Performance Analysis of the Vehicular Delay Tolerant Network

Transcription

1 Performance Analysis of the Vehicular Delay Tolerant Network Dusit Niyato, Ping Wang, and Joseph Chee Ming Teo School of Computer Engineering, Nanyang Technological University (NTU, Singapore Institute for Infocomm Research, Singapore Abstract Delay tolerant network (DTN based on vehicular communications (ie, vehicular delay tolerant network or VDTN is considered in this paper In VDTN, there is no direct end-toend connection between the source and destination (ie, sink In this case, the traffic source transmits data to a mobile router This mobile router in a vehicle receives and stores data in a buffer The vehicle can move and once it is in the transmission range, the data in a buffer is forwarded to the sink The buffer management and its queueing model are proposed to analyze the performances of a mobile router in this vehicular delay tolerant network With this analytical model, various performance measures (eg, throughput and delay can be obtained This queueing model is then used as a tool to study the behavior of the traffic source in a competitive environment which is due to the fact that the transmission resources of a mobile router are shared among multiple traffic sources Therefore, the traffic sources have to noncooperatively optimize their transmission strategies to achieve the highest utility This queueing model formulation will be useful to investigate the performance and behavior of the vehicular delay tolerant network Keywords-Delay tolerant network, queueing analysis I INTRODUCTION Delay or disruption tolerant network (DTN has been introduced for the situation where the connection between the nodes is sparse As a result, unlike traditional mobile ad hoc network (MANET, the end-to-end path between a source and destination (eg, gateway or sink will only be available for a brief and unpredictable period of time DTN has gained research attention due to its variety of applications in military, disaster discovery, and emergency response systems where the communication infrastructure may not exist In DTN, the data from the source is relayed through mobile nodes to the destination However, when the connection to other nodes is not available, the data is stored in the buffer Once the mobile node travels into the transmission range of other nodes, the data in a buffer can be forwarded to the next hop In this way, the packet can reach the destination by hopping over the mobile nodes even though the connection between the mobile nodes may not be always available The major research issues in DTN are the routing protocol [], [2], [3], the investigation of DTN in various applications [4], [5], [6], and the performance analysis [7], [8], [9], [0] However, the current literature on DTN research does not consider the buffer management mechanism nor queueing model for a mobile router More importantly, the interaction among the traffic This work was supported by a grant from the Nanyang Institute of Technology, Singapore, and in part by the Natural Sciences and Engineering Research Council (NSERC of Canada sources in the DTN under noncooperative environment was never considered in the literature In this paper, we consider delay tolerant network based on the vehicular communications which is referred to as vehicular delay tolerant network (VDTN In VDTN, the traffic sources and sinks do not have a direct transmission path among each other However, a vehicle is used as a carrier to carry the data from traffic sources to sinks When a vehicle moves into the transmission range of traffic source, the roadside unit of traffic source transmits the data to a mobile router deployed in that vehicle This vehicle can travels among places and again once it moves into the transmission range of the sink, a mobile router transmits data in its buffer to the roadside unit of the sink Note that this packet delivery scheme is similar to the core-aided scheme in [7], in which the packet is stored and forwarded by the core node (ie, a mobile router The performances of a mobile router in a vehicle is studied by formulating the queueing model With this analytical model, various performances of the mobile router to forward data from the traffic sources to the sink can be obtained Then, since the data from multiple traffic sources share the resources (ie, buffer and transmission time of a mobile router, the transmission parameter (ie, transmission rate or transmission probability of one traffic source will affect the performance and hence the utility of other traffic sources (ie, opponents We study this competitive situation by formulating a noncooperative game model The solution of this game is obtained as the Nash equilibrium which ensures that none of the traffic source will change the strategy, given a set of strategies of other traffic sources The queueing model for a mobile router and the noncooperative game model for the traffic sources will be useful to analyze the performance and behavior of the independent entity in the vehicular delay tolerant network II RELATED WORK Routing is one of the important issues in delay tolerant network (DTN, [], [2], [3] The major objectives of routing in DTN is to deliver packets from the source to the destination by means of mobility of the node Since the end-to-end path may not be available, routing schemes have be optimized the data dissemination by utilizing the connectivity information and network conditions maintained by each node For example, in [], the routing scheme based on the estimates of the average inter-contact time between the mobile nodes in the network was proposed This routing scheme was designed to minimize the packet delivery time The routing properties in

2 2 terms of loop-free forwarding and polynomial convergence were studied which ensure the performances of the packet delivery in DTN In [2], the packet delivery scheme based on the super node architecture and epidemic routing was introduced With epidemic routing, the packet is forwarded to other contacted nodes (ie, nodes with direct connection Unlike traditional epidemic routing, the packet is forwarded to the super nodes to improve the performance and reduce overhead The super nodes are then responsible to carry the packet to the destination In [3], the routing in DTN based on thermodynamics was presented In this scheme, the concept of temperature is applied to each node to measure the amount of data that can be delivered to the destination The control of temperature (ie, packet forwarding is based on the principles that govern the heat transfer between object For example, the amount of heat (ie, packets to be transferred between two nodes is proportional to the difference in their temperature With this thermodynamics inspired routing scheme, the rate of successful packet delivery can be significantly improved DTN was applied to many applications (eg, [4], [5], [6] In [4], vehicle-to-vehicle (V2V communication based on DTN was proposed The issues of V2V communication in high and predictable mobility, the large scale network, and partitioned network were discussed when applying DTN routing and packet delivery policy Also, the experimental platform was developed In [5], the sensor network based on DTN was proposed This sensor network based on DTN was applied to monitor lake water quality in rural lake and noise level logging in urban areas and along highways Again, the prototype for these applications was developed In [6], the application of DTN in business application was reported and a coordination protocol was developed Such a protocol can be used for financial application in a mobile network environment With DTN architecture, the distributed transaction processing and management can be supported even though the connection among business entities is not always available To understand the performance of DTN under node mobility, the analytical models were proposed (eg, [7], [8], [9], [0] For examples, in [7], the mobility model for a mobile node in DTN was proposed Given this mobility model, the packet delivery ratio and delay were analyzed In addition, the queueing model of the traffic source was formulated In [8], the performance of epidemic routing scheme was studied using continuous-time Markov chain The state of the system is the number of nodes in the network having the packet The packet reaches the sink which is considered to be the absorbing states in the model The delay of the packet delivery was derived In [9], the performances of homing pigeon based DTN were analyzed In such a network, each node has a dedicated messenger (ie, pigeon This messenger periodically carries a batch of packet from the home node (ie, source node, delivers to the destinations, and returns home The travel of a messenger has the fixed route and speed The analytical model was developed to obtain the waiting time of the individual and bulk packets However, none of the abovementioned work considered the queue at a mobile router III SYSTEM MODEL We consider a network which is composed of I locations In this network, there are multiple traffic sources sending data to the sinks However, there is no direct connection between the traffic source and sink In this case, there are total N mobile routers, each of which is installed on a vehicle, in this network A mobile router receives data from the traffic sources This data is stored in a buffer Then, once the vehicle moves into the transmission range of a sink, the data is retrieved from a buffer and forwarded to the sink We assume that the vehicle moves among locations in a network randomly with random speed The traffic sources and sinks are connected with the roadside units communicating with a mobile router (Fig A mobile router uses a single queue to buffer data delivering to the same sink regardless the traffic source In particular, the data of multiple traffic sources whose destination is sink i (ie, a roadside unit of sink i is at location s i is aggregated into the same queue The transmission between the roadside unit and mobile router on the vehicle is time-slot based The successful transmission between a traffic source, mobile router n, and a sink at any location s i is denoted by µ (n i for i {,, I} and n {,, N} Fig Traffic source s 2 Traffic source s 4 s 3 s System model for the MMR network Traffic source s 5 Sink Note that this system model can be applied to the application of environment monitoring In this case, a data source is a sensor node The vehicle of the observer visits these sensors occasionally The data collected from the sensors is transported to the data center IV QUEUEING ANALYSIS OF VEHICULAR DELAY TOLERANT NETWORK ROUTER In this section, the queueing model based on discretetime Markov chain is formulated for a particular buffer in a mobile router of a vehicle We first define the state space The probability transition matrix is derived The method to obtain the steady state probability is presented, and the performance measures are obtained A State Space and Transition Matrix Let S denote a set of the locations in a network The state space of a queue in a mobile router buffering the packet with destination at sink i can be expressed as follows: Ψ (n i = {(S, X ; S S, X {0,, }} (

3 3 where S is the location of a vehicle and X is the number of packets in a queue At a traffic source i, the packets are transmitted to a mobile router n when a vehicle is in the transmission range of a roadside [ unit of a traffic source at location ] s i Let d (n i i = d (n i i,0 d (n i i,k d (n i i,d denote a row matrix of packet transmission probability by a traffic source i to a mobile router n with a destination sink at location s i (ie, sink i in short D is the maximum batch size where k = {0,, D} The element of this matrix d (n i i can be obtained, for example, from the probability of using different modulation and coding rate [] At a mobile router n, the packet arrival probability of a queue for the packet with destination at sink i can be obtained from D a (n i i,k = ( d (n k i i,k (µ (n k i k ( µ (n i k k (2 k =k for k = {0,,, D} The average transmission rate of a traffic source i to a mobile router n with destination sink i can be obtained from λ (n i i = D k= ka(n i i,k and total transmission rate is λ i i = N n= λ(n i i, where N is the total number of vehicles in the network The traffic source can control this transmission rate to achieve the highest utility In this regard, the equilibrium transmission rates will be obtained from a noncooperative game formulation which will be presented later in this paper Similarly, the departure probability of a queue in a mobile router n transmitting to a sink i can be obtained from r (n i,k = D k =k e (n i,k ( k k (µ (n i k ( µ (n k i k where e (n i,k is the probability of transmitting k packets by a mobile router in a time slot For a queue buffering the packet with destination sink i of a mobile router n, the state representing the location in a network can be divided into three subsets These subsets are a subset of locations of traffic sources, a subset of location of a sink, and a subset of locations without traffic source and sink which are respectively denoted by S sour n,i, Ssink n,i, and Sroad n,i For an example of network in Fig, we have s, s 2, s 3 S sour,5, s 4 S road,5, and s 5 S sink,5 for mobile router n = and sink i = 5 The mobility of a vehicle with mobile router n among the locations in a network can be modeled using transition matrix M (n which is defined as follows: M (n =,,I I, I,I (3 (4 where I = S is the total number of locations in a network, where S is the cardinality of set S (eg, I = 5 for a network shown in Fig for i,î Iî= = denotes the i,î probability of a vehicle n staying at location s i in the current time slot and moving to location sî in the next time slot B Transition Matrix The state transition matrix of a queue in a mobile router is denoted by P which is defined as follows: D E F G H P = F 2 G 2 H 2 (5 where D = E = F k = G k = H k = p 0,0 p 0,D p D,0 p D,D p 0,D p D,D p D,2D p kd,(k D p kd,kd p (k+d,kd p kd,kd p kd,(k+d p (k+d,kd p (k+d,(k+d p kd,(k+d p (k+d,(k+d p (k+d,(k+2d where each row of this matrix P indicates the number of packets in queue The element p x,x denotes the probability matrix for the number of packets in queue changes from x in the current time slot to x in the next time slot This matrix can be defined as follows: p, (x, x p x,x = M (n (6 pi,i(x, x where each row of this matrix p x,x indicates the location of a vehicle The element of this matrix p x,x can be obtained from a (n p i,i (x, x i i,x x, i Ssour n,i, x x = r (n i,x x, i Ssink n,i, x x (7 0, otherwise For matrix p x,0 which captures the case that the number of packets in queue is smaller than the transmission rate of a mobile router The element p x,0 of matrix D is denoted by p i,i (x, 0 where p i,i (x, 0 = D k=x r (n i,k, for i Ssink n,i (8 Note that F = = F k =, G = = G k =, and H = = H k = The stability of a queue can be determined from the condition θh k < θf k, where θ = θk, θ =, K = F k +G k +H k, and is a row matrix of

4 4 with a proper size If the stability condition is satisfied, there is a matrix R which is the minimal non-negative solution of such that R = F k + RG k + R 2 H k (9 π i+ = π i R (0 This matrix R can be obtained iteratively by using R(t + = F t + R(tG k + R 2 (th k ( until the condition max i,j R i,j (t + R i,j (t < ɛ is satisfied Here, R i,j (t is the element of matrix R(t and ɛ is a small number (eg, ɛ = 0 9 Next, the matrices of steady state probabilities π 0 and π are obtained by solving the following equations: [ ] D E B(R = (2 F k G k + RH k [π 0, π ] = [π 0, π ] B(R (3 = π 0 + π (I R (4 where I is an identity matrix with a proper size The steady state probability of a queue with x packets when a vehicle is at location s i can be obtained from π(i, x = [ ] π x/d (5 xd+i which is the xd + i element of a row matrix π x/d C Performance Measures Average Number of Packets in Queue of a Mobile Router: The average number of packets in queue in a mobile router n for the packet with destination sink i can be obtained from ( I x (n i X = x x= i= π(i, x (6 where this calculation is truncated at X for which X I x= i= π(i, x < ɛ 2 Throughput: The throughput of a traffic source i transmitting packet to a mobile router n to the destination sink i can be obtained from τ (n i i = φ(n i λ (n i i, for i Ssour n,i (7 where φ (n i is the probability that a vehicle n is at location s i This probability φ (n i can [ be obtained by solving φ = φm ] (n and φ =, and φ = φ (n φ (n i φ (n The I total queue throughput is τ (n i = (n φ i λ (n i i (8 i S sour n,i 3 Average Packet Delivery Delay: The average delay can be obtained using the Little s law as follows: w (n i = x(n i (9 τ (n i D Queueing Performances We consider the networks as shown in Fig The maximum transmission range between the roadside unit and mobile router is 25 meters The typical vehicle speed is 45km/h The successful transmission probability is µ = 095 We assume that a single rate transmission is used by a traffic source and a mobile router (ie, D = In this regard, a traffic source chooses a transmission probability in which d (n i i, = λ(n i and d (n i i,0 = λ(n i for i = 5 For a network model shown in Fig, the mobility transition matrix can be expressed as follows: M (n =, 0 0, 0 0 2,2 0 2, ,3 3,3 0 4, 4,2 4,3 i 4 m(n 4,i 4, ,5 5,5 With an average vehicle speed v (n i at location s i (, the probability i,i can be obtained from i,i = min, v(n i T 2E i where E i is the transmission range and T is the length of time slot For the numerical results, we assume that a vehicle travels to locations (ie, states s, s 2, s 3, and s 5 with probabilities 009, 02, 05, and 064, respectively Fig 2 shows an average packet delivery delay under different vehicle speeds As expected, as the speeds of vehicle increases, the duration of a mobile router without connection to the traffic sources and a sink becomes shorter Consequently, the packet delivery delay decreases Also, as the transmission probabilities of all traffic sources increase (ie, , the average packet delivery delay increases since there is more average number of packets in a queue of a mobile router For brevity of the paper, we omit the plot of queueing performances whose results are expected (eg, as the transmission probability increases, the performances degrade, and so on Avearge delay (seconds Fig =005 i =0020 i Speed of vehicle (km/h Packet delivery delay under different speeds of vehicle V COMPETITION AMONG TRAFFIC SOURCE In this section, the competition among traffic sources to share the resource of a mobile router to deliver their packets to the sinks is formulated as a noncooperative game The definitions of the utility and the Nash equilibrium solution for the strategies of the traffic sources are presented

5 5 A Noncooperative Game Formulation The noncooperative game formulation of this network can be described as follows The players of this game are the traffic sources The strategy of each player is a set of the transmission probabilities to the different mobile routers The payoff is defined as the utility which is the function of the throughput and cost as follows: U i (λ i, λ i = N ( ( u log + u 2 τ (n i i (λ n= i u 3 C (x (n i (λ (20 where u, u 2, and u 3 are the constants λ i is a set of strategies of a traffic source [ i for all mobile routers and all destination ] sinks, ie, λ i = λ (n i λ(n λ I i is a set of strategies of all other opponents, and λ is a set of strategies of all traffic sources C (x is the cost function of a traffic source (eg, price charging by a mobile router or delay In this paper, we assume that this cost is a linear function of the average number of packets in queue which is a function of the strategies of all traffic sources (ig, x (n i (λ If all traffic sources are rational to maximize their utilities, the Nash equilibrium can be considered as the solution for the transmission strategies The Nash equilibrium of a noncooperative game is a set of strategies λ i with the property that no player can increase his payoff by choosing a different action, given other players sets of strategies λ i That is, U i (λ i, λ i U i (λ i, λ i, i (2 The Nash equilibrium can be obtained from best response of each player This best response is defined as an optimal set of strategies of a particular player given the strategies of other players The best response of a traffic source i is defined as follows: λ i = BR i (λ i = arg max λ i U i (λ i, λ i (22 However, since the utility which is a function of the throughput and the average number of packets in queue (ie, τ (n i i and x (n i are obtained from the queueing model, numerical method is applied to obtain the best response of each traffic source The Nash equilibrium is considered to be the solution of the following optimization formulation Minimize: for î i I ([ λ i BR i λî ] (23 i= B Numerical Results We consider the case of a single vehicle and a single sink as shown in Fig Fig 3 shows the utility of a traffic source where 2 = 3 = 004 As the transmission probability increases, the utility of a traffic source first increases due to the achievable throughput τ ( 5 However, at a certain point, the utility decreases, since a queue of a mobile router becomes congested and the increase in cost is at a higher rate than that of throughput The highest point of the utility is defined as the best response of a traffic source given the strategies 2 and 3 of the opponents This best response is different for the different transmission duration of a vehicle at a sink In other woard, as a vehicle stops at a sink longer, more number of packets can be forwarded from a mobile router to a sink Therefore, a traffic source can increases its transmission probability to achieve higher utility Utility Fig Best response of traffic source 73 Transmission duration at sink seconds Transmission duration at sink 6667 seconds Utility under different strategy (ie, packet transmission probability Similarly, Fig 4 shows the total utility of a traffic source when there are two independent vehicles in a network Note that the mobility model of the second vehicle is similar to that of the first vehicle (ie, as in (20 However, the probability of going to the locations is different In this case, a roadside unit of a traffic [ source can adjust ] the transmission probabilities (ie, λ = for the mobile routers in both vehicles independently Again, there is a certain set of strategies such that a traffic source can achieve the highest total utility and this point is the best response [ given a set of strategies from ] λ (2 other opponents (ie, λ i= = This best response can be used to obtain the Nash equilibrium for the transmission probabilities of all traffic sources in the network Note that to simplify the presentation, the following results consider the network with a single vehicle However, the similar results are expected for the network with multiple vehicles The best responses of the traffic sources and 2 are shown in Fig 5 As expected, when one traffic source changes the strategy, the best responses of other traffic sources change For example, as a traffic source increases a transmission probability, the best strategies of other traffic sources are also to increase the transmission probabilities In this case, an intersection of all best responses is the point where the Nash equilibrium is located Similarly, as the transmission duration of a vehicle increases, the transmission probabilities of the traffic sources increases due to the longer transmission time of a mobile router Consequently, the throughput increases which is shown in Fig 6 We also observe that the throughput of a traffic source is higher than that of traffic source 2 and both are higher than that of traffic source 3 Since a vehicle travels to location s with the lowest probability, a traffic source has to transmits more data to a mobile router to achieve the highest utility The same reason is also applied to a traffic 2 λ (2 2 3 λ (2 3

6 6 Total utility Fig Best response of traffic source with two vehicles 006 λ ( Utility of a traffic source with two vehicles in a network source 2 whose throughput is higher than that of a traffic source 3 (ie, probability of a vehicle to visit location s 2 is larger than that of location s 3, but smaller than that of location s Transmission duration at a sink = 6667 seconds Nash equilibrium BR BR 2 Transmission duration at a sink = 200 seconds Fig 5 Best responses in terms of packet transmission probabilities of the traffic sources and 2 Throughput (packets/second τ ( > i τ ( 2 > i τ ( 3 > i 008 VI SUMMARY We have considered the vehicular delay tolerant network (VDTN A vehicles has the mobile router communicating with roadside unit to receive data from the traffic sources and deliver to the sink First, the queueing model to investigate the performances of a mobile router has been presented With this queueing model, various performance measures, eg, average number of packets in a queue of a mobile router, throughput, and average delay, can be obtained considering the mobility model of the vehicle Then, we have considered the noncooperative environment of the traffic sources In such an environment, the utility of a traffic source is defined based on the throughput and the cost of packet delivery which is a function of the number of packets in queue of a mobile router The noncoopertive game has been formulated The Nash equilibrium for the sets of strategies of the traffic sources has been considered as the solution of this game For the future work, the property of the Nash equilibrium, ie, existence and uniqueness will be analytically investigated REFERENCES [] V Conan, J Leguay, and T Friedman, Fixed point opportunistic routing in delay tolerant networks, IEEE Journal on Selected Areas in Communications, vol 26, pp , June 2008 [2] H Samuel, W Zhuang, and B Preiss, Routing over Interconnected Heterogeneous Wireless Networks with Intermittent Connections, in Proceedings of IEEE International Conference on Communications (ICC, pp , May 2008 [3] M Kalantari and R J La, A DTN packet forwarding scheme inspired by thermodynamics, in Proceedings of Annual Conference on Information Sciences and Systems (CISS, pp 26-22, March 2008 [4] L Franck and F G-Castineira, Using Delay Tolerant Networks for Car2Car communications, in Proceedings of IEEE International Symposium on Industrial Electronics (ISIE, pp , June 2007 [5] P McDonald, D Geraghty, I Humphreys, S Farrell, and V Cahill, Sensor Network with Delay Tolerance (SeNDT, in Proceedings of International Conference on Computer Communications and Networks (ICCCN, pp , August 2007 [6] I Carreras, J Rana, and L Telesca, Coordination protocol for financial application in delay tolerant networks, in Proceedings of International Conference on Communication Systems Software and Middleware and Workshops (COMSWARE, pp , January 2008 [7] M Abdulla and R Simon, The Impact of the Mobility Model on Delay Tolerant Networking Performance Analysis, in Proceedings of Annual Simulation Symposium (ANSS, pp 77-84, March 2007 [8] Y K Ip, W-C Lau, and O-C Yue, Performance Modeling of Epidemic Routing with Heterogeneous Node Types, in Proceedings of IEEE International Conference on Communications (ICC, pp , May 2008 [9] H Guo, J Li, A N Washington, C Liu, M Alfred, R Goel, L Burge, P Keiller, Performance Analysis of Homing Pigeon based Delay Tolerant Networks, in Proceedings of IEEE Military Communications Conference (MILCOM, October 2007 [0] A Krifa, C Baraka, and T Spyropoulos, Optimal Buffer Management Policies for Delay Tolerant Networks, in Proceedings of IEEE Communications Society Conference on Sensor, Mesh and Ad Hoc Communications and Networks (SECON, pp , June 2008 [] Q Liu, S Zhou, and G B Giannakis, Queuing with adaptive modulation and coding over wireless links: cross-layer analysis and design, IEEE Transactions on Wireless Communications, vol 4, no 3, pp 42-53, May Transmission duration at a sink (seconds Fig 6 Adaptation of the Nash equilibrium