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USC Computer Science Technical Reports, no. 878 (2006)
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USC Computer Science Technical Reports, no. 878 (2006)
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An Enhanced Link Availability Model for Supporting Multimedia Streaming in MANETs Min Qin and Roger Zimmermann Abstract—As wireless connectivity is integrated into many handheld devices, streaming multimedia content among mobile ad-hoc peers is becoming a popular application. One of the major challenges in mobile streaming is the requirement that the link must be continuously available for a period of time to enable uninterrupted data transmission and a smooth media performance. Hence, an accurate prediction of future link availability is very desirable. In our previous work, we provided an iterative algorithm for estimating future link availability by using the random walk model. However, this algorithm assumes that all nodes’ current speeds and directions are uniformly distributed between [0, v max ] and [0, 2 π], respectively. With the help of GPS equipment, it is possible for mobile hosts to accurately calculate their current velocity. In this paper, we provide an enhanced link availability model based on our previous approach by utilizing the current velocity information of mobile nodes. To demonstrate the advantage of our model, we compared it with two other link availability models in selecting the best choice among a number of sources. Simulation results show that our model can reduce the number of link breaks and achieve smooth streaming experiences among mobile peers. Index Terms—Link availability, Mobile ad-hoc networks, Mobility models, Stationary regime, Streaming I. INTRODUCTION ITH the widespread use of PDAs and other handhelds, streaming multimedia content between mobile ad-hoc peers is becoming a popular application. Songs, video clips and pictures can all be streamed from one user to another if they get close to each other. Exemplar systems that implement such ideas include Bubbles [1], Mercora [16] and MStream [13, 21]. Most of the recent handheld devices can operate via 802.11 wireless networks, which provide adequate bandwidth and communication range of more than 100 meters. Therefore, streaming among mobile ad-hoc peers is possible in many situations, for example between two patrons visiting a museum. One challenge in sharing multimedia content among mobile peers is to deliver the content, usually large in size, over a dynamic peer-to-peer based network where link availability is constantly changing. To achieve a smooth media performance, link reliability is of crucial importance to media streaming in mobile ad-hoc networks. Since wireless streaming applications require two peers to be continuously connected for a period of time, it is very helpful if we can provide an accurate analysis on future link availability. When a mobile user finds that another user in her vicinity has a song she is interested in, the probability that she can stream that song before the link breaks up is of special interest to her. For example, a typical MP3 music file is 3 MB in size. If the available bandwidth is 256 kbps, a link has to be continuously available for 120 seconds for a song to be successfully streamed. If the file is available from multiple peers, the user should select the source that has the highest probability to stay connected for 120 seconds. B Content holder C Requester Current node movement A Content holder Fig 1. Multimedia content sharing among PDAs. As shown in Fig. 1, the link between A and C and that between B and C are constrained by C’s communication range. If both peer A and B have the file that C requested, it is better to choose peer A as the source since A and C are moving in a similar direction. Therefore, providing an accurate prediction of continuous link availability in the future can help mobile ad-hoc peers determine hand-offs or select the best choice among a number of sources. It is also helpful to many areas in mobile ad-hoc networks, for example: 1) audio/video streaming between mobile peers, 2) file sharing in wireless p2p networks, 3) serving as a basis for existing clustering protocols in wireless ad-hoc networks, and 4) improving existing ad-hoc routing protocols such as DSR[10] and AODV[17]. Due to the unpredictability of human movement, computing future link availability is a very challenging problem. In our previous work [21], we introduced an iterative method for predicting future link availability based on the random walk mobility model [14, 15]. This algorithm assumes that all mobile nodes’ current speeds and directions are uniformly W Manuscript received January 31, 2006 distributed between [0, v max ] and [0, 2 π], respectively. However, the result is unintuitive, namely that that all links have the same future link availability as long as v max and the initial distance between the two nodes remains unchanged. The current velocity of two mobile hosts does have a great impact on future connectivity between them. Therefore, if either one or both nodes’ current velocity is known, this algorithm may not be very accurate in predicting the future link status. With the availability of inexpensive global positioning system (GPS) [26] receivers, more and more mobile clients are able to estimate their velocity accurately. For example, the Dell Axim X51v PDA includes a GPS receiver and sells for $500 dollars. In addition to GPS, Received Signal Strength (RSS) [5, 18], Time of Arrival (ToA) [19, 24] and acoustic sensing [7] can all be used to estimate the location and velocity of a mobile host. Hence it is very helpful if we can take such information into consideration to compute a more accurate estimation of future link availability. In this paper, we extend the result of our previous work to the scenario when either one or both nodes’ current velocities are known. Compared with the original algorithm, this new model proves to be more accurate in predicting future link availability. Like our previous iterative algorithm, our new link availability model is based on the random walk mobility model. In reality, people do walk somewhat unpredictably in environments such as museums, crowded areas, etc. However, our work can be easily extended to other mobility models. To the best of our knowledge, there have been few studies on accurately predicting future link availability over any period of time. Furthermore, our study can be extended to analyze path availability in mobile ad-hoc networks. The paper is organized as follows. In Section II, related work is introduced. Section III describes the assumptions we made for our study. Details of our link availability model are introduced in Section IV and Section V presents its performance. Section VI compares our work with other link availability models. Finally, we summarize our contributions and provide suggestions for further research in Section VII. II. RELATED WORK There are numerous studies on link and path durations in mobile ad-hoc networks (MANET). Many of them are based on the random waypoint model [2]. According to [27], the random waypoint model is considered harmful because it suffers from speed decay and non-uniform node distribution. In [23], the authors presented a numerical study on link and path duration with different mobility models. In [6], the authors validated the results of [23] by using the palm calculus [3]. Both studies analyze the behavior of the network when it has reached the stationary regime, which means the network has run for a long time and node distribution is likely to be fixed [11]. Therefore, these approaches analyze the “average” link or path duration. Also, none of these works predict the future link availability by taking the present node location and velocity into consideration. Therefore, it is inappropriate to apply these models to media streaming applications that often last for a certain period of time. A similar analysis on path availability is given in [4, 28]. Improvements for existing ad-hoc network protocols by utilizing mobility information of mobile hosts are introduced in [12, 20, 25]. The authors predict the disconnection time by utilizing the current location and velocity information of the nodes. All of these techniques assume that when two nodes become neighbors, they will not change their current velocity before the link breaks up. However, this is unrealistic since mobile nodes do change their velocity frequently in many situations. In [14, 15], the authors introduced a probabilistic model for predicting the future status of a link. Their work is based on the random walk mobility model. In their model, link availability is defined as the probability that a link is available at time t 0 +t given that the link is available at t 0 . This definition considers the link as available even if it has experienced disconnections during the interval [t 0 , t 0 +t]. Consequently, their work is not very useful for streaming applications, which require the link to be continuously available over a period of time. An analysis of continuous link availability is given in [8, 9]. In [9], the author first estimates a time period T p that the current link will last if both nodes of the link keep their current movement. Then a statistical method for estimating the possibility L(T p ) that the link can last from t 0 to t 0 +T p is given. In [8], the authors improve their method in [9] by separating the estimation of two statistical constants. Because a link with high L(T p ) may have a very small T p value, the authors use T p ×L(T p ) as a metric to evaluate the reliability of a link. However, for a given t that is not equal to T p , this approach cannot compute the continuous link availability from t 0 to t 0 +t. In [21], we introduced an iterative algorithm to predict L(d,t), which is of special interest to streaming applications. For example, if a song requires 200 seconds to stream, it is more informative to know the probability that the link can last for 200 seconds. This algorithm makes it possible to use L(d,t) directly as a metric in evaluating the reliability of a link. The algorithm assumes that all mobile nodes are unable to estimate their current velocity. Therefore, each node’s current speed and direction are randomly distributed between [0, v max ] and [0, 2 π], respectively. Experimental results show that our algorithm can accurately estimate the future link status with an error margin lower than 7%. Based on this random initial velocity model, we extended it to the case that the current relative velocity between the two nodes can be estimated. However, there are many possible combinations for both mobile nodes’ velocities given the relative velocity between them. As a result, our model shows the average link availability given the current relative velocity. Simulation results show that this relative velocity model works well only when the initial relative speed is low. In this paper, we introduce an algorithm that can predict future link availability given the current velocity of either or both of the nodes. Compared to the results of [21], our new algorithm is more accurate if mobile nodes are able to calculate their velocity through signal strength or GPS systems. III. PROBLEM STATEMENT For simplicity, we assume that the two mobile peers of a given link have the same radio coverage, which is a perfect circle of radius R. The initial distance between the two mobile nodes is approximated by d 0 (d 0 ≤R). An accurate estimation of d 0 can be obtained through Received Signal Strength (RSS) [5, 18], Time of Arrival (ToA) [19, 24] and acoustic sensing [7] or GPS, if applicable. As shown in Fig. 2, let 1 v J K and 2 J J K v represent the current velocities of node n and m. In [21], we provided an iterative algorithm for predicting the probability L(d 0 ,t) that the link will be continuously available from t 0 to t 0 +t given that and are unknown. 1 JK v 2 JJ K v For a given t, our simulation in [21] shows that L(d 0 ,t) does not differ a lot for different d 0 values. This is due to the fact that nodes can either move towards or move away from each other. In this paper, we extend our calculation of 0 (,) Ldt to 0 1 (,, ) JK Ldtv and 012 (,, , ) JK J J K Ldtv v , which are the link availability if either or both nodes’ current velocities can be estimated. Since d 0 ≤R, we have and . 01 (,0, ) 1 = JK Ld v 012 (,0, , ) 1 Ld v v = JK J J K d 0 m n 1 V JK 2 V JK Fig. 2. The current link status between node n and m. We assume the following properties between two mobile ad-hoc peers: 1) Battery power can support the wireless communication for a long time. 2) Two nodes can communicate with each other as long as they are within each other’s transmission range. 3) The wireless bandwidth is enough to support streaming applications, regardless of signal attenuation. To model the movement of a mobile node, we use the random walk model as introduced in [14]. Compared with the random waypoint model [2], the random walk model does not suffer from speed decay and non-uniform node distribution. However, our model can be easily extended to other mobility models. According to [14], a node's movement is divided into a sequence of intervals called mobility epochs. Each epoch is a random period of time that is exponentially distributed with mean λ n -1 . During each mobility epoch, a node moves with a constant speed and direction. The speed is a random variable uniformly distributed between [0, v max ] and the direction is uniformly distributed over [0, 2 π]. Thus given a large mean epoch length, a node is likely to go straight for a long period of time. How to calculate v max and λ n -1 is beyond the scope of this paper. Let λ n -1 and λ m -1 denote the mean epoch lengths of two independent mobile nodes n and m. The possibility that n or m does not change its velocity within t seconds is λ − n t e or λ − m t e , respectively. According to [8], the link duration between n and m can be divided into a number of link epochs. Each link epoch is a time period during which both n and m do not change their velocities. The distribution of each link epoch is also exponential with mean λ -1 , where λ = λ n + λ m . Therefore, the possibility that there is no change in velocities to this link within t seconds is given by λ − t e . IV. CALCULATION OF CONTINUOUS LINK AVAILABILITY A Known Velocity of Single Peer We begin with the case that one node’s current velocity is known. In Fig. 3, for example, node n has GPS equipment and is able to estimate its current speed v 1 and direction θ 1 . Therefore, our goal is to give an accurate estimation of 0 1 (,, ) Ld t v K , which is the probability that both nodes will be continuously connected during [t 0 ,t 0 +t] given that the current velocity of node n is 1 v K . d 0 θ 1 d(t) mn n’ v 1 ω(t) R r r Fig. 3. Link availability if the current velocity of node n is known. Let v 2 and θ 2 denote the current speed and direction of node m. Because m’s current velocity is unknown, v 2 and θ 2 are randomly distributed between [0, v 2max ] and [0, 2 π], respectively. Let 0 1 (,, ) n_variablev L dtv JK and _0 (,, ) n fixedv 1 L dtv J K denote the probability that m and n will be continuously connected for t seconds given that n changes or does not change its current velocity during [t 0 , t 0 +t], respectively. As we have discussed in Section 3, the probability that n does not change its velocity within t seconds is given by λ − n t e . Therefore, the continuous link availability 0 1 (,, ) Ldtv J K is given by: 01 _ 0 1 0 1 (,, ) (,, ) (1 ) ( ,, ) nn tt n fixedv n_variablev L d tv e L d t v e L d tv λ λ − − =+− JKJK K (1) 1) Estimation of 01 JJ K _ (,, ) nfixedv Ldtv Similar to the calculation of 0 1 (,, ) Ldtv JK , we divide the calculation of _ () n fixedv L t into two cases: a) m keeps its velocity during [t 0 , t 0 +t] and b) m changes its current velocity during [t 0 , t 0 +t]. Since n does not change its current velocity, as shown in Fig. 3, it will move to n’ after t seconds. The distance between the current position of m and n’ is given by 222 01 01 1 () 2 cos θ =+ + dt d v t d vt (2) a) m keeps its current velocity during [t 0 ,t 0 +t]. In order for m and n to be continuously connected, m has to be within the shaded region shown in Fig. 3 at t 0 +t. Therefore, we have 2 0 1 12 2 1 12 2 (cos cos)(sin sin) θθ θ θ +− + − ≤ dvt vt vt vt R 22 From the above equation, we get 222 2 2 2 () sin( ) 2() θα + − +≤ dt vt R vtd t 2 (3) where α is determined by 1 sin sin () 1 θ α =− vt dt and 01 1 cos cos () θ α + = dvt dt . Since θ 2 is randomly distributed between [0, 2 π], for a given v 2 , the probability that Equation (3) can be satisfied is 222 2 2 2 11 () arcsin(max(min( ,1), 1)) 22() π +− − dt vt R vtd t − . Therefore, the chance that m and n are continuously connected in this case is given by 2max 22 2 2 2 0 1 2max () arcsin(max(min( ,1), 1)) 2() 1 () 2 v v m dt vt R dv vtd t Lt v π = +− − =− ∫ (4) b) m changes its velocity during [t 0 , t 0 +t]. We use the following method to approximate the probability in this case. Let the random mobility vector () K m R t represent the distance and direction of node m’s position at time t 0 +t with respect to its position at time t 0 . According to [15], () K m R t is approximately Raleigh distributed with a phase uniformly dispersed between [0, 2 π]. Because the maximum distance node m can travel in t seconds is v 2max t, we extend the result of [15] by conditionally limiting the distance range. Thus we have 2 2max 2 (() | ) () α αη − =≤ = m r m m r fR t r r v t e t (5) Where 2 2 (2 / )( ) mmm t m α λδ µ =+ and 2 2max 0 2 () m r vt r m r te α η α − = = ∫ dr . Here m δ and 2 m µ are the mean and variance of node m’s speed. As shown in Fig. 3, m has to be within the shaded region at t 0 +t in order to be connected with n. Therefore, we have . Given R max( ( ) ,0) ( ) ( ) −≤ ≤ + m dt R R t d t R m (t)=r, the probability that m is within the shaded region is constrained by the angle ω(t) shown in Fig. 3. We have 22 2 1 () 2cos , ( ) 2() () 2,0 0,0 ω π − ⎧ +− −< ⎪ ⎪ = ⎨ << − ⎪ ⎪ << − ⎩ rd t R dt R r rd t t rR dt rdt R () () (6) As a result, the probability that m is within n’s range at t 0 +t is 2 2max max( ( ) , ) 2 0 1 () () () m r dt Rv t m r m Lt t α ω πα η − + = = ∫ retdr (7) Here the calculation of 2 () m L t includes the possibility that the link is broken at t 0 +s (s ≤t) and is recovered afterwards. However, when t is small, (1 is close to 0; when t is large, is close to 0. As a result, we can regard the chance that m leaves the communication range of n and then comes back as slim. ) m t e λ − − 2 (/ ) m r e α − Because the probability that m does not change its velocity within t seconds is given by m t e λ − , we have: _01 1 2 (,, ) () (1 ) () m m t t n fixedv m m L dtv e L t e L t λ λ − − =+− J K (8) 2) Calculation of 01 (,, ) JJ K n_variablev Ldtv Now we consider the case that n changes its velocity during [t 0 , t 0 +t]. Suppose node n first changes its velocity at time t 0 +s(s ≤t). Because both n and m’s velocities are random after t 0 +s, we can use our previous result in [21] to calculate the link availability during [t 0 +s, t 0 +t]. As indicated in [21], when the current velocities of both peers are random, different initial distances do not have a big impact on future link availability. This is due to the fact that nodes can either move towards or away from each other. As a result, we can calculate the expectations of the probability that the link is continuously available for t-s seconds. We have 2 0 1 () 2 ( , ) = = ∫ R r prob t rL r t dr R (9) where L(r,t) is the result of our iterative algorithm in [21]. Because n does not change its velocity before t 0 +s, the probability that the link is continuously available during [t 0 , t 0 +s] is given by _ 0 (,, ) n fixedv 1 L dsv JK . Therefore, we have 01 _ 0 1 0 (,, ) (,, ) ( ) n s t n_variablev n n fixedv s L d t v e L d s v prob t s ds λ λ − = =− ∫ JKJK (10) B Known Velocity for Both Nodes When both 1 v J K and 2 v J J K are known, we can extend our result from Section A to derive a more accurate prediction of future link availability. If neither node changes its velocity during [t 0 , t 0 +t], the distance between n and m at t 0 +t will be: 22 0 1 12 2 1 12 2 () ( cos cos ) ( sin sin ) 2 Dtd vt vt v v t θθ θ θ =+ − + − (11) Let T p denote the time at which the link between m and n will break if both of them keep their current velocities. T p can be easily obtained by solving the equation D(T p )=R. Let L 0 (t) represent the probability that both peers are continuously connected and there is no velocity change to the link during [t 0 , t 0 +t]. The possibility that there is no velocity change within t seconds is . Therefore, L (λλ −+ nm t e ) ) 0 (t) is equal to when t ≤T (λλ −+ nm t e p or 0 when t>T p . If there is at least one velocity change to the link during [t 0 , t 0 +t], we can divide t into two parts s(s ≤ t) and t-s so that the first velocity change takes place at t 0 +s. According to the property of a Poisson process [22], the probability that m or n changes its velocity first is given by m λ λ and n λ λ , respectively. Because the link has to be continuously available from t 0 to t 0 +t, we have s ≤T p . At t 0 +s, one node keeps its velocity and the other node randomly changes its velocity. As a result, the situation at t 0 +s becomes the same as what we have discussed in the Section 4. Therefore, we have min( , ) 12 0 0 min( , ) 0 (, , , ) () ( (), , ()) ((), , ()) p p tT s nn n s tT s mm m s L td v v L t e L Ds t s v s ds eL Dst sv sds λ λ λ λ − = − = =+ − ∫ +− ∫ JJJ JJ G JK J J K JJ JJ J J G (12) Because we use the location of m as the reference point in Fig. 3, here and are the velocities of node n and m after adjusting the coordination system to make the position of m and n at t ( ) n v s JJJ JJ G ( ) m v s JJJ JJ J G 0 +s the reference point. V. SIMULATION RESULTS To verify the accuracy of our algorithm, we compared the analytical results of our new link availability model with the actual simulation results. The simulation environment is a two dimensional space. For each simulation, we placed two mobile peers a certain distance apart and conducted 10,000 independent experiments. Then we statistically calculated the probability that the link was continuously available for t seconds based on all the simulation results. For each experiment, we fixed node n’s initial velocity and let node m start with a random velocity. The communication radius R was set to 100m for both nodes. The major issue of our enhanced link availability model is the computational complexity in calculating 0 1 (,, ) n_variablev L dtv J K . As we have discussed in [21], prob(t) can be calculated offline. However, we need to calculate _ 0 (,, ) n fixedv 1 L dsv J K for all s<t. It takes about 4.8 seconds to compute Equation (10) when t=200 on a Pentium 4 1.6GHz laptop. To reduce the computation complexity, we calculate _ 0 (,, ) n fixedv 1 L dsv J K at the following intervals: t, t/2, t/4, and so on. The remaining values are approximated through linear methods. This reduces the computation time to less than 100 milliseconds when t=200 and the maximum error ratio measured between the two methods is within 2%. Fig. 4 shows the results of 14 independent simulations with two different initial speed settings for node n. In Fig. 4, solid lines represent the simulation results and the corresponding dotted lines illustrate the results by using Equation (1). In each figure, different solid lines represent different directions of the initial velocity of n. The mean epoch length is set to 30 seconds in our simulation. In Fig. 4(a) to (c), we set the current speed of node n to 2m/s. In Fig. 4(d) to (f), the current velocity of n is set to 4m/s. The maximum velocity of both nodes is set to 5m/s. When the initial distance is equal to 0 (Fig. 4(a,d)), different θ 1 values produce the same result. As a result, we only show one pair of lines when d 0 =0. 0 50 100 150 200 0.0 0.2 0.4 0.6 0.8 1.0 θ 1 =0 d o =0 Continuous link availability t (sec) Simulation results Predicted results 0 50 100 150 200 0.0 0.2 0.4 0.6 0.8 1.0 θ 1 = π θ 1 = π/2 θ 1 =0 d 0 =50 Continuous link availability t (sec) 0 50 100 150 200 0.0 0.2 0.4 0.6 0.8 1.0 θ 1 = π/2 θ 1 = π θ 1 =0 d 0 =80 Continuous link availability t (sec) (a) v 1 =2 m/s, d 0 = 0 m (b) v 1 =2 m/s, d 0 = 50 m (c) v 1 =2 m/s, d 0 = 80 m 0 50 100 150 200 0.0 0.2 0.4 0.6 0.8 1.0 θ 1 =0 d 0 =0 Continuous link availability t (sec) 0 50 100 150 200 0.0 0.2 0.4 0.6 0.8 1.0 θ 1 = π/2 θ 1 = π θ 1 =0 d 0 =50 Continuous link availability t (sec) 0 50 100 150 200 0.0 0.2 0.4 0.6 0.8 1.0 θ 1 =0 θ 1 = π/2 θ 1 = π d 0 =80 Continuous link availability t (sec) (d) v 1 =4 m/s, d 0 = 0 m (e) v 1 =4 m/s, d 0 = 50 m (f) v 1 =4 m/s, d 0 = 80 m Fig. 4. Continuous link availability with known current velocity of node n, v max =5 m/s, λ n -1 = λ m -1 =30 sec, R=100m. (a) t= 20 sec (b) t= 70 sec Fig. 5. Distribution of continuous link availability L(t) as a function of d 0 and θ 1 , v max =5 m/s, λ n -1 = λ m -1 =30 sec, R=100 m, v 1 =2 m/s. When the current velocity of node n increases from 2m/s to 4m/s, there is a big change on continuous link availability for small t values. However, link availabilities are getting close to each other when t>50. Since the mean epoch length is 30 seconds, node n is likely to move with a random velocity after that period of time. As a result, both nodes can either walk towards or away from each other when t is large. According to our simulation results in [21], a different initial distance between the two nodes does not have a big impact on future link availability. Therefore, the current velocity of node n has a limited impact on continuous link availability in the far future. Fig. 5 shows the distribution of for two given t values. We use the same simulation settings as those used in Figs. 4(a)-(c). As illustrated in Figs. 4 and 5, θ 0 1 (,, ) Ld t v K 1 does not have a big impact on future link availabilities when d 0 is small. However, when d 0 increases from 50m to 100m, we can see a big difference on future link availability for different θ 1 values. This is due to the fact that node n will keep its current velocity during a certain period of time. When d 0 increases, different θ 1 values have a large impact on how far node n can move in one direction before it reaches the boundary of m’s communication range. Fig. 6 shows the average error between the predicted results and the simulation results for all possible θ 1 values. As we have discussed in Section 4, the calculation of 2 () m L t incorporates the random mobility vector () K m R t from [15]. However, as discussed in [15], () K m R t works best for large t and normally distributed speed values. As a result, the predicted results have a bigger error margin for small t values. The error reaches its maximum when t is equal to the mean epoch length. After that, n is more likely to walk with a random velocity and 2 () m L t become a less dominant factor in calculating Equation (1). The maximum prediction error is less than 12%, and for most t values, the error is less than 2%. This demonstrates that our algorithm is very accurate in predicting continuous link availability. 0 50 100 150 200 0.00 0.05 0.10 0.15 Absolute prediction error t (sec) d 0 =0 d 0 =50 d 0 =80 0 50 100 150 200 0.00 0.05 0.10 0.15 Absolute prediction error t (sec) (a) v 1 = 2m/s (b) v 1 = 4m/s Fig. 6. Absolute prediction errors with known current velocity of node n, v max =5 m/s, λ n -1 = λ m -1 =30 sec, d 0 = 50 m, R=100m. 050 0.0 0.2 0.4 0.6 0.8 1.0 100 Predicted results Simulation results Relative velocity model[21] v 1 =v 2 =2m/s, θ 1 =0, θ 2 = π v 1 =1m/s,v 2 =3m/s, θ 1 =0, θ 2 = π Continuous link availability Duration (sec) Fig. 7. Continuous link availability with known initial velocities for both nodes, v max =5 m/s, λ 1 -1 = λ 2 -1 =30 sec, d 0 = 50 m, R=100m. Fig. 7 shows the simulation results when the initial velocities of both nodes can be estimated. We compared the results of our enhanced link availability model with the previous model for known relative velocity in [21]. Given the current relative velocity, there are many possible combinations of both nodes’ velocities. Different combinations may result in different future link availabilities. Therefore, our previous relative velocity model may not be very accurate if both nodes’ velocities are known. In Fig. 7, the current relative velocity is set to 4m/s and the direction is from m to n. The dotted line is the prediction result from our relative velocity model in [21]. We also experimented with two different velocity combinations for the given relative velocity. The solid lines are the simulation results for two different velocity combinations and the corresponding dashed lines are the predictions results. Because it is very likely that the current relative velocity keeps unchanged for a period of time, both models produce the same continuous link availability when t is small. However, when t increases, our algorithm works more accurately than the relative velocity model from [21] if the velocities of both nodes are known. VI. APPLY LINK AVAILABILITY MODEL TO MOBILE STREAMING Mobile devices have recently become a popular platform for streaming applications. Most streaming applications require continuous link availability for a smooth streaming experience, and hence they can benefit greatly from our link availability model to reduce the number of link breaks and to achieve a smoother streaming performance. One benefit that our link availability algorithm can provide is to help mobile users select the best choice among a number of sources or destinations. To demonstrate the benefits of our link availability model in maintaining smooth streaming experiences, we integrated our link availability algorithm into the MStream system. MStream [13, 21] is designed to provide a location sensitive audio streaming service to multiple mobile devices. It runs on Microsoft Windows Mobile 2003 and utilizes 802.11 wireless networks. The viability of such an approach has been enabled by the proliferation of affordable wireless networking, most notably the pervasive availability of 802.11 networks. The bandwidth provided by different forms of the 802.11 standard is sufficient for audio streaming, especially since modern audio compression algorithms provide excellent aural quality at a moderate data rate. In addition, new generation handheld devices such as the HP5555 PDA now provide high computing capabilities along with longer battery life, which together make our application feasible. The original MStream protocol requires a central server to distribute multimedia content initially. Here we extend it to pure mobile peer-to-peer (p2p) streaming scenarios. The interaction between two mobile peers unfolds in several phases as follows. The application periodically polls the GPS reading from an attached GPS unit as shown in Fig. 7. It utilizes such information to calculate its own speed distribution. If the GPS is unavailable, fixed speed distribution and position information is used. To request streaming service, a mobile peer broadcasts the streaming request to nearby neighbors. After receiving the request, neighbors that store the requested multimedia content reply to the peer with their velocity and location information. The peer then contacts the neighbor that has the highest continuous link availability for the remaining streaming process. Fig. 8. The MStream application running on an HP iPaq h5555 PDA with a Pharos GPS unit support. A Support MStream with Known Streaming Time When wireless bandwidth is stable, it is possible for streaming applications to predict the transmission time. Therefore, we can use the remaining streaming time with our link availability model to select the best source among a number of neighboring nodes. For example, if an audio file requires 100 seconds to stream and the client has already recorded 30% of the content, then our algorithm chooses an available neighbor that has the highest continuous link availability for streaming the remaining 70% of the content. TABLE I SIMULATION SETTINGS Parameters Value Total number of clients 100 Simulation area [0, 300m] 2 Communication range of all nodes 100 m Mean epoch length of each client 30 sec Number of initial content holders 10 Time to stream the multimedia file 150 sec Connection setup time (buffering, negotiation, etc) 1 sec To demonstrate the usefulness of our link availability model, we conducted 200 independent simulations with the settings shown in Table 1. We assume that all nodes are location aware and are able to measure their current velocity through GPS or acoustic sensing. 100 clients are randomly dispersed into the simulation area. Ten of them store the multimedia content that will be requested by the other nodes. The streaming time is set to 150 seconds for the multimedia content to be successfully streamed. We chose random walk with reflection as the mobility model. When a user reaches the boundary of the simulation area, she changes her direction as if she was reflected by a mirror. During every second, each user has a 0.5% probability of requesting the multimedia content. After finishing streaming the content once, the client no longer requests it and becomes a potential source for further requests. We run the system until all users in the area have streamed the content once. If the link breaks up during the streaming, a client waits until an alternative link is available and requests the remaining stream from that link. Each client is given a random maximum velocity from 1m/s to 4m/s. For a comparison with our algorithm, we incorporated the link availability models from [9] and [20]. For the link availability model from [9], we first estimate a time period T p that the current link between the peer and its neighbor will last if both nodes keep their current velocity. Then we let the peer choose the neighbor that has the highest T p ×L(T p ) value. For the model from [20], we assume that all nodes will move with the current velocity before the link breaks up. Therefore, we let the mobile peer choose the source that has the highest T p value. Fig. 9 shows the simulation results by using these three different link availability models with various mean epoch length settings. To have a smooth streaming experience, the number of link breaks during streaming should be kept to a minimum. Fig. 9(a) shows the average number of link breaks a client suffers during the streaming process. Our link prediction model exhibits the smallest number of link breakdowns. As described in Section II, using T p ×L(T p ) cannot reflect the actual link availability over time. The result of using T p ×L(T p ) (see dashed line in Fig. 9) is even worse than that of assuming nodes do not change their velocities in the future. However, it keeps improving when the mean epoch length increases. On the other hand, our link availability model can predict continuous link availability over any short period of time. Therefore, it is more accurate in predicting the reliability of a link, especially when nodes tend to change their velocities frequently. According to our study in [21], smaller epoch lengths result in higher future link availability. When the mean epoch length reduces from 40 to 10 seconds, as indicated in Figs. 9(a, b), our link availability model can reduce the number of link breaks by 0.31 and increase the percentage of clients that do not suffer any link breaks by 19%. These results demonstrate a significant advantage of our algorithm over the other two link prediction models. Assuming no velocity change Link availability model of [9] Our enhanced link availability model 10 20 30 40 0.6 0.9 1.2 1.5 # of link breaks Mean epoch length (sec) 10 20 30 40 30 40 50 60 % of nodes Mean epoch length (sec) 10 20 30 40 60 70 80 90 Continuous duration (sec) Mean epoch length (sec) (a) Average number of link (b) Percentage of clients that (c) Average continuous streaming breaks during the streaming do not suffer any link breaks duration before a link breaks or streaming finishes Fig. 9. Simulation results of supporting mobile p2p streaming with different link availability models. Fig. 9(c) shows the average duration that a streaming process can last without any interruptions. When the streaming process starts or when it recovers from a link break, it is often desirable to prolong the duration that it can continuously stream the audio until a link breakdown takes place. Compared with the other two scenarios, our algorithm yields a longer continuous streaming duration. Therefore, even if there are link breaks, the streaming process is continuous most of the time. As shown in Fig. 9, the performances of these three link availability models are converging when the mean epoch length increases. As the mean epoch length increases, nodes tend to move in a straight direction. All three models should have a similar performance when assuming nodes do not change their velocities in the future. Therefore, our link prediction model is particularly suited for environments in which velocity change is frequent. B Locating Stable Links with Unknown Streaming Time In many situations, predicting the actual streaming time can be very hard due to bandwidth variations. Therefore, it is more desirable to select a media source that has the longest continuous link duration. For example, consider the scenario where a tourist is wandering in a dark forest and several firefighters are searching to try to locate her. If there is no cell phone signal in the surrounding area, ad-hoc live audio streaming becomes the preferred communication method. It may require several minutes for the tourist to explain her situation clearly to firefighters. Thus how to select the best nearby firefighter so that she can talk to him as long as possible is very crucial. In such a situation, it is hard to determine how long the streaming application is going to last. Therefore, we should choose the source that has the maximum value. 0 () tL t dt ∞ ∫ However, computing is very time consuming since it involves the calculation of L(t) for all possible t values. Therefore, it is impractical to use in evaluating link reliabilities in real time. To reduce the computation time, we can select a certain t and compare different links’ continuous availability during [t 0 () tL t dt ∞ ∫ 0 () tL t dt ∞ ∫ 0 , t+t 0 ]. To evaluate the correctness of such an approximation, we conducted 300 independent simulations by randomly placing 20 moving media sources around a mobile requester. Each node starts with a random speed between 1 to 4m/s and a random direction between [0, 2 π]. When the simulation begins, the requester chooses a neighboring source that has the highest continuous link availability during [t 0 +t]. Then we calculate the actual continuous link duration between the requester and the source. We experimented with three different t values and compared our results with those of the other two link prediction models in the previous section. Fig. 10 shows the average continuous link duration between the source and the requester with different mean epoch length settings. As shown in Fig.10, our link availability model achieves similar link durations for different t values. Therefore, we can randomly choose a reasonable t value and it will not largely affect the performance of our algorithm. Unlike what is shown in Fig. 9, the performance of the link availability model from [9] shown in Fig. 10 works better than that of assuming there will be no future velocity change. Therefore, it is more suited for predicting the reliability of a link. Since all three link prediction models try to find the link that is possibly the most reliable, it is probable that they do not locate the link that is actually the longest lasting. Therefore, as shown in Fig. 10, the maximum possible link duration in the simulation is much higher than that of using our enhanced model. Our link prediction model outperforms the other two models by 16- 80% when the mean epoch length decreases from 60 to 10 seconds. This demonstrates a significant advantage when velocity change is frequent. 10 20 30 40 50 60 100 200 300 400 500 600 Continuous link duration (sec) Mean epoch length (sec) Our enhanced model,t=50 Our enhanced model,t=100 Our enhanced model,t=150 Maximum possible duration Assuming no velocity change Link availability model of [9] Fig.10. Average continuous link duration between the requester and the source with different link prediction models. VII. CONCLUSIONS In this paper, we introduce a new algorithm for predicting future link availability by utilizing the current velocity information of mobile hosts. This algorithm can help to improve the streaming experience and select better sources in a wireless p2p streaming environment. Compared to our previous techniques, this work provides a more accurate prediction if velocity information of mobile hosts is known. With an average error margin of less than 2%, our algorithm is excellently suitable and advantageous for many applications. To study the usefulness of our link prediction model, we integrated our algorithm with the MStream mobile p2p streaming architecture. Simulation results illustrate that our algorithm can improve the streaming experience by reducing the number of link breaks, increasing the probability of not suffering from any link breaks and providing a longer continuous streaming duration. We plan to extend our work in multiple directions. First, we intend to study other mobility models for their link availability estimation. Second, we will integrate our link availability model into existing routing protocols, such as DSR and AODV. We believe these protocols will benefit significantly from our algorithm. For mobile ad-hoc networks, constraints such as battery power and available bandwidth are not addressed in this paper. We will extend our current research to further analyze these issues. ACKNOWLEDGMENT This research has been funded in part by NSF grants EEC- 529152 (IMSC ERC), MRI-0321377, and CMS-0219463, and unrestricted cash/equipment gifts from the Lord Foundation, Hewlett-Packard, Intel, Sun Microsystems and Raptor Networks Technology. REFERENCES [1] E. Bach, S. S. Bygdås and M. Flydal-Blichfeldt, et al. “Bubbles: Navigating Multimedia Content in Mobile Ad-hoc Networks,” Proc. 2nd International Conference on Mobile and Ubiquitous Multimedia, Norrköping, Sweden, December 2003. [2] F. Bai, N. Sadagopan, A. Helmy. “IMPORTANT: A framework to systematically analyze the Impact of Mobility on Performance of RouTing protocols for Adhoc NeTworks,” Proc. IEEE INFOCOM 2003, San Francisco, CA, March 2003. [3] F. Baccelli and P. Br´emaud. Palm Probabilities and Stationary Queues. Springer Verlag Lecture Notes in Statistics, 1987. [4] M. Gerharz, C. Waal, P. Martini, P. James. “Strategies for Finding Stable Paths in Mobile Wireless Ad-hoc Networks,” Proc. of the 28th IEEE Conference on Local Computer Networks (LCN), pp. 130-139, Königswinter/Bonn, Germany, October 2003. [5] L. Girod and D. Estrin. “Robust range estimation using acoustic and multimodal sensing,” Proc. IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2001), Maui, Hawaii, October 2001. [6] Y. Han, R. J. La, and A. M. Makowski. “Distribution of path durations in mobile ad-hoc networks -- Palm's theorem at work,” 16th ITC Specialist Seminar, Belgium, September 2004. [7] J. Hightower, R. Want, and G. B. Spoton. “An indoor 3d location sensing technology based on RF signal strength,” Technical Report UW CSE 00-02-02, University of Washington, Department of Computer Science and Engineering, Seattle, WA, February 2000. [8] S. M. Jiang. “An Enhanced Prediction-Based Link Availability Estimation for MANETs,” IEEE Trans. on Communications, Vol. 52, No. 2, Feb. 2004, pp. 183-186. [9] S. M. Jiang, D. J. He and J. Q. Rao. “A Prediction-based Link Availability Estimation for Mobile Ad-hoc Networks,” Proc. IEEE INFOCOM 2001, Alaska, USA, April 2001. [10] D. Johnson and D. Maltz. Dynamic source routing in ad hoc wireless networks. Mobile Computing, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1996. [11] J.-Y. Le Boudec and M. Vojnovic. “Perfect Simulation and Stationarity of a Class of Mobility Models,” Proc. IEEE INFOCOM 2005, Miami, Florida, 2005. [12] B. Li, K. H. Wang. “NonStop: Continuous Multimedia Streaming in Wireless Ad Hoc Networks with Node Mobility,” IEEE Journal on Selected Areas in Communications, Vol. 21, No. 10, December 2003, pp. 1627-1641, [13] L. S. Liu, R. Zimmermann and W. Carter. “MStream: Position-aware Mobile Music Streaming,” Proc. Third Annual International Conference on Mobile Systems, Applications and Services (Mobisys 2005), Seattle, Washington, June, 2005. [14] A. B. McDonald and T. Znati. “A Path Availability Model for Wireless Ad-Hoc Networks,” Proc. IEEE Wireless Communications and Networking Conference, NewOrleans, LA, September 21-24, 1999. [15] A. B. McDonald, and T. Znati. “A Mobility Based Framework for Adaptive Clustering in Wireless Ad-Hoc Networks,” IEEE Journal on Selected Areas in Communications, Vol. 17, No. 8, Aug. 1999, pp. 1466- 1487. [16] Mercora, http://www.mercora.com/ [17] C. E. Perkins and E. M. Royer. “Ad hoc On-Demand Distance Vector Routing,” Proc. 2nd IEEE Workshop on Mobile Computing Systems and Applications, New Orleans, LA, February 1999, pp. 90-100. [18] N. Patwari, A. O. Hero, M. Perkins, N. S. Correal and R. J. O'Dea. “Relative Location Estimation in Wireless Sensor Networks,” IEEE Trans. on Signal Processing, vol. 51, no. 8, August 2003, pp. 2137-2148. [19] N.B. Priyantha, A. Chakraborty, and H. Padmanabhan, “The cricket location support system,” In Proceeding of 6th ACM International Conference on Mobile Computing and Networking (MOBICOM), pp.32-43, Boston,MA, Augest 2000. [20] L. Qin and T. Kunz, “Increasing packet delivery ratio in DSR by link prediction,” Proc. 36th Hawaii International Conference on System Sciences (HICSS-36), Hawaii, January 2003, pp. 300-309 [21] M. Qin, R. Zimmermann and Leslie S. Liu. “Supporting Multimedia Streaming Between Mobile Peers with Link Availability Prediction,” ACM Multimedia 2005, Singapore, November 6-12, 2005 [22] S. M. Ross. Introduction to Probability Models, Academic Press, December 2002. [23] N. Sadagopan, F. Bai, B. Krishnamachari and A. Helmy. “PATHS: analysis of PATH duration statistics and their impact on reactive MANET routing protocols,” Proc. 4th ACM International Symposium on Mobile Ad-hoc Networking and Computing, Maryland, USA, June 2003, pp 245-256. [24] A. Savvides, C.-C. Han, and M. Srivastava, “Dynamic fine-grained localization in ad-hoc networks of sensors,” In 7th ACM Int. Conf. on Mobile Computing and Networking (Mobicom), pages 166 -179, Rome,Italy, July 2001. [25] W. Su , S. J. Lee , M. Gerla. “Mobility prediction and routing in ad hoc wireless networks,” International Journal of Network Management, Vol.11, No.1, Jan. 2001, pp.3-30. [26] B. H. Wellenhoff, H. Lichtenegger, and J. Collins, Global positioning system: theory and practice, Fourth Edition. Springer Verlag, 1997. [27] J. Yoon, M. Liu, and B. Noble. “Random Waypoint Considered Harmful,” Proc. IEEE INFOCOM 2003, San Francisco, CA, March 2003. [28] D. Yu, H. Li and I. Gruber. “Path Availability in Ad-hoc Network,” International Conf. on Telecommunications (ICT 2003), Tahiti France, February 2003.
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Min Qin, Roger Zimmermann. "An enhanced link availability model for supporting multimedia streaming in MANETs." Computer Science Technical Reports (Los Angeles, California, USA: University of Southern California. Department of Computer Science) no. 878 (2006).
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