active node. (b) If there is at least one common core node, it removes the link to the one-hop away neighboring active node. (c) Ifthereisnocommoncorenode,theactivenodecalculatesthedistances, d(x,y), for all core node pairs [x,y], where node x belongs to the list of its core nodes and node y belongs to the list of its neighboring active node. (d) Ifmin x,y d(x,y)>d max , whered max isthemaximumtransmissionrange, the active node keeps the link to the one-hop away neighboring active node. Otherwise, the active node removes the link. (e) RepeatSteps(a)-(d)untiladecisionismadeoneverylinktoitsone-hop away neighboring active node. d. Each active node removes the redundant links to the core nodes through the following pruning procedure. (a) Among the links to the core nodes that are obtained in Step a. , the shortest one is always kept. (b) For the remaining links, an active node calculates the distance between the closest one-hop away neighboring core node and other one-hop away neighboring core nodes. If the distance is less than the maximum trans- mission range, d max , its links to other core nodes are removed. 95 (c) Following a similar way, an active node keeps the next shortest link among links that are not yet removed. Then, go to Step (b) again. (d) Repeat Steps (b) and (c) until a decision is made on every link. (e) Finally, each active node uses the connectivity information from its one- hopneighboringcorenodestocheckifthereisapathbetweencorenodes obtained in Steps (b)-(d). If there is a path, the longer link is removed. e. Finally,eachactivenodesendsitsconnectivityinformationtotheneighboring passive nodes. The active node connectivity has two important properties. First, any active node is just one-hop away from a core node. This property is a direct consequence of the constructing algorithm. Second, some active nodes may make connection to more than one core node if there exist more than one core node and the distance between the two core nodes is greater than d max . Some of these additional links to the one-hop away neighboring core nodes are to connect disjointed sets of core nodes. In the mean time, other additional links to the one-hop away neighboring core nodes may be redundant. 5.1.2.4 Passive node connectivity The procedure for passive node connectivity is the same as that of active node: the passivenodesappliesthesamealgorithmtotheactivenodesandthepassivenodes. Also, some passive nodes may have more than one link to connect disjoint sets of core nodes. Thus, some links to neighboring active nodes are to connect disjointed sets of core nodes while other links to neighboring active nodes may be redundant. 96 5.2 Performance Evaluation 5.2.1 Proof for global connectivity Let G = (V,E) be the graph for the original topology. V is the set of all nodes and E is the set of all edges. We assume the original topology is connected. Also, let G 1 = (V,E 1 ) be the graph for the topology generated by our algorithm but before the pruning procedure where E 1 is the subset of E, and let G 2 = (V,E 2 ) be the graph for the topology generated by our algorithm after the pruning procedure where E 2 is the subset of E 1 . Lemma 2 G 1 is a connected graph. Proof: We define CN as the set of all core nodes and NCN as the set of all non-core nodes. Note that CN and NCN are subset of V such that V = CN S NCN. According to our algorithm, each node that belongs to CN performs a power- efficient topology control algorithm that satisfies requirements with weighted link cost. It should be noted that the nodes belonging to CN may not be connected. We define CCN i as the ith subset of CN such that for any two node u and v that belongs to CCN i , there exists a path. Also, note that CN = S CCN i . In similar way, CNCN i is defined as the ith subset of NCN such that for any two node u and v that belongs to CNCN i , there exists a path and NCN = S CNCN i . Note that G 1 is the graph for the topology before each active and passive node performspruningprocedure. Weprovetheglobalconnectivitybyprovingthatonce each active node and passive node in G 1 performs the topology control algorithm describedinSection5.1andmakesconnectionstothevirtualbackboneconstructed 97 by the core nodes and active nodes, but before performing the pruning procedure, there exists a path between any two nodes. First, we consider each set CCN i and CNCN j as a single virtual node and denote CCN i by vnode ccn i and CNCN j by vnode cncn j. Then, we define the distance between two virtual nodes as min u,v d(u,v) where real node u belongs to the one virtual node and real node v belongs to the other virtual node. Note that the distance between any two vnode ccn is greater than d max and the distance between any two vnode cncn is greater than d max . Now, consider the algorithm that the passive nodes make connection to the active nodes. This is the same as putting edges between vnode cncn v and vn- ode cncn w, ifthedistancebetweenvnode cncn vandvnode cncn wislessthanor equal to d max . We define CNCN2 i as the new subset of NCN resulting from the algorithm that the passive nodes make connection to the active nodes, and denote CNCN2 i by vnode cncn2 i. Note that these new vnode cncn2 contains at least one active node. Next, consider the algorithm that the active nodes make connection to the core nodes. This is the same as putting edges between vnode ccn x and vnode cncn2 y, if distance between vnode ccn x and vnode cncn2 y is less than or equal to d max . Thentheresultinggraphisconnectedsinceeveryvnode cncn2containsatleastone active node and every vnode cncn2 is one-hop away from at least one vnode ccn (distance is less than d max ). If the resulting graph is not connected, it violates the assumption that the original topology is connected. Theorem 1 G 2 is a connected graph. Proof: 98 Theprooffortheglobalconnectivityafterpruningprocedureofactive(passive) nodes is straight forward. The pruning procedure of active (passive) nodes is equivalent to checking the existence of a path for the link considered. The existence of a path is guaranteed by the algorithm itself. Thus, whenever active (passive) nodes remove a link, it is guaranteed that there exists a path that replaces the removed link. 5.2.2 Simulation results To exercise our power-aware algorithm, we choose two power-efficient topology controlalgorithms: LocalizedMinimumSpanningTree(LMST)basedandShortest Path Tree (SPT) based topology control algorithms. These two algorithms meet the requirement described in Section 5.1. To measure the performance of our power-aware topology control algorithm, we compare the six performance metrics with the power-efficient algorithms: the network lifetime (in unit time), the network partition time (in unit time), the node decreasing time (in unit time), the number of delivered packets, the packet delivery ratio, and the number of dead nodes. The network lifetime is defined as the time span from the start of the network to the first death of nodes, the same way as defined in many other papers. The network partition time is defined as the time span from the start of the network to the time that the network is disconnected amongthosealivenodes. Thenodedecreasingtimeisdefinedasthetimedifference between network lifetime and network partition time. The number of delivered packets is counted until the first death of nodes, and the number of dead nodes is counted until the network is partitioned. The packet delivery ratio is defined as 99 the number of delivered packets to the number of generated packets until the first death of nodes. The simulations are set up for the randomly distributed 50 nodes with uniform distribution in 750(m)×750(m) grid. The maximum transmission range is set to 250(m). It is assumed that the data packet length is fixed and the transmission timeofapacketis5unittimes. Thepathlossexponentissetto4(usuallybetween 3 and 4) such that 0.5% of initial energy consumption is assumed for data packet transmission to maximum transmission range. It is set up that the initial energy level of each node is the same for all nodes. The random traffic that follows the Poisson arrival process with the rate of 1.0× 10 −3 packet per unit time is used in the simulation. Connection duration is modelled by geometric random variable with parameter value set to 1.0×10 −4 , and inter-connection time is also modelled by geometric random variable with parameter value set to 5.0×10 −4 . The slightly modified 802.11b MAC layer is used in the simulation. Each node transmit RTS-CTS messages with adjusted power such that it is transmitted with the power to reach the outmost one-hop neighboring node. In addition to that, the perfect MAC is assumed. Thus, there is contention but no collision. Due to the use of bidirectional links in the topology control algorithms, a modified link-state routing protocol that uses the same link cost for the both directions of a link is implemented in the simulation. RefertoFigs.5.1and 5.3forthecomparisonofmeanandstandarddeviationof network lifetime. Simulation is performed for 10 different random topologies with different random traffic. In the simulation, we assume that network is static and make the network updated at every 25000 unit time from the start. The simulation results show that, with power-aware topology control, the mean network lifetime is 100 Power-aware LMST algorithm LMST algorithm 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 x 10 5 mean std Figure 5.1: Mean and standard deviation of network lifetime Power-aware LMST algorithm LMST algorithm 0 0.5 1 1.5 2 2.5 x 10 5 mean std Figure 5.2: Mean and standard deviation of network partition time increasedby65.27%and51.92%,respectively,comparedwiththoseofusingLMST- based and SPT-based power-efficient topology control. Figs. 5.2 and 5.4 show the comparison of mean and standard deviation of network partition time. The mean network partition time of power-aware topology control is less than that of power-efficienttopologycontrol. Inpower-awaretopologycontrol,theenergyofthe nodes with low residual energy is saved by forcing the network to put more routing tasks on the shoulder of the nodes with higher residual energy. Thus, the energy consumption over all nodes is more evenly distributed, but the network partition 101 Power-aware SPT algorithm SPT algorithm 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 x 10 5 mean std Figure 5.3: Mean and standard deviation of network lifetime Power-aware SPT algorithm SPT algorithm 0 0.5 1 1.5 2 2.5 3 x 10 5 mean std Figure 5.4: Mean and standard deviation of network partition time timeisdecreased,comparedwiththoseofusingLMST-basedandSPT-basedpower- efficient topology control. This fact can also be verified by other performance metric. Refer to Tables 5.1 and 5.2 for the mean node decreasing time. The mean node decreasing time for the power-aware algorithm is approximately one third of the power-efficient algorithm in either LMST-based or SPT-based way. This result exactly verifies that the energy consumption under power-aware topology control is more evenly distributed. As a result, we can conclude that in our power-aware 102 1000 5000 25000 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 x 10 5 Topology update interval mean network lifetime mean network partition time Figure 5.5: Mean network lifetime and network partition time with different topol- ogy update interval for LMST-based power-aware topology control 1000 5000 25000 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 x 10 5 Topology update interval mean network lifetime mean network partition time Figure 5.6: Mean network lifetime and network partition time with different topol- ogy update interval for SPT-based power-aware topology control algorithm, the energy consumption is more evenly distributed over the nodes as expected. RefertoTables5.1and 5.2forexactvaluesandcomparisonofotherperformance metric. First, note that the mean number of delivered packets until the first dead node is also improved and is proportional to the increase of the network lifetime. Themeanpacketdeliveryratioisalmostthesameforbothpower-awareandpower- efficient algorithms. Finally, note that the mean number of dead nodes of power- aware algorithms is less than that of power-efficient ones. 103 Table 5.1: Performance comparisons for LMST-based case power-aware TC LMST TC mean network lifetime (unit time) 187000 113150 mean network partition time (unit time) 232550 246113 mean node decreasing time (unit time) 45541 132960 mean number of delivered packets 7806.3 4704.6 mean packet delivery ratio 0.99929 0.99835 mean number of dead nodes 10.3 13 Table 5.2: Performance comparisons for SPT-based case power-aware TC SPT TC mean network lifetime (unit time) 197330 129890 mean network partition time (unit time) 242130 275520 mean node decreasing time (unit time) 44802 145620 mean number of delivered packets 8236.3 5406.1 mean packet delivery ratio 0.99952 0.99941 mean number of dead nodes 10.2 11.8 Now, an arising question is: how much the performance is affected by the dif- ferent topology update interval values? In Figs. 5.5 and 5.6, the performance is measured for a random topology with different traffic patterns and with the chang- ing topology updated interval values. Surprisingly, the performance is not much affected by the topology update interval value. However, note that the mean node decreasing time is decreased as the topology update interval is decreased. The ex- act numerical value of the mean node decreasing time of LMST-based power-aware topology control, when the topology update interval is set to 1000 unit time, is 4342.6 unit time. When the topology update interval is set to 5000 and 25000 unit 104 time, it is 13662 and 31537 unit time, respectively. The exact numerical value of the mean node decreasing time of SPT-based power-aware topology control, when thetopologyupdateintervalissetto1000unittime, is3967.2unittime. Whenthe topology update interval is set to 5000 and 25000 unit time, it is 11216 and 34561 unit time, respectively. These results indicate that as the number of topology up- dateisincreased, theenergyconsumptionismoreevenlydistributedoverallnodes. However, due to the overhead required in topology update, over all performance is degraded if too many topology updates took place. 5.3 Conclusions In this research, we present a power-aware topology control algorithm. Due to the limited connectivity of the power-efficient topology control, the power saving is not evenly distributed over all nodes, namely, some nodes are over utilized for packet forwarding and thus consume up their energy more quickly than others. In our power-aware topology control algorithm, the topology is changed, when it is needed, to conserve the energy for highly utilized nodes. When a node is making a decision on whether a wireless link between itself and a reachable neighboring node should be preserved or not in the topology being constructed, the decision is made based on not only the distance from its neighboring nodes but also the residual energy levels of itself and its neighboring nodes. Through the extensive simulations, we show that our algorithm greatly improves the network performance in terms of both network lifetime and throughput. In our current simulations, the mobility is not considered. It is assumed that the network is static. However, in our future research, the mobility will be taken into account. If the mobility of each node is considered, periodic updates of the 105 topology are required to overcome the link break due to the mobility. The same situation also occurs in power-efficient topology control. 106 Chapter 6 CSMA/CA MAC Protocol Design for Topology Controlled Ad-Hoc Networks: A Cross Layer Approach In this chapter, we present CSMA/CA based MAC protocol that transmit RTS- CTS with variable power, as well as DATA and ACK, when a topology is given by the topology control algorithm. In our proposed algorithm, each node deter- mines its transmission power for RTS-CTS as well as for DATA-ACK from the given topology. Also, the hidden node problem becomes very significant in wireless ad-hoc networks when multi-hop environment is considered. There exist several distributed MAC protocols to alleviate the hidden node problem, among which CSMA/CA (Carrier Sense Multiple Access with Collision Avoidance) protocol is the basis collision avoidance MAC protocol and the basis for DCF (Distributed Coordination Function) mode of 802.11 MAC protocol. We observe that asymmet- ric RTS-CTS ranges due to variable transmission power causes the hidden node problem when RTS-CTS range is determined without considering the location of the neighboring nodes. In our proposed algorithm, each node starts with minimal RTS-CTS range and increases RTS-CTS range until symmetric RTS-CTS range is 107 achieved. Then, it also adjust the transmission power for DATA-ACK. We also develop an analytical model for modeling the throughput performance for our al- gorithm. 6.1 RTS-CTSRangeforTopologyControlledWireless Ad-Hoc Networks In this section, we show that the asymmetric RTS-CTS ranges due to different reduced transmission powers can cause severe hidden node problem in topology controlled wireless ad-hoc networks. Then, we propose an algorithm that finds minimalRTS-CTSrangetoresolvethehiddennodeproblemcausedbyasymmetric RTS-CTS range. 6.1.1 Hidden node problem due to asymmetric RTS-CTS ranges Suppose that topology control using variable transmission powers is adopted in a wireless ad-hoc network, then CAMA/CA MAC protocol can adjust transmission power for RTS and CTS as well as DATA and ACK. This means that RTS-CTS range maintained by each node can be different, and the RTS range of the sender and the CTS range of the receiver can be asymmetric for any pair of sender and receiver. Properly setting up RTS-CTS range is crucial since it is mostly related to the performance of the network in terms of the throughput of each node. Without choosing proper RTS-CTS range, some nodes may monopolize the channel, and 108 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 5 5 5 5 Figure 6.1: Hidden node problem in topology controlled wireless Ad-Hoc networks thus there can arise serious fairness problem among nodes. The degradation of the throughputofsomenodesoccursmainlywhenthereishiddennodeproblemdueto improperRTS-CTSrangesetup. Thus, weinvestigatetheconditionforthehidden node problem caused by asymmetric RTS-CTS ranges and find minimal symmetric RTS-CTS range for each node. Suppose that a topology is given by a topology control algorithm, and each nodemakesconnectionstothespecificneighboringnodesaccordingtothetopology control algorithm. The minimum requirement for each node to reduce RTS-CTS rangeistosetupRTS-CTSrangeuptoandincludingthefurthestconnectednode. Thus, RTS-CTS range is the same as the longest link length. Otherwise, there can beapossibilitythattheconnectedneighboringnodesbecomehiddentoeachother. 109 However, this is not sufficient to prevent hidden node problem due to asymmetric RTS-CTS range. See Fig. 6.1 for illustration. In Fig. 6.1, node 1 makes connection to node 2 and 3. Hence, it should set its RTS-CTS range up to and including node 2. Meanwhile, node 4 makes two connections to node 3 and 5, and sets its RTS- CTS range equal to the longest link, the link between node 4 and node 5. Now, suppose that node 5 initiates transmission to node 4. Node 5 sends RTS to node 4, and node 4 will reply to it with CTS if RTS is successfully delivered to node 4. However, the range of RTS and CTS does not covers node 1. Thus, there are chancesfornode1toinitiatetransmissiontonode2. Ifnode1sendRTStonode2, the RTS from node 1 will collide with RTS(DATA) from node 5 to node 4. Similar situation also applies to node 4. If node 4 initiates transmission, CTS(ACK) from node 5 is vulnerable to any transmission from node 1 to node 2. As a result, node 4 and 5 will experience more collisions and node 1 will hold up the channel more than node 4 and 5 most likely. This is the hidden node problem due to asymmetric RTS-CTS ranges, and node 1 is hidden from node 5 in Fig. 6.1. To address the hidden node problem due to asymmetric RTS-CTS ranges rig- orously, we present the sufficient and necessary condition for the problem. Sufficient and Necessary Condition 1 Supposethatnodeiandnodej aremore than 1-hop away under given topology. Let d(i,j) be the Euclidean distance between node i and j. Also, let R(i) and R(j) be the RTS-CTS range of node i and node j, respectively. Under the condition that R(i) < d(i,j) and the degree of node i is 2 if node i and node j are two-hops away (otherwise the degree of node i is greater than or equal to 1), if and only if d(i,j)≤R(j), then the transmission (reception) of node i can be corrupted by the transmission of RTS(CTS) of node j. Proof: 110 The sufficient condition is obvious. (Refer to Fig. 6.1.) We prove the necessary condition as follows. We prove the necessary condition by proving the negation, which is that if d(i,j) > R(j), then node j is not hidden from node i. Note that d(i,j) > R(j) just means that there is no collision between node i and j since node i is out of RTS-CTS range of node j, and node j is also out of the RTS-CTS range of node i. Therefore, node j can’t be a hidden node of node i. This proves the necessary condition. 6.1.2 Algorithm for resolution of hidden node problem due to asymmetric RTS-CTS ranges We propose the MAC protocol based hidden node resolution algorithm. The main idea of the algorithm is that if the node, which receives RTS(CTS) from other nodes than its directly connected neighboring nodes, then it increases the RTS- CTS range enough for other nodes to receive its RTS(CTS). In other words, our algorithm makes RTS-CTS range symmetric. This algorithm uses the information fromtheheaderofthereceivedRTS(CTS).IfanodereceivesRTS(CTS)fromother nodes than its directly connected neighboring nodes, it immediately acknowledges that the condition for increase of RTS-CTS range is met and decides which node should be included within its RTS-CTS range from the information of the header of the received RTS(CTS). Here, we assume that each node has the location infor- mation about nodes within its maximum transmission range. This assumption is reasonable since many topology control algorithms require such information. Also, the reception of RTS(CTS) means that the node that transmitted the RTS(CTS) 111 1 2 3 4 5 7 6 23 m 57 m 100 m 43 m 28 m 60 m Figure 6.2: Test topology is located within the maximum transmission range. We further assume that each node can estimate the transmission power based on the location information and channel information (e.g. path loss exponent). The details of algorithm are given below. 1. After the topology was given, each node initially sets its RTS-CTS range up to the furthest directly connected neighboring node. Then, each node sets its transmission power for RTS-CTS-DATA-ACK to the value that is enough for the reception at the peer node. 2. When receives RTS(CTS), checks from which node it is transmitted a. if RTS(CTS) came from its directly connected neighboring nodes, do nothing. b. if RTS(CTS) came from other nodes than its directly connected neigh- boring nodes, increases RTS(CTS) range up to the node transmitting the RTS(CTS). 3. Keep doing the step 2. 6.1.3 Performance comparison by simulation In this section, we show the performance comparison between CSMA/CA MAC protocol with variable RTS-CTS range based on our algorithm and the one with maximum RTS-CTS range. We built a simple event driven simulator instead of us- ingns-2torealizevariableRTS-CTSrange. Thisisduetothefactthatns-2involves 112 all layers of networking. We choose the average throughput of CSMA/CA MAC protocol as performance metric. The average throughput is defined as the time fraction that node spends in transmitting DATA for successful 4-way handshakes (RTS-CTS-DATA-ACK)overentireoperationaltime. Tomeasuretheperformance of MAC protocol, we assume the saturated network, i.e. every node always has a data packet to send. Each node chooses a receiving peer node among directly connected neighboring nodes equally likely. The system parameters used in the simulation are listed in Table 6.1. The system parameters are chosen according to the 802.11 specification [23]. One major difference between 802.11 MAC protocol and our MAC protocol is the absence of BEB (Binary Exponential Backoff) algo- rithm. This is due to the fact that BEB algorithm suffers from inherent fairness problem. In our simulation, we assume that every node has the sameCW max value and BEB is not used. We set CW min = 8 and used several CW max values such as 64, 128, 256, 512, 1024, and 2048. We also assume that maximum transmission range is 200 m and sensing range is two times of the transmission range. Finally, retransmission in MAC protocol is implemented in our simulator and it re-tries three times for the unsuccessful transmission. We set up chain network topology that consists of 12 nodes, and it is shown in Fig.6.2. Notethatnode1, 2, 3, 4, and5areinthesamescenarioshowninFig.6.1. Weaddedtwomorenodesequallyspacedat60mintheleftsideofnode7andthree more nodes equally spaced at 60 m in the right side of node 6 to remove the edge effect. As shown in Fig. 6.3, the CSMA/CA MAC protocol with variable RTS-CTS range outperforms the CSMA/CA MAC protocol with maximum RTS-CTS range. Note that theCW max value for maximum throughput is larger in CSMA/CA MAC protocol with maximum RTS-CTS range for overall performance of node 1 to node 113 Table 6.1: System parameters used in simulation DATA payload 8184 bits MAC header 272 bits PHY header 128 bits ACK 112 bits + PHY header RTS 160 bits + PHY header CTS 112 bits + PHY header Transmission Rate 1 Mbps Propagation Delay 1 μs Slot Time 50 μs DIFS 128 μs SIFS 28 μs EIFS 396 μs 6. This means that as the RTS-CTS range increases, we expect more collision. Thus, the maximum throughput is obtained at larger CW max value. 6.2 TransmissionPowerAdjustmentforRTS-CTS Range In this section, we show that symmetric RTS-CTS range is not sufficient for a solution to the hidden node problem. This is due to the fact that RTS-CTS only ensures the virtual carrier sensing. We further develop our algorithm proposed in Section 6.1.2 by considering the physical carrier sensing. 114 0 500 1000 1500 2000 2500 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Node1 CW max Throughput 0 500 1000 1500 2000 2500 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 Node2 CW max Throughput 0 500 1000 1500 2000 2500 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Node3 CW max Throughput 0 500 1000 1500 2000 2500 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Node4 CW max Throughput W/ variable RTS-CTS range W/ maximum RTS-CTS range Figure 6.3: Performance comparison between variable RTS-CTS range and maxi- mum RTS-CTS range 115 6.2.1 Hidden node problem due to carrier sensing Note that even though RTS-CTS ranges are symmetric, there still remains the same hidden node problem. This is due to the fact that the RTS(CTS) only en- sures virtual carrier sensing. The hidden node problem in Section 6.1.1 is only avoided when RTS(CTS) from node 4 is successfully delivered to node 1. In order to further resolve the same hidden node problem, we need to ensure the physical carrier sensing. Suppose that in Fig. 6.1, transmission power of node 5 is enough for successful reception at node 4 but not enough for carrier sensing at node 1. If node 5 initiates transmission to node 4, but CTS from 4 collides with RTS from node 2 at node 1, node 1 will not sense the ongoing DATA transmission from node 5 to node 4 and may initiate transmission to node 2. Then, RTS from node 1 will collide at node 4 with DATA transmission from node 5 to node 4. This case also holds for the transmission initiation from node 4 to node 5. If node 4 initiates transmission, CTS(ACK) from node 5 is vulnerable to any transmission from node 1 to node 2. 6.2.2 Algorithm for resolution of hidden node problem due to carrier sensing In this section, we further develop our MAC protocol based hidden node resolution algorithminSection6.1.2toresolvethehiddennodeproblemduetophysicalcarrier sensing. The main idea of the algorithm is that if the node receives RTS(CTS) from other nodes than its directly connected neighboring nodes, then it increases theRTS-CTSrangeenoughforothernodestoreceiveitsRTS(CTS).Inadditionto that, the node informs the directly connected neighboring nodes of the additional power required for carrier sensing. The details of algorithm are given below. 116 1. After the topology was given, each node initially set its RTS-CTS range up to the furthest directly connected neighboring node. Then, each node sets its transmission power for RTS-CTS-DATA-ACK to the value that is enough for the reception at the peer node. 2. In the header of RTS(CTS), each node inserts the additional power infor- mation for directly connected neighboring nodes. The additional power is calculated by each node such that the transmission of directly connected neighboring node is sensed by all nodes within its RTS-CTS range. 3. Upon receiving RTS(or CTS), each node follows the steps below: a. ifRTS(CTS)camefromitsdirectlyconnectedneighboringnodesandno additional power information is specified, do nothing. b. ifRTS(CTS)camefromitsdirectlyconnectedneighboringnodesandad- ditional power information is specified, increases the transmission power by the amount specified in RTS(CTS). c. if RTS(CTS) came from other nodes than its directly connected neigh- boring nodes, (1) increasesRTS(CTS)rangeuptothenodetransmittingtheRTS(CTS). (2) calculates the addition powers required for each directly connected neighboring node, which is enough for the node that transmitted the RTS(CTS) to sense the transmission of each directly connected neighboring node. Then, inserts the calculated value in the header of RTS(CTS) to each directly connected neighboring node. 4. Repeat the above steps if updates are required. 117 6.2.3 Performance comparison by simulation In this section, we show that there still exists the hidden node problem without considering carrier sensing range and this hidden node problem results in fairness problem among nodes. Fig. 6.4 shows the throughput of nodes 1, 3, 4, and 5 using CSMA/CA MAC protocol with variable RTS-CTS range but without considering carrier sensing range. As stated in Section 6.1, we can see that the performance of node 5 significantly compromised. Note that the performance of node 4 didn’t comprise due to EIFS (Extended Inter Frame Space) feature of 802.11 MAC pro- tocol. From Fig. 6.5, we can see that there is no compromised throughput when carrier sensing power adjustment is implemented with variable RTS-CTS range in CSMA/CA MAC protocol. 6.3 Approximate Throughput Analysis Inthissection, wepresenttheapproximatethroughputmodelforCSMA/CAMAC protocol with variable RTS-CTS range and carrier sensing power adjustment in a topology controlled wireless ad-hoc network. We are mainly interested in the throughput for a specific link after each node updates its RTS-CTS range and transmission power using our proposed algorithm. To analyze the throughput of a link, we only consider local information available to the node. After getting the throughput models for all links, we can obtain the throughput model for a node. To obtain the throughput model, we use Markov chain model. The Markov chain model was introduced in [50] to provide the throughput model of Ad-Hoc networks. Although our way of developing Markov model and getting throughput model looks similar to that of [50], there are fundamental differences. First of all, the channel and node activity were modelled by separate Markov chains in [50]. 118 0 500 1000 1500 2000 2500 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 CW max Throughput node 1 node 3 node 4 node 5 Figure 6.4: Performance comparison among node 1, 3, 4, and 5 with CSMA/CA MAC protocol with variable RTS-CTS range but without carrier sensing power adjustment 119 0 500 1000 1500 2000 2500 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 CW max Throughput node 1 node 3 node 4 node 5 Figure 6.5: Performance comparison among node 1, 3, 4, and 5 with CSMA/CA MAC protocol with variable RTS-CTS range and with carrier sensing power ad- justment 120 This is reasonable since their network does not adopt any topology control and same RTS-CTS range and transmission power are assumed. Therefore, the local view over the network of each node is more or less the same each. However, once topology control is adopted and variable RTS-CTS range and transmission power are used, the local view over network of each node may be quite different from each other. Thus, we develop Markov chain model based on the view of each node by combining channel status and node activities. We also note that Markov chain model obtained by combining channel status and node activities is actually close to the approach of [8] as can be seen in Section 6.4. However, the approach of [8] is only applicable to the single-hop ad-hoc networks. 6.3.1 System model and assumption The exact throughput analysis of CSMA/CA MAC protocol under multi-hop case is hard to obtain since we need to know the exact behavior of entire network at any giventime. Thus, toobtainthethroughputofanodeoralinkforagiventopology, we only consider the local information available to the node. We first define the terms used in the analysis. • For node i, let B(i) be the set of nodes within RTS-CTS range of node i. • Let B ∗ (i) =B(i) S {i}. • For node i, let D(i) be the set of nodes directly connected to node i. Tomodelthethroughputofanode,wefirstneedtomodelthethroughputofthe links that the node maintains. We model the throughput of the link from nodei to nodej∈D(i)onlybyconsideringthenodesthatbelongtoB ∗ (i) S B(j) S k∈D(j) D(k), 121 since they are mostly involved with node i’s medium access. As explained previ- ously, we assume that BEB algorithm is not used. Thus, each node is assumed to uses a common CW max . Also,weassumethetime-slottedp-persistentoperationofnodes. Nodesinitiate the transmission in a time-slot with probability p if channel is sensed idle. It has been shown by [8] that the performance of time-slotted MAC protocol is well matchedwiththatofcontinuoustimeMACprotocolandp-persistentMACprotocol is a good approximation of backoff algorithm if p is chosen as p = 1 E(cw)+1 = 2 CW min +CW max +2 , where r.v. cw is the contention window that is uniformly distributed between CW min and CW max . We denote the length of time slot by τ. Note that τ should be long enough to account for the propagation delay, RF delay in tranceiver, trans- mission and reception turn around time, MAC processing delay, etc.. Thus, it is quite reasonable to assume that τ is the same as the Slot Time defined in IEEE 802.11standard[23]. Then,ThetransmissiontimesofRTS,CTS,DATA,andACK normalized by τ are L RTS , L CTS , L DATA , and L ACK , respectively. (We assume the fixed length DATA packet.) Also, note that we do not consider DIFS (Distributed Inter Frame Space) and SIFS (Short Inter Frame Space) for simplicity. Finally, the saturated static network is assumed. Namely, each node always has DATA packet to send and there is no mobile node. 6.3.2 Approximate analysis WiththeassumptionsgiveninSection6.3.1, wemodelthelinkfromnodeitonode j ∈ D(i) using the discrete time Markov process and analyze it using imbedded 122 Waiting Transmission Collision1 Block Collision2 P ww P wt P tw P wc1 P c1w P wb P bw P wc2 P c2w Figure 6.6: Imbedded Markov Chain Markovchainmodel. SeeFig.6.6forillustrationofimbeddedMarkovchainmodel. In Fig. 6.6, imbedded Markov chain has five states. To obtain the throughput model, we need to specify the state transition probabilities and information about state durations. We first define each state and find the state duration. The Waiting state is the state when node i and all nodes that belong to B(i) or D(j) sense the channel idle. Its duration is obviouslyτ. The Tx state is the state when nodei successfully 123 initiatesfour-wayhandshakeinthelinkfromnodeitonodej. Thus,thenormalized duration of Tx state is given as T tx =L RTS +L CTS +L DATA +L ACK +4. (6.1) The Collision1 state is the state when node i fails to initiate four-way handshake. The normalized duration of Collision1 can be given as T Col1 =L RTS +L CTS +2. (6.2) The Collision2 state is the state when node i senses the channel is busy due to the collision of RTS messages from neighboring nodes. The normalized duration of Collision2 can be given as T Col2 =L RTS +L CTS +2. (6.3) NotethatthenormalizeddurationsoftheCollision1 andCollision2 statesaregiven under the assumption that a node, which can’t receive RTS due to collision, waits during EIFS, and this EIFS covers the time interval of L CTS +τ. The Block state isthestatewhennodeiisblockedbysuccessfulfour-wayhandshakeofneighboring nodes. The normalized duration of Block is given as T blk =L RTS +L CTS +L DATA +L ACK +4. (6.4) The state transition probability, P ww , is simply given as P ww = Pr{No node transmits in the slot} = (1−p) N ij (6.5) 124 where N ij ≡||B ∗ (i) S B ∗ (j) S k∈D(j) D(k)||. Now, to calculate the state transition probabilities, P wt , P wc1 , P wb , and P wc2 , we need to specify the interference for capture property. However, it is hard to quantify the interference since transmission power is variable. In order not to deal withtheactualvariablepowerassignmentandinterferencemeasure, weassumethe perfect capture. Unless a node receives more than one packet at the same time, node can always receive the intended packet successfully. Under the perfect capture, the state transition probability, P wt , can be calcu- lated as P wt =P 1 ·P 2 ·P 3 ·P 4 . (6.6) P 1 is the probability that node i transmits in the slot and obtained as p. P 2 is the probability that node j doesn’t transmit in the slot and obtained as (1−p). P 3 is the probability that the nodes, which belongs to B(i) and B(j), do not transmit in the slot. It is calculated as P 3 = (1−p) N ′ ij where N ′ ij ≡||B(i) T B(j)||. P 4 istheprobabilitythatthenodes,whichbelongsto(B(j) S k∈D(j) D(k))−B(i), donottransmitduringL RTS +L CTS +1. NotethatthedurationofL RTS +L CTS +1 is the vulnerable period for RTS-CTS exchange between node i and j [17,49]. It is calculated as P 4 = (1−p) L RTS +L CTS +1 N ∗ ij where N ∗ ij ≡||(B(j) S k∈D(j) D(k))−B(i)||. As a result, P wt is given as P wt =p·(1−p) N ′ ij +1 · (1−p) L RTS +L CTS +1 N ∗ ij . (6.7) 125 Forthestatetransitionprobability,P wc1 ,wefirstnotethatstatetransitionfrom Waiting state to Transmission state or Collision1 occurs with probability p since nodei transmits to nodej in the slot with probabilityp. Thus, P wt +P wc1 =p. As a result, P wc1 is calculated as P wc1 =p 1− P wt p =p h 1−(1−p) N ′ ij +N ∗ ij ·(L RTS +L CTS +1)+1 i . (6.8) For the state transition probability, P wb , we simply assume that there is only one transmitting node among N ij nodes. Then, P wb is calculated as P wb = (1−p)· N ij −1 1 p 1 ·(1−p) N ij −2 (6.9) Under the perfect capture property assumption, it is little bit complicated to calculate P wc2 directly. Instead of direct calculation of P wc2 , the state transition probability, P wc2 , is simply given as P wc2 = 1−P ww −P wt −P wc1 −P wb . (6.10) Finally, the rest of the state transition probabilities, P tw , P c1w , P bw , and P c2w , are simply ‘one’. Having calculated the state transition probabilities, we can now calculate the steady-state probability for each state by solving the equations below. Π = Π·P (6.11) π w +π tx +π col1 +π blk +π col2 = 1 (6.12) 126 where P is the transition probability matrix and Π is the steady-state probability vector. After solving (6.11) and (6.12), we have π w = 1 2−P ww , (6.13) π tx = P wt 2−P ww , (6.14) π col1 = P wc1 2−P ww , (6.15) π blk = P wb 2−P ww , (6.16) π col2 = P wc2 2−P ww . (6.17) Usingthecalculatedsteady-stateprobabilitiesandstatedurations,thethrough- put for the link from node i to j is given as Th(ij) = π tx ·L DATA π w +π tx ·T tx +π col1 ·T col1 +π blk ·T blk +π col2 ·T col2 . (6.18) To calculate the throughput of node i, we have to calculate the throughput of eachlinkthatnodeimaintains. Inaddition,wehavetoknowlinkaccessprobability of node i. The link access probability is how often node i access the specific link. Let P (ij) be the link access probability of node i for the link from node i to node j. Then, the throughput of node i is the sum of the link throughput weighted by the link access probability. Thus, the throughput of node i is obtained as Th(i) = X j∈D(i) Th(ij)·P (ij) . (6.19) 127 If we assume that each node access the link equally likely, (6.19) becomes Th(i) = 1 ||D(i)|| X j∈D(i) Th(ij). (6.20) 6.3.3 Numerical results Fig. 6.7 shows the numerical results that our throughput model produces using the test topology shown in Fig 6.2. We can see that results from our throughput model quite matches with the simulation results. 6.4 Throughput, Fairness, and Energy Efficiency In wireless ad-hoc networks, throughput, fairness, and energy efficiency are im- portant performance measurement metrics and are directly or indirectly related to MAC protocol. In this section, we show that our throughput model can give the relation between each performance measure metric. Let’s suppose that node i just have successfully transmitted a packet to node j and tries to send another packet. Until node i successfully send a packet to node j, node i may take different actions based on the channel status. It may decrease thebackoffcounter, maysensethechannelbusyduetothetransmission(s)ofother nodes or due to the collision(s) of control packets from other nodes, or may try the unsuccessful transmission. However, it will eventually grab the idle channel and successfully send a packet to node j. We note that this process of actions taken by node i is regenerative process and is well described by our imbedded Markov chain model if we observe node i’s behavior at the time immediately after each action. Then, we can calculate, on the average, how many actions node i takes until it successfully send a packet to node j. Let r.v. w be the number of actions node 128 i takes until it successfully send a packet to node j and q be the probability that node i takes such actions. From the imbedded Markov chain model, q is obtained as q =π w +π blk +π col1 +π col2 . (6.21) Then, we can calculate the expected value of w and it is given as E(w) = ∞ X k=1 k·(1−q)·q k−1 −1 = q 1−q . (6.22) From (6.22), we can calculate, on the average, how many times node i enters each state (takes each action). For example, the average number of entering Block state is calculate as E(# of entering Block state) =E(w)· π blk q = q 1−q · π blk q = π blk π tx . (6.23) In the same way, we have E(# of entering Waiting state) = π w π tx , (6.24) E(# of entering Col1 state) = π col1 π tx , (6.25) E(# of entering Col2 state) = π col2 π tx . (6.26) If we calculate Th(ij) using (6.23), (6.24), (6.25), and (6.26), we obtain Th(ij) = L DATA πw πtx + π blk πtx ·T blk + π col1 πtx ·T col1 + π col2 πtx ·T col2 +T tx . (6.27) Note that (6.27) is exactly same as (6.18). 129 From (6.23), (6.24), (6.25), (6.26), and (6.27), we can immediately observe the relation between each performance measurement metrics. For example, we can find maximum throughput from (6.27). Then, from (6.23), we can measure the fairness metric for the link at maximum throughput if we define the fairness as the average number of transmissions of neighboring nodes per its transmission. Or, we can measuretheenergyefficiencyfrom(6.25): averagenumberoftransmissiontrialuntil successfultransmission. Thesearetheimportantinformationwhenwedesignupper level protocol as well as measure the performance of MAC protocol. For example, we observe that the links that a node maintains shows very different throughput performance based on the given topology. Thus, topology control protocol may use this information for restructuring the topology if there is a need. 6.5 Conclusion In this chapter, we showed that the properly adjusted RTS-CTS range is crucial to the performance of wireless ad-hoc networks. When a power-efficient topology control algorithm is adopted, RTS-CTS range can be reduced as small as possible based on the topology information. However, improper adjustment of RTS-CTS range without taking the topology of the local nodes into account can result in asymmetric RTS-CTS range. The asymmetric RTS-CTS range causes the hidden node problem in MAC pro- tocol. We showed that the hidden node problem caused by asymmetric RTS-CTS range gives rise of severe fairness problem. We also showed that symmetric RTS- CTS range is not sufficient for the solution of the hidden node problem caused by asymmetric RTS-CTS range. We found that transmission power adjusted for carrier sensing is essential to the solution. 130 We proposed a MAC protocol based algorithm that makes asymmetric RTS- CTS ranges symmetric using the information available from the given topology. Then,wefurtherdevelopedourMACprotocolbasedalgorithmforthetransmission power adjustment for carrier sensing. We verified the effectiveness of our algorithm through extensive simulations. We also presented the throughput model for a link and a node in topology controlled wireless ad-hoc networks. The advantages of our throughput model are that it not only gives quite accurate throughput information for a link and a node butalsogivesvaluableinformationaboutseveralperformancemeasurementmetrics and their relations that are useful for the upper-layer protocols. 131 0 500 1000 1500 2000 2500 0.04 0.06 0.08 0.1 0.12 0.14 0.16 CW max Throughput Analysis Simulation (a) node 1 0 500 1000 1500 2000 2500 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 CW max Throughput Analysis Simulation (b) node 2 0 500 1000 1500 2000 2500 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 CW max Throughput Analysis Simulation (c) node 3 0 500 1000 1500 2000 2500 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 CW max Throughput Analysis Simulation (d) node 4 0 500 1000 1500 2000 2500 0.04 0.06 0.08 0.1 0.12 0.14 0.16 CW max Throughput Analysis Simulation (e) node 5 0 500 1000 1500 2000 2500 0.04 0.06 0.08 0.1 0.12 0.14 0.16 CW max Throughput Analysis Simulation (f) node 6 Figure 6.7: Numerical results from analysis 132 Chapter 7 Conclusion and Future Work 7.1 Conclusion Inthefirstpartofthisthesis, theexpressionfortheminimumexpectedfiledelivery time of the CFDP Deferred NAK Mode and bounds on the expected file delivery time of the CFDP Immediate NAK mode were derived under the constraint that the throughput efficiency is maximized in the sense that there is no unnecessary duplicate retransmission. It was observed that the throughput efficiency can be compromised in the form of unnecessary duplicate retransmissions of an identical PDU. Due to a very limited power budget in the deep space networking, the op- erational constraint not to compromise the throughput efficiency was adopted in the performance analysis. To maximize the throughput efficiency (in other words, to avoid unnecessary duplicate retransmissions) and to minimize the expected file delivery time at the same time, we proposed a timer control scheme to be used in the Deferred NAK and the Immediate NAK of CFDP. It is worthwhile to point out that the expected file delivery time depends upon several variables, e.g., the file size, the PDU size, propagation delay, etc. With results of our mathematical derivation, we can generate numerical values for the 133 expected file delivery time quickly without computationally intensive random sim- ulation for a range of different environmental and design variables. It is also worth- while to point out that the CFDP or its variant may be useful beyond space ap- plications, although the CFDP has been standardized by CCSDS for use in space networking. For example, the feature of no ACK message for the file data PDUs (i.e. NAKonly)mayalsobeusefulforsecurecommunicationinwhichthereceiver’s emission should be small to hide its presence or location. In the second part of this thesis, we presented a power-aware topology control algorithm. Due to the limited connectivity of power-efficient topology control, powerusageisnotevenlydistributedoverallnodes. Inotherwords,somenodesare over utilized for packet forwarding so that their energy is consumed more quickly than others. In the proposed power-aware topology control algorithm, we can modify the topology to conserve the energy for highly utilized nodes whenever it is needed. The decision whether a wireless link between a node and its reachable neighboring nodes should be preserved is made based on the node distance as well their residual energy levels. It was shown by extensive simulations that the proposed algorithm improves the network performance greatly in both throughput and network lifetime. Furthermore, it was shown that a properly adjusted RTS-CTS range is crucial to the performance of wireless ad-hoc networks. When a power-efficient topology control algorithm is adopted, the RTS-CTS range can be reduced as small as possi- blebasedonthetopologyinformation. However,theRTS-CTSadjustmentwithout taking the topology of local nodes into account can result in an asymmetric RTS- CTS range. The asymmetric RTS-CTS range in turn leads to the hidden node problem and the fairness problem in the MAC protocol. Even a symmetric RTS- CTSrangeisnotsufficienttosolvethehiddennodeproblemcausedbyasymmetric 134 RTS-CTS.Toaddressthisproblem,weproposedaMACprotocolthatmakesasym- metric RTS-CTS ranges symmetric using the information available from the given topology. Furthermore, we developed a MAC protocol that adjusts the transmis- sion power for carrier sensing. The effectiveness of the proposed MAC algorithm was demonstrated by extensive simulation results. Finally, a throughput model for a link and a node in a topology-controlled wireless ad-hoc network was presented. This throughput model not only gives accurate throughput information for a link andanodebutalsoprovidesvaluableinformationaboutperformancemeasuresand their relations, which are useful to upper-layer protocols. 7.2 Future Work Mobility has not yet been considered in the design of power-aware topology control and CSMA/CA based MAC protocol for wireless ad-hoc networks in this work. This should be an interesting topic for future study. If mobility is considered, frequenttopologyupdatesarerequiredtoovercomethebrokenlinkproblem, which implies frequent exchange of control messages between nodes. Thus, it will have a significantimpactontheenergyconsumptionofnodes. Besides,sincemobilitymay affecttheresidualenergydistributionamongneighboringnodes, nodeclassification algorithms will be different in static and mobile networks. The MAC protocol will be affected by mobility, too. In the current CSMA/CA based MAC protocol, the RTS-CTSrangeandthecarriersensingrangeareadjustedbasedontheinformation of a given topology. With mobility, the topology information will vary along time so that the corresponding MAC protocol should be modified accordingly. Another problem of interest is the cross layer design between the MAC protocol and the topology control algorithm. In this research, the CSMA/CA based MAC 135 protocol was designed based on the given topology information. However, we have not yet considered the dependence of the topology control algorithm on the oper- ation of the MAC protocol. By taking the advantage of the proposed throughput model, we should be able to get enhanced performance for upper-layer protocols. 136 References [1] [Online]. Available: http:// www.ccsds.org [2] [Online]. Available: http:// www.ipnsig.org [3] [Online]. Available: http:// www.dtnrg.org [4] R. Alena, B. Gilbaugh, B. Glass, and S. P. Braham, “Communication system architecture for planetary exploration,” IEEE Aerosp. Electron. Syst. Mag, Feb. 2001. [5] W. Baek and D. C. Lee, “Caution for initializing and closing CFDP transac- tion,” in Proc. International Telemetering Conference, Las Vegas, NV, Oct. 2001. [6] D.BertsekasandR.G.Gallager,Data Networks,2nded. UpperSaddleRiver, NJ: Prentice Hall, 1962. [7] S. Burleigh, A. Hooke, L. Torgerson, K. Fall, V. Cerf, B. Durst, K. Scott, and H. Weiss, “Delay-tolerant networking: An approach to interplanetary inter- net,” IEEE Commun. Mag., pp. 128–136, June 2003. [8] F.Cali, M.Conti, andE.Gregori, “DynamictuningoftheIEEE802.11proto- col to achieve a theoritical throughput limit,” IEEE/ACM Trans. Networking, vol. 8, pp. 785–799, Dec. 2000. [9] CCSDS File Delivery Protocol (CFDP), Part 1: Introduction and Overview, CCSDS Std. CCSDS 720.1-G-1, January 2002. [10] CCSDS File Delivery Protocol (CFDP), Part 2: Implementers Guide, CCSDS Std. CCSDS 720.2-G-1, January 2002. [11] CCSDS File Delivery Protocol (CFDP), Recommendation for Space Data Sys- tem Standards, CCSDS Std. CCSDS 727.0-B-2, October 2002. [12] J.-H. Chang and L. Tassiulas, “Energy conserving routing in wireless ad-hoc networks,” in Proc. IEEE INFOCOM 2000, Tel Aviv, Israel. 137 [13] X.Cheng,B.Narahari,R.Simha,M.X.Cheng,andD.Liu,“Strongminimum energytopologyinwirelesssensornetworks: NP-completenessandheuristics,” vol. 2, no. 3, pp. 248–256, Jul.-Sep. 2003. [14] K. K. Choi, G. Maral, and R. Rumeau, “The implementation and validation of the new standard CCSDS file delivery protocol for multi-hopped space file transfer,” in Proc. IEEE Aerospace Conference, March 1999. [15] ——, “A new generation space communication protocol standard for multi- hopped file transfer,” in Proc. IEEE Vehicular Technology Conference, May 1999. [16] ——, “Space link simulator for development of a new standard CCSDS file delivery protocol,” in Proc. IEEE Aerospace Conference, March 1999. [17] C. L. Fullmer and J. J. Garcia-Luna-Aceves, “Solution to hidden terminal problems in wireless networks,” in Proc. ACM SIGCOMM’97. [18] R.G.Gallager,Discrete Stochastic Processes. Boston,MA:KluwerAcademic, 1996. [19] S.Gobriel,R.Melhem,andD.Mosse,“Aunifiedinterference/collisionanalysis for power-aware adhoc networks,” in Proc. IEEE INFOCOM 2004. [20] J. Gomez and A. T. Campbell, “A case for variable-range transmission power control in wireless multihop networks,” in Proc. IEEE INFOCOM 2004. [21] J. Gomez, A. T. Campbell, M. Naghshineh, and C. Bisdikian, “Conserving transmissionpowerinwirelessashocnetworks,” in Proc. of IEEE ICNP,Nov. 2001. [22] P. Gupta and P. R. Kumar, “The capacity of wireless networks,” IEEE Trans. Inform. Theory, vol. 46, no. 2, 2000. [23] WirelessLANMediumAccessControl(MAC)andPhysicalLayer(PHY)Spec- ification, IEEE Std. 802.11, 1999. [24] E.-S. Jung and N. H. Vaidya, “A power control MAC protocol for ad-hoc networks,” in Proc. MobiCom’02. [25] L. N. Kanal and A. R. K. Sastry, “Models for channels with memory and their applications to error control,” vol. 66, pp. 724–744, July 1978. [26] S. R. Kim and C. K. Un, “Throughput analysis for two ARQ schemes using combined transistion matrix,” IEEE Trans. Commun., vol. 40, pp. 1679–1683, Nov. 1992. 138 [27] N. R. Kuo, “Mars network operation concept,” in Proc. IEEE Aerospace Con- ference, March 2000. [28] C. H. C. Leung, Y. Kikumoto, and S. A. Sorensen, “The throughput efficiency of the Go-Back-N ARQ scheme under markov and related error structures,” IEEE Trans. Commun., vol. 36, pp. 231–234, 1988. [29] L. Li and J. Halpern, “Minimum energy mobile wireless networks revised,” in Proc. ICC 2001, Helsinki, Finland. [30] N. Li, J. Hou, and L. Sha, “Design and analysis of an MST based topology control algorithm,” in Proc. IEEE INFOCOM 2003, San Francisco, CA, USA. [31] S. Lin, D. J. Costello, and M. J. Miller, “Automatic-repeat-request error- control schemes,” IEEE Commun. Mag., vol. 72, pp. 5–17, Dec. 1984. [32] D. L. Lu and J. F. Chang, “Performance of ARQ protocols in nonindependent channel errors,” IEEE Trans. Commun., vol. 41, pp. 721–730, May 1993. [33] D.S.Mitrinovi´ c, J.E. Pe˘ cari´ c, and A.M.Fink, Classical and New Inequalities in Analysis. Dordrecht, Netherlands: Kluwer Academic, 1993. [34] J. Monks, V. Bharghavan, and W. Hwu, “A power controlled multiple access protocol for wireless packet networks,” in Proc. IEEE INFOCOM 2001. [35] H. Prodinger, “Combinatorics of geometrically distributed random variables: Left-to-right maxima,” Discrete Mathematics, vol. 153, pp. 253–270, 1996. [36] M. Pursley, H. Russell, and J. Wysocarski, “Energy-efficient transmission and routing protocols for wireless multiple-hop networks and spread-spectrum ra- dios,” in EUROCOMM 2000. [37] R. Ramanathan and R. Rosales-Hain, “Topology control of multihop wireless networks using transmit power adjustment,” in Proc. IEEE INFOCOM 2000, Tel Aviv, Israel. [38] V. Rodoplu and T. H. Meng, “Minimum energy mobile wireless networks,” IEEE J. Select. Areas Commun., no. 8, pp. 1333–1344, Aug. 1999. [39] M.Schwartz, Telecommunication Networks: Protocols, Modeling and Analysis. Reading, MA: Addison-Wesley, 1988. [40] S. Singh, M. Woo, and C. S. Raghavendra, “Power-aware routing in mobile ad hoc networks,” in Proc. MobiCom’98, Dalla, Tx, USA. [41] W.Stallings,High-SpeedNetworks: TCP/IPandATMDesignPrinciples. Up- per Saddle River, NJ: Prentice-Hall, 1998. 139 [42] R. M. Taylor, “Space communications,” IEEE Spectr., vol. 29, Feb. 1992. [43] C.-K. Toh, “Maximum battery life routing to support ubiquitous mobile com- puting in wireless ad hoc networks,” IEEE Commun. Mag., 2001. [44] D. Towsley, “A statistical analysis of ARQ protocols operating in a noninde- pendenterrorenvironment,”IEEETrans.Commun.,vol.com-29,pp.971–981, July 1981. [45] W. Turin, “Throughput analysis of the Go-Back-N protocol in fading radiio channels,” IEEE J. Select. Areas Commun., vol. 17, no. 5, May 1999. [46] W. Turin and M. Zorzi, “Performance analysis of delay-constrained communi- cations over slow rayleigh fading channels,” IEEE Trans. Wireless Commun., vol. 1, no. 4, Oct. 2002. [47] H. S. Wang and N. Moayeri, “Finite state markov channel - a useful model for radio communication channels,” IEEE Trans. Veh. Technol., vol. 44, pp. 163–171, Feb. 1995. [48] S.-C.Wang, D.S.L.Wei, andS.-Y.Kuo, “SPT-basedpower-efficienttopology control for wireless ad hoc networks,” in Proc. IEEE MILCOM 2004. [49] X.WangandK.Kar,“ThroughputmodelingandfairnessissuesinCSMA/CA based ad-hoc networks,” in Proc. IEEE INFOCOM 2005. [50] Y. Wang and J. J. Garcia-Luna-Aceves, “Performance of collision avoidance protocols in single-channelad hoc networks,” in Proc. IEEE ICNP,Nov. 2002. [51] S. L. Wu, Y. C. Tseng, and J. P. Sheu, “Intelligent medium access control for mobile ad hoc networks with busy tones and power control,” IEEE J. Select. Areas Commun., vol. 18, pp. 1647–1657, Sep. 2000. [52] J. H. Yuen, M. K. Simon, W. Millar, F. Pollara, C. R. Ryan, D. Divsalar, and J. C. Morakis, “Modulation and coding for satellite and space communi- cations,” in Proc. IEEE, vol. 78, July 1990. [53] M. Zorzi and R. R. Rao, “On the use of renewal theory in the analysis of ARQ protocols,” IEEE Trans. Commun., vol. 44, no. 9, Sep. 1996. [54] ——,“Onthestatisticsofblockerrorsinburstychannels,”IEEE Trans. Com- mun., vol. 45, no. 6, June 1997. 140
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Asset Metadata
Creator
Baek, Wonseok
(author)
Core Title
Reliable and power efficient protocols for space communication and wireless ad-hoc networks
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Electrical Engineering
Publication Date
11/15/2006
Defense Date
09/07/2006
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
OAI-PMH Harvest,wireless communication,wireless network
Language
English
Advisor
Kuo, C.-C. Jay (
committee chair
), Lee, Daniel C. (
committee chair
), Krishnamachari, Bhaskar (
committee member
), Ordonez, Fernando I. (
committee member
)
Creator Email
wbaek@usc.edu
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-m138
Unique identifier
UC1290271
Identifier
etd-Baek-20061115 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-28093 (legacy record id),usctheses-m138 (legacy record id)
Legacy Identifier
etd-Baek-20061115.pdf
Dmrecord
28093
Document Type
Dissertation
Rights
Baek, Wonseok
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Repository Name
Libraries, University of Southern California
Repository Location
Los Angeles, California
Repository Email
cisadmin@lib.usc.edu
Tags
wireless communication
wireless network