Coalitional Game Theoretic Approach for Cooperative Transmission in Vehicular Networks

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1 Coalitional Game Theoretic Approach for Cooperative Transmission in Vehicular Networks arxiv:.795v [cs.gt] 8 Feb Tian Zhang, Wei Chen, Zhu Han, an Zhigang Cao State Key Laboratory on Microwave an Digital Communications, Tsinghua National Laboratory for Information Science an Technology (TNList) Department of Electronic Engineering, Tsinghua University, Beijing 84, China School of Information Science an Engineering, Shanong University, Jinan 5, China Department of Electrical an Computer Engineering, University of Houston, Houston, TX tianzhang.ee@gmail.com, wchen, czgee}@tsinghua.eu.cn, zhan@uh.eu Abstract Cooperative transmission in vehicular networks is stuie by using coalitional game an pricing in this paper. There are several vehicles an roasie units (RSUs) in the networks. Each vehicle has a esire to transmit with a certain probability, which represents its ata burtiness. The RSUs can enhance the vehicles transmissions by cooperatively relaying the vehicles ata. We consier two kins of cooperations: cooperation among the vehicles an cooperation between the vehicle an RSU. First, vehicles cooperate to avoi interfering transmissions by scheuling the transmissions of the vehicles in each coalition. Secon, a RSU can join some coalition to cooperate the transmissions of the vehicles in that coalition. Moreover, ue to the mobility of the vehicles, we introuce the notion of encounter between the vehicle an RSU to inicate the availability of the relay in space. To stimulate the RSU s cooperative relaying for the vehicles, the pricing mechanism is applie. A non-transferable utility (NTU) game is evelope to analyze the behaviors of the vehicles an RSUs. The stability of the formulate game is stuie. Finally, we present an iscuss the numerical results for the -vehicle an -RSU scenario, an the numerical results verify the theoretical analysis. I. INTRODUCTION Vehicular networks, from which rivers can obtain useful messages such as traffic conitions an real-time information on roa to increase traffic safety an efficiency, has gaine much attention []. Meanwhile, vehicular networks can also provie entertainment content for passengers an collect ata for roa an traffic managers. In vehicular networks, vehicles an roasie units (RSUs) can communicate with each other through vehicle-to-vehicle (VV), roasie-to-vehicle (RV), vehicle-to-roasie (VR) an roasie-to-roasie (RR) communications. As an important mous operani of substantially improving coverage an communication efficiency in wireless networks, cooperative transmission has gaine consierable attention recently. In cooperative communications, some neighboring noes can be use to relay the source signal to the estination, hence forming a virtual antenna array to obtain spatial iversity. Decoe-an-forwar (DF) is a commonlyuse cooperative protocol []. In DF relaying, the relay noe first ecoes the receive signal from the source, re-encoes it, an then forwars it to the estination. For the purpose of improving the system spectral efficiency, the cooperative relaying with relay selection [], [4] has been introuce on one han. On the other han, the non-orthogonal relaying protocols have been investigate [5]. Since the coalitional game theory provies analytical tools to moel the behaviors of rational players when they cooperate, it is a powerful tool for esigning robust, practical, efficient, an fair cooperation strategies an has been extensively applie in communication an wireless networks, which inclues the vehicular networks [6]. In [7], the coalitional game theory was utilize to investigate the cooperation between rational wireless users, an the stability of the coalition was analyze. Cooperative transmission between bounary noes an backbone noes was stuie base on coalition games in [8]. In [9], banwith sharing was stuie by using coalition formation games in VR communications. In [], the coalition formation games for istribute cooperation among RSUs in vehicular networks were stuie. In [], the coalitional game theory was applie in stuying how to stimulate message forwaring in vehicular networks. The coalition formation problem for rational noes in a cooperative DF network was formulate in []. The coalitional game theoretic approach for seconary spectrum access in cooperative cognitive raio networks was stuie in []. The stability of cooperation in multi-access systems was analyze in [4]. In [5], the coalitional game was utilize to stuy the cooperative packet elivery in hybri wireless networks. In cooperative relay networks, there are costs (e.g., energy consumption, operational cost, banwith) at the relays for forwaring the other users signals. Hence, a proper compensation mechanism is inispensable to provie the relays with incentives to forwar the signals. Pricing mechanism was stuie accoringly [6]. In this paper, we investigate the cooperative transmission in vehicular networks uner the framework of the coalitional game theory an pricing mechanism. On one han, the vehicles can form coalitions to cooperatively scheule their transmissions. On the other han, the RSUs can join the coalitions to cooperate the transmission of the vehicles. In the consiere scenario, as the vehicles are ynamic with respect to the RSUs, the vehicles an RSUs may be very far away. In this case, the cooperative transmission may be unprofitable if not impossible. Accoringly, we propose the notion of encounter

2 Fig.. RSU RSU NoP RSU Cooperative transmission with coalitions in vehicular networks between the vehicles an RSUs. Two conitions shoul be satisfie before a RSU cooperates a vehicle s transmission: ) the RSU an vehicle are in the same coalition; ) the RSU an vehicle encounter each other. When the two conitions hol, the RSU can use cooperative transmission to help the vehicle. In return, the vehicle shoul pay for the RSU. We consier the problem as a non-transferable utility (NTU) game. The stability of the existing coalition is stuie. Numerical results emonstrate the efficiency of the propose game. The reminer of the paper is structure as follows. Section II presents the system moel. Next, the coalitional game approach for the consiere problem is propose in Section III. We first formulate a NTU game to moel the cooperative transmission in the consiere vehicular network, an then the analysis of the propose coalitional game is carrie out. In Section IV, the numerical results are iscusse. Finally, we conclue the paper in Section V. II. SYSTEM MODEL Consier a wireless network in Fig., which consists of a network operator (NoP), K vehicles, an M RSUs. The vehicles an RSUs can form coalitions an the RSUs can cooperate the transmissions of the vehicles when they are in the same coalition. Let enote the NoP, an V =,,,K} an R = K +,,,K + M} represent the set of the vehicles an RSUs, respectively. We consier the uplink communications from the vehicle to the NoP. Each i V has its transmission range i. When RSU i R is in the transmission range of vehicles j V, we call i encounters j. Vehicle i V is active in each time-slot with probability p i, inepenently of other vehicles. When two or more vehicles transmit simultaneously, it is calle a collision, an we suppose that the transmissions will fail when a collision occurs. The cooperative protocol utilize in this paper is the non-orthogonal ecoe-an-forwar (NDF) [5]. In the first half of the time-slot, the source transmit to the The concept of relay noe has been introuce in IEEE 8.6j for WiMAX networks. It is assume that within the transmission range, the correct ecoing at the receiver can be guarantee. relay an estination; In the secon half, the relay ecoes an forwars the source message. Meanwhile, the source transmits a new message to the estination. We assume that vehicles in the same coalition can cooperate to scheule the transmissions, an only one vehicle transmits at a time to avoi interference. In each coalition, a scheuler etermines the active user that can transmit while other active users remain silent. When vehicle j is scheule to transmit at a time-slot, it selects one RSU from the feasible RSU set (i.e., the set of RSUs that are in the same coalition with vehicle j an encounter vehicle j) as relay to assist its transmission. Then one vehicle only employs at most one RSU as relay for each transmission. Furthermore, as no more than one vehicle is scheule to transmit at a given time-slot, one RSU assists the most one vehicles at a given time-slot. When the vehicle j utilizes RSU i as relay for its transmission, RSU i charges vehicle j with price ξ ij per transmission. When some vehicles an RSUs form a coalition, the vehicles woul share the channel with each other in TDMA moe, an they nee to pay for the RSU s relaying. However, the vehicles can avoi collision an gain iversity as well as rate increase. On the other han, although there are costs in receiving an forwaring the vehicles signals [7], the RSUs coul achieve revenues by charging the vehicles. In a wor, both vehicles an RSUs have incentives to form coalitions. III. COALITIONAL GAME APPROACH In this section, we first formulate the coalitional game in Section III-A, an then we analyze the formulate game in Section III-B. A. Coalitional game formulation A coalitional gameg is uniquely efine by the pair(n,v), where N is the set of players, any non-empty subset S N is calle a coalition, an v is the coalition value, it quantifies the worth of a coalition in a game. In our paper, the players are the vehicles an RSUs, i.e., N = V R. S N is a coalition. Define S V := S u ans R := S r. Consier a time-slot, let i j enote i encounters j uring the whole time-slot an P ij = Pri j}. The ata rate increase of vehicle i with the cooperation from the RSU j is enote as ij. Formally, the scheuler in S is a map f S : S S such that f S (Ψ) Ψ for all Ψ S an f S (Ψ) = iff Ψ =. 4 The average effective throughput for vehicle i can be expresse as T i (S) = E Ψ fs(ψ)=i}} (+ζi (S)) ( p j ), j V\S u where E Ψ fs(ψ)=i}} enotes the ratio of time-slots that vehicle i is chosen to transmit. For example, we can assume f S (Ψ) chooses the minimal element from the set of active We assume that the selection is performe accoring to a uniform probability istribution for simplicity. 4 Similar efinitions can be foun in [4].

3 vehicles Ψ. Let S u = s,,s Su } with s > > s Su, then } E Ψ fs(ψ)=s Su } = p s Su () an } E Ψ fs(ψ)=s k } S u = p sk i=k+ ( p si ),k =,, S u. () ζ i (S) is the average increase of ata rate for vehicle i an it is given by ζ i (S) = ij P ji ( P ki ) k ij + ik + P ji P ki ( P li ) j<k S r l j,l k S r ij + ik + il + P ji P ki P li j<k<l S r ij ( P ri )+ + P ji, n r j,r k,r l S r where n = S r. If S r =, i.e., n =, ζ i (S) =. Suppose ij = i, i.e., the ata increase for vehicle i is irrelevant to the selection of RSUs, then the average throughput for vehicle i can be simplifie as T i (S) = E Ψ fs(ψ)=i}} (+Pi i ) ( p j ), where P i = j V\S u ( P ji ) is the probability that at least one RSU in the coalition encounters vehicle i. Remark: If there are active vehicles outsie S at a given time-slot, at least one vehicle outsie S transmits simultaneously with the scheule vehicles in S no matter how the vehicles outsie S form coalitions. Thus, there is no collision if an only if (iff) all vehicles outsie S is inactive. For vehicle i, the average payment mae to the RSUs can be given by P i (S) = E Ψ fs(ψ)=i}} χi (S) with χ i (S) = ξ ji P ji ( P ki ) k ξ ji +ξ ki + P ji P ki ( P li ) j<k S r l j,l k S r ξ ji +ξ ki +ξ li + P ji P ki P li j<k<l S r ξ ji ( P ri )+ + P ji. n r j,r k,r l S r If n =, χ i (S) =. Assume ξ ij = ξ j, i.e., all the RSUs set the same price for vehicle j, then the average payment can be simplifie as P i (S) = E Ψ fs(ψ)=i}} Pi ξ i. Remark: The RSU charges the vehicles once the vehicles employs the RSU as the relay for a transmission, it oes not take the collisions into account. That is to say, the actions in other coalitions o not affect the charging. The payoff of vehiclei is etermine byu i (S) = α i T i (S) β i P i (S). For RSU j in S, the revenue charge from the vehicles can be given by R j (S) = } fs(ψ)=i} ηij (S)ξ ji, () E Ψ where η ij (S) is the probability that vehicle i employs RSU j as its relay for transmission, an it is given by [ η ij (S) = P ji ( P ki ) k + P ki ( P li ) k l j,l k S r + P ki P li ( P ri ) k<l,k j,l r j,r k,r l S r + + ]. (4) n k P ki Assume that RSU j receives the signal of vehicle i at cost c r ji an the cost of forwaring the signal to NoP as cf ji. The average cost of RSU j can be expresse as C j (S) = E Ψ fs(ψ)=i} } [ c f ji η ij(s)+p ji cji] r. (5) Remark: RSU j receives the message of vehicle i once it encounters vehicle i (with probability P ji ), an it forwars the message only when it is selecte as the relay by vehicle i (with probability η ij (S)). The payoff of RSU j is etermine by ũ j (S) = γ j R j (S) µ j C j (S). Define v(s) R Su + Sr be the set of feasible payoff vectors for S, we formulate the consiere cooperation problem as a coalitional NTU-game G : (V R,v). B. Analysis of the formulate coalitional game In this section, we first present two observations. Next, we analyze the stability of the game an propose a sufficient conition for the existence of the core. In the beginning, we have the following observation. Observation. Let f(s) = u i (S)+ ũ j (S) enote the sum payoff of S. When γ j = an β i =, we have f(s) = α i T i (S) µ j C j (S). That is to say, the pricing has no effect on the sum payoff in this case. Proof: First we can prove that χ i = η ij (S)ξ ji. Then E Ψ fs(ψ)=i}} χi } = E Ψ fs(ψ)=i} η ij (S)ξ ji (a) = } fs(ψ)=i} ηij (S)ξ ji. (6) E Ψ

4 (a) hols since E Ψ fs(ψ)=i}} is irrelevant to j Sr. Next, base on (6), we can erive } E Ψ fs(ψ)=i} χi = } E Ψ fs(ψ)=i} ηij (S)ξ ji. (7) Exchanging the summation orer on the right sie, we get P i (S) = R j (S). (8) When γ j = an β i =, f(s) = α i T i (S) µ j C j (S)+ P i (S) R j (S). Using (8), we erive f(s) = α i T i (S) µ j C j (S). Remark: Observation reveals the fact that the total revenues obtaine by the RSUs equal to the payments of all the vehicles. In aition, we obtain the secon observation. Observation. A coalitions shoul have at least one vehicle. Otherwise, ũ i (S) = = ũ i (i}) an v(s) = ũ i (S) =. i S That is to say, when there are only the RSUs, the RSUs have no stimuli to form coalitions an each RSU will act alone. Proof: When S u =, we get R j (S) = an C j (S) = accoring to () an (5), respectively. Thus, ũ i (S) =. Specifically, ũ i (i}) =. As ũ i (S) = ũ i (i}) in this case, each RSU will act alone. Remark: The function of the RSU is relaying the vehicle s signal. So when there is no vehicle, it is meaningless to group only the RSUs together. On the other han, when there is no} RSU in a coalition S, i.e., S V, u i (S) = E Ψ fs(ψ)=i} ( p j ) for j V\S i S an v(s) = u i (S) >. Specially when S = i}, i S we erive u i (i}) = p i ( p j ). Hence, when S j V\i} V & S i satisfying u i (S) > u i (i}), the vehicles will form coalitions to improve the utility. Specifically, let S = s,,s S } with s > > s S, base on () an (), we can erive that if ( p j ), i = S ; j S\s i} ( p j) (9) j S\s i } S ( p sk ) k=i+, otherwise, forming coalition S is profitable. 5 Specially, when p i = p, i.e., all vehicles have the same active probability, we can erive that (9) hols, then forming coalitions is always profitable in the case. 5 Although forming S may be not optimal, it is at least better than acting alone. Next, as the core is one of the most important stability concepts efine for coalitional games, we investigate the core of our propose coalitional game in the following. The efinition for the core of our coalitional game is given as follows. Defination. The core of (V R,v) is efine as C = x v(v R) : S, y v(s),s.t. y i > x i, i S }. The following observation gives a sufficient conition for the existence of the core. Observation. The core of (V R,v) is nonempty once the following conitions hol (S V R): ) α i >, β i >, γ j >, an µ j >. ) α i T i (S) > β i P i (S) or γ j R j (S) > µ j C j (S). ) α i T i (V R) β i P i (V R) > α i T i (S) β i P i (S), an γ j R j (V R) µ j C j (V R) > γ j R j (S) µ j C j (S). Proof: When ) hols, we can fin α i, β i, γ i, an µ j to satisfy ). If ) oes not hols, we have u i (i}) = ( p j ) u i (S) for i S u an ũ j (S) = j V/i} ũ j (j}) for j S r. Then, each vehicle an RSU will act alone. In this case, the core is empty. When ) hols, we can prove that (V R,v) is balance [8]. Thus, the core is nonempty accoring to the Bonareva-Shapley theorem [9]. Remark: The core is possibly non-empty in practice. For example, when the consiere vehicles wait for the traffic light, the vehicles as well as the nearby RSUs are probable to form the coalition together. IV. NUMERICAL RESULTS In this section, we emonstrate the numerical evaluations for the performance of the cooperative transmission scheme with coalitions. In the simulations, we assume that the noes are uniformly locate in a square area of km km. 6 The network topology changes at the beginning of each timeslot an remains static uring the whole time-slot. That is to say, the locations of the noes are generate accoring to the uniform istribution at the beginning of a time-slot, the locations o not change uring the time-slot, an we regenerate the locations at the beginning of the next time-slot. We consier the scenario that there are vehicles ( an vehicle ) an RSUs (RSU an ) in the area. Fig. shows the encounter probability with ifferent transmission ranges for an vehicle. In the simulations, we set = = an the probability is obtaine from 6 time-slots. We can observe that RSU &, &, RSU & vehicle, an & vehicle have similar encounter probabilities. It is because that since all noes are uniformly istribute, an vehicle as well as RSU an are exchangeable in location. In aition, we can see that the encounter probability increases with the increase of the transmission range. In the evaluations 6 The area has been ivie to.

5 Encounter probability Fig RSU & & RSU & vehicle & vehicle 4 5 Encounter probability with ifferent transmission ranges TABLE I POSSIBLE COALITIONAL STRUCTURE C :,,,4} C 6 :,},,4} C :,},,4} C :,,4},} C 7 :,,},4} C : },},,4} C :,},},4} C 8 : },,,4} C :,,4},} C 4 : },},},4} C 9 :,4},,} C 4 :,4},},} C 5 : },},,4} C : },4},,} C 5 : },4},,} vehicle RSU 4 5 Fig.. performance in C of utility performance, we set ij =.5, p i =.6, ξ ij =.5, c f ji =.5,cr ji =.,α i =,β i =, anγ j = µ j =. There are totally 5 coalitional structures for vehicles an RSUs as illustrate in Table I. Using Observation, we nee not consiering C an C. Meanwhile, as an vehicle as well as RSU an are exchangeable, 7 we only nee to consier C - C 7. 8 Fig. plots the utility performance for 4 noes when they form the coalition together(c ). The utility performance increases when we increase the transmission range. The reason is that the encounter probability will increase when the transmission range increases (see Fig. ). Consequently, 7 an vehicle are not exchangeable because of the scheuling when they are in the same coalition. However, as exchanging elements in the same coalition is meaningless, it oes not affect the analysis here. 8 C 8 is similar as C ; C 9 is similar as C 6 ; C, C 4 an C 5 are similar as C 5 ; an C is similar as C vehicle RSU (a) C vehicle RSU 4 5 (b) C Fig. 4. performance in C an C vehicle RSU 4 5 (a) C vehicle RSU 4 5 (b) C 5 Fig. 5. performance in C 4 an C 5 the probability of cooperative transmission will increase. As cooperative transmission coul benefit both the vehicle an RSU, 9 the utility performance increases. Another observation is that the utility performance for is better than that of vehicle, an the utility performance for RSU an RSU 4 is similar. This can be explaine as follows: when vehicle an vehicle are in the same coalition an both of them are active, the scheuler selects to transmit, i.e., the has higher transmission priory than vehicle. Consequently, the utility performance for is better. In contrast, RSU an have same priority in the relay selection of vehicle an they have same encounter probability with (or vehicle ), the same relaying price, an the same cost for receiving an forwaring, so they have similar utility performance. Fig. 4(a) - Fig. 6(a) illustrate the utility performance for C - C 7, respectively. As compare with Fig., the utility performance of eviently ecreases, an the utility performance of vehicle, RSU, an slightly ecreases in Fig. 4(a). Base on the scheuling scheme, the successful transmission probability of RSU is p =.6 in C. In contrast, it is p ( p ) =.4 in C. That is to say, the successful transmission probability obviously ecreases. Thus, the utility ecreases eviently. With respect to vehicle, the successful transmission probabilities are the same in C an C (i.e., ( p ) p =.4). However, there are no RSUs that are in the same coalition with vehicle in C. Then no cooperative transmission can be implemente for vehicle 9 Uner the simulation settings, cooperative transmission is preferable for both vehicle an RSU.

6 vehicle RSU 4 5 (a) C vehicle RSU 4 5 (b) C 7 Fig. 6. performance in C 6 an C 7, an the utility performance ecreases accoringly. In C, both an vehicle may utilize RSU (or ) for cooperative transmission. In contrast, only may utilize RSU (or ) in C, i.e., the probability of being utilize as a relay will ecrease in C. As being utilize as a relay is profitable in our settings, the utility performance of RSU () ecreases. Comparing Fig. 4(b) with Fig. 5(a), it can be observe that the utility performance of is much better in Fig. 4(b), an the utility performances of the other three noes (vehicle, RSU, an ) are the same. It can be explaine by using (9). Firstly, S =,} with s = an s =. Then we have ( p j ) = p =.4 <, i = ; j S\s i} [ ] S () ( p j ) ( p sk ) j S\s i} k=i+ = ( p )[ p ] =, i =. That is to say, the utility of RSU s = will increase an the utility of RSU s = will remain the same when they form the coalition, }. Finally, we can see that the utility performance in C is better than other coalitional structures an the utility is positive in all coalitional structures. Meanwhile, α i = >, β i = >, an γ j = µ j = >. Thus, the conitions in Observation hol. Applying Observation, we claim that the core of the coalitional game is nonempty uner the simulation settings. Furthermore, (u (C ),u (C ),u (C ),u 4 (C )) is in the core. V. CONCLUSION Cooperation among vehicles an cooperation between vehicle an RSU in vehicular networks have been stuie. We propose the notion of encounter to characterize the relative location between the vehicle an RSU when the vehicle is locomotive. Utilizing the coalitional game theory an pricing mechanism, we have formulate a NTU coalitional game to analyze the behaviors of the vehicles an RSUs. Moreover, the stability of the propose game is stuie. A sufficient conition for the non-empty of the core is obtaine. Numerical results for the -vehicle an -RSU scenario verify the theoretical analysis. ACKNOWLEDGMENT This work is partially supporte by the National Basic Research Program of China (97 Program) uner Grants CB66 an CB6, the National Nature Science Founation (NSF) of China uner Grants 688, 69, an 6, US NSF CNS-756, CNS- 9577, ECCS-878, CNS-95556, CNS-6568, an Qatar National Research Fun. REFERENCES [] G. Karagiannis, O. Altintas, E. Ekici, G. J. Heijenk, B. Jarupan, K. Lin, an T. Weil, Vehicular networking: a survey an tutorial on requirements, architectures, challenges, stanars an solutions, IEEE Commun. Surv. Tut., vol., no. 4, pp ,. [] J. N. Laneman, D. N. C. Tse, an G. W. Wornell, Cooperative iversity in wireless networks: efficient protocols an outage behavior, IEEE Trans. Inf. Theory, vol. 5, no., pp. 6-8, Dec. 4. [] A. Bletsas, A. Khisti, D. P. Ree, an A. Lippman, A simple cooperative iversity metho base on network path selection, IEEE J. Sel. 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