IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 1, NO. 1, MARCH 2013 1

A Graph-based Cooperative Scheduling Scheme forVehicular Networks

Kan Zheng, Senior Member, IEEE, Fei Liu, Qiang Zheng, Wei Xiang, Senior Member, IEEE, Wenbo WangMember, IEEE,

Abstract— Vehicle-to-vehicle (V2V) communications are con-sidered as a significant step forward towards a highly secureand efficient intelligent transportation system (ITS). In this paper,we propose the use of graph theory to formulate the problemof cooperative communications scheduling in vehicular networks.In lieu of exhaustive search with intractable complexity for themaximum sum rate (MSR), we propose a bipartite graph-basedscheduling scheme to allocate the vehicle-to-infrastructure (V2I)and V2V links for both 1-hop and 2-hop communications. TheKuhn-Munkres algorithm is adopted to solve the problem ofmaximum weighted matching of the constructed bipartite graph.Simulation results indicate that the proposed scheme performsextremely close to the optimal one, and results in better fairnessamong vehicle users with considerably lower computationalcomplexity. Moreover, cooperative communications can improveboth the throughput and spectral efficiency of vehicular networks.

Index Terms— V2V communications, cooperative communica-tions, vehicular networks, bipartite graph, maximum weightedmatching.

I. INTRODUCTION

Vehicular networks are one of the essential componentsof intelligent transportation systems (ITSs) [1]. There hasbeen an increasing demand for broadband in-vehicle services,which imposes unique challenges on the design of inter-vehiclecommunications in vehicular networks. There are usually twotypes of communication paradigms for vehicle services, i.e.,vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I)communications. V2I communications enable vehicles to con-nect to the Internet via a roadside base station. Intensiveinvestigations and trials have been carried out to advance V2Itechnology with the aim of supporting in-vehicle applicationssuch as real-time update of congestion, weather conditionsand so on [2], [3]. Meanwhile, extensive research has hasbeen dedicated to short range radio-based V2V communicationtechnologies, such as dedicated short-range communications(DSRC) [4], to support active safety applications.

This work was funded in part by China NSFC (No.61271183), Program forNew CenturyExcellentTalentsinUniversity (NCET-11-0600), and the NationalKey Technology R&D Program of China under Grant 2013ZX03003005.

Kan Zheng, Fei Liu, Qiang Zheng and Wenbo Wang are with WirelessSignal Processing and Network (WSPN) Lab, Key laboratory of UniversalWireless Communication, Ministry of Education in Beijing University ofPosts&Telecommunications, China (e-mail:kzheng@ieee.org).

Wei Xiang is with Faculty of Engineering and Surveying, University ofSouthern Queensland, Toowoomba, QLD 4350, Australia.

Copyright (c) 2013 IEEE. Personal use of this material is permitted.However, permission to use this material for any other purposes must beobtained from the IEEE by sending a request to pubs-permissions@ieee.org.

Rapid development in special vehicular applications such assafety requires vehicular networks to be capable of providingservices with expected quality in terms of reliability and delay.However, vehicular networks are usually subject to impair-ments induced by the underlying radio channel and topologyvariation due to the change of vehicle locations. Cooperativerelaying communications are one of the most promising tech-niques for improving the wireless communication performancethrough the use of transmission diversity offered by relaynodes [5]. It reduces the transmission distance and increasesthe number of users under more favorable channel conditions,allowing for better channel quality and higher throughput [6].Several repetition-based cooperative relaying schemes, suchas amplify-and-forward (AF) and decode-and-forward (DF),have been already developed to fully exploit the spectraldiversity to reduce the outage probability [7]. In [8], inter-vehicle communications are assisted by a roadside accesspoint (AP) with AF relaying. However, its performance isanalyzed only from the physical layer aspects. In order towell support cooperative relaying services between vehicles,various improvements on cooperative media access control(MAC) protocols have been proposed [9]–[12]. Cross-layerapproaches for cooperative diversity networks are also in-vestigated, combining the cooperative diversity concept withjoint optimization of the physical and MAC layers [13],[14]. However, the relevant literature on resource schedulingschemes for cooperative vehicular networks is sparse to date.Since there are more heavy service data in the downlink thanin the uplink, e.g., broadcasting messages related to safetyand traffic information [15], efficient downlink transmissionbecomes more important, which is the focus of this paper.

Since cellular networks, such as the third-generation (3G)long-term evolution (LTE) and its Advanced networks, canprovide wide service coverage and well support user mobility,they are good solutions for V2I communications in vehicularnetworks [16]. Vehicle equipment (VE) close to the basestation (BS) may enjoy a favorable channel quality resultingin high data rates. However, the others far away from the BScan only have much lower data rates due to poor radio links.To tackle this challenge, a cooperative relaying mechanismamong neighboring vehicles is desired to be established forV2V communications through DSRC. Due to the broadcastnature of the wireless channel, intermediate nodes are able toreceive the transmitted signals, but only some of them takepart in cooperative relaying. The problem we face is howto determine non-cooperative or cooperative transmission foreach VE, and how to schedule VEs in proximity to the BS

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 1, NO. 1, MARCH 2013 2

to help others. In this paper, we investigate these cooperativerelaying problems in cellular-based vehicular networks withV2V communications by using a graph-based approach. Mostexisting graph-based resource scheduling methods fall undertwo categories, i.e., 1) graph coloring [17]–[20], and 2)maximum weighted matching (MWM) in a weighted bipartitegraph [21]. This paper focuses on the latter one, which isrelatively less well-investigated.

In this paper, we employ graph theory to formulate theproblem of scheduling the V2I and V2V links in vehicular net-works. Due to the tree structure of a relay network, a feasibleapproach is to solve the spanning tree of a complete graph,which contains all the possible links in the network. However,this brute-force approach results in intractable computationalcomplexity owing to exhaustive searching. Therefore, wepropose a bipartite graph (BG)-based scheduling scheme,consisting of the following of three stages: 1) construct theweighted bipartite graph; 2) solve the maximum weightedmatching (MWM); and 3) optimize the number of relayedVEs. More specifically, we first construct a bipartite graph bygrouping the VEs with one subset containing the 1-hop VEs,and the other subset comprising the 2-hop VEs. The edges areweighted according to the capacity of the links between VEs.Then, we use the Kuhn-Munkres (KM) algorithm to solve theMWM problem of the constructed bipartite graph. Throughstages 1) and 2), one can obtain an optimized solution ofthe link arrangement in the vehicular network according tocertain separation of the VE set. And at stage 3), a searchalgorithm, such as binary search or golden section search,can be employed to find the optimal separation, throughrepeating stages 1) and 2) [22]. The proposed BG-basedscheme leads to a much lower complexity than the exhaustivesearch for the optimal solution, and can be demonstrated toperform extremely close to the optimal one. In addition, itprovides better fairness among VEs, and can improve the datarates of the VEs under poor channel conditions. The maincontributions of this work are summarized as follows:

• Formulation of the scheduling problem in the 2-hopvehicular network with graph theory;

• Proposal of a low-complexity bipartite graph-basedscheduling scheme for V2V communications;

• Analysis on the computational complexity of the exhaus-tive search and the proposed schemes;

• Performance evaluation with/without cooperative com-munications.

The remainder of this paper is organized as follows. SectionII gives a brief description of the system model and formulatesthe link scheduling problem in vehicular networks. A graph-based cooperative relaying scheme for vehicular networks isproposed in Section III. In Section IV, simulation results arepresented and discussed. Finally, Section V concludes thispaper.

II. SYSTEM MODEL AND PROBLEM FORMULATION

A. System Model

As illustrated in Fig. 1, a wireless network with N VEs onan urban road for downlink transmission is considered in this

Core network

Base station

DV

V2V

V2I

V2I

V2V

V2I

RV

RV

DV

Internet Server

V2V: vehicle-to-vehicle

V2I: vehicle to-infrastructure

RV: relay vehicle

DV: destination vehicle

Fig. 1. Illustration of 1-hop and 2-hop communications with the V2I andV2V links in a vehicle network.

paper. Each VE can play a different role of communicationsin the network. Similar to the normal user equipment (UE) inLTE-Advanced networks, a VE has the ability to establish adirect link with the BS. Meanwhile, VEs can help each otherto forward data or not, depending on their channel conditionsand network requirements. Therefore, the communicationsbetween the VEs and BS can be established either directly(i.e., 1-hop) or via 2-hop cooperation. Relaying should occuronly when it can improve the end-to-end throughput or thecoverage.

1) 1-hop communications: In infrastructure-based LTE-Advanced networks, the communications via a direct linkbetween a VE and the BS, i.e., the V2I link, are basedon the LTE-Advanced specification [23]. The entire radioresources are divided into resource blocks (RBs) along thetime and/or frequency domain. Users share all the RBs througha scheduling algorithm. For simplicity, the round-robin (RR)algorithm is used to evenly distribute the RBs to each V2Ilink. Assume that there are KB RBs available for the downlinktransmission in the network. Thus, the achievable rate of theith V2I link in cell B is given by

ηB,i = NI log2

(1 +

βB,iPB,i∑NC

m=1,m=B βm,iPm,i + σ2N

),(1)

1 ≤ i ≤ N,

where NI is the floor value of KB/N , i.e., NI = ⌊KB/N⌋,NC is the number of cells occupying the same radio resources,Pm,i is the transmit power from the BS of cell m on the ithV2I link, βm,i is the path loss attenuation factor from theBS of cell m to the ith V2I link user, and σ2

N is the noisepower of the additive white Gaussian noise (AWGN). Thetransmit power is assumed to be the same for all V2I links,i.e., Pm,i = PT , 1 ≤ m ≤ NC , 1 ≤ i ≤ N .

2) 2-hop communications: When one of the VEs is far fromthe BS, its data may be forwarded by another VE in proximityto the BS via out-of-band relaying communications using theIEEE 802.11p specification at a higher frequency band [24].For the sake of exposition, the VE that is assisted by anotherVE is termed the destination vehicle (DV), while a relayvehicle (RV) is the one that can help its destination vehicle.In order to avoid high signaling overhead and schedulingcomplexity, we assume that one RV can help only one DV

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 1, NO. 1, MARCH 2013 3

at a time, and vice versa. For 2-hop communications, datacommunications between the BS and the DV involve boththe V2I and V2V links. Assuming that decode-and-forward(DF) relaying is applied at the relay vehicle [7], the equivalentachievable data rate of 2-hop transmission can be given by

min{ηB,i, ηi,j}, 1 ≤ i, j ≤ N, i = j, (2)

where ηi,j is the achievable data rate from the i-th relay vehicleto the j-th destination vehicle. Under the assumption that KV

radio resource units are allocated to L V2V links by RR, ηi,jcan be expressed by

ηi,j = NS log2

(1 +

βi,jPi,j

σ2N

), 1 ≤ i, j ≤ N, i = j, (3)

where NS is the floor value of KV /L, i.e., NS = ⌊KV /L⌋,Pi,j is the transmit power from the i-th relay vehicle to the j-thdestination vehicle, βi,j is the path loss attenuation factor fromthe i-th relay vehicle to the j-th destination vehicle, and σ2

N isthe noise power of the additive white Gaussian noise (AWGN)of the V2V link. The transmit power is assumed to be the samefor all the relay vehicles, i.e., Pi,j = PC , 1 ≤ i, j ≤ N, i = j.

B. Problem formulation

The links in the wireless vehicular network involving bothof 1-hop and 2-hop transmission result in a complicated topol-ogy. For optimal link scheduling in vehicular communications,a graph-based problem formulation is presented in the sequel.

Based on a given network topology, we can first constructa link graph G = (U,E). The vertex set U denotes thecommunication nodes, i.e.,

U = {uB} ∪U′ = {uB} ∪ {ui|i = 1, 2, . . . , N}, (4)

where uB and ui represent the BS and VE i, respectively,and U′ is the set of the VEs. Thus, there are |U| = N + 1vertexes in graph G. E is the set of all the links that may beestablished that includes not only the edge set EB of the V2Ilinks but also the edge set EV of V2V, i.e.,

E = EB ∪EV (5)= {eB,i|i = 1, 2, . . . , N} ∪ {ei,j |i, j = 1, 2, . . . , N, i = j} ,

where eB,i denotes the edge from uB to ui, and ei,j is the edgefrom ui to uj . Each edge in G is associated with a weight,dependent on the transmission capacity of the link, i.e.,

w(eB,i) = ηB,i, eB,i ∈ EB , (6)w(ei,j) = min{ηB,i, ηi,j}, ei,j ∈ EV . (7)

It is noted that the resources of V2I links are first evenlyallocated to all the mobile nodes either by 1-hop or by 2-hop communication. If one node helps another one as arelay vehicle, it may use the V2I resources allocated notonly to it but also the one that it helps. The destinationvehicle communicates with its relay vehicle using the V2Vlink. Hence, no data rate loss of a relay vehicle is causeddue to relaying because it has been assigned with extra radioresources for relaying. Moreover, if the 2-hop date rate of a

1

3

2

4

1

3

2

4

BS

Vehicles

BS

Vehicles

Spanning tree TAll-connected graph G

B B

1u

Bu

2u

3u 4u

1u

Bu

2u

3u 4u

Fig. 2. An exemplary link graph and its spanning tree in a 4-VE network.

destination vehicle as defined in (7) is higher than that with1-hop transmission, the throughput gain can be achieved bycooperative relaying.

Graph G is complete since each ui is connected with uB byeB,i, and any pair of the nodes are linked by ei,j . A practicaland feasible 2-hop vehicular network topology is with a treestructure T = (U,M), namely a spanning tree, which is asubgraph of G. The root node of T is uB , i.e., the BS. Theremay be various spanning trees of G and each of them containsall the nodes in G but without any cycles.

For the purpose of illustration, Fig. 2 gives a simple exampleof the spanning tree of a complete graph corresponding toa network with only four VEs. We add some additionalconstraints for the spanning trees in vehicular networks whileconsidering the power consumption and timing sequence com-plexity. The first constraint imposes that any VE must connectto its transmitter, being either the BS or a relay vehicle. Onedestination vehicle can receive data forwarded by only onerelay vehicle, which has a V2I link to the BS. The second oneimplies that a VE can help at most one another vehicle, actingas a relay. The last one limits the number of the relaying hops,i.e., at most two hops. Corresponding to Fig. 2(a), one possiblespanning tree is shown in Fig. 2(b). Vertexes u1, u2, and u4

represent the VEs which establish direct communications withthe BS using the V2I links. The destination vehicle denoted byu3 communicates with the BS through 2-hop links, includingthe V2I and V2V links, with the aid of RV u2.

Therefore, the additional constraints of a allowable spanningtree T of the complete graph G are summarized as follows:

• The in-degree of each ui (i = 1, 2, . . . , N) is limited tobe 1;

• The out-degree of each ui (i = 1, 2, . . . , N) is no morethan 1;

• The depth of the spanning tree is no more than 3.Let M be the set of edges in tree T, where M ⊂ E. The

edges in M come from both the V2I and V2V links, i.e.,M = MB ∪MV , where MB and MV are the subset of EB

and EV , respectively. It is clear that the vertexes in T areidentical with those in G. Then, we can rewrite the vertex setas U = {uB}∪UB ∪UV , in which UB is the set containingthe nodes connected to uB and UV is the set containing thenodes linked to those in UB . Due to the characteristics of thetree structure, the number of the edges in T can be easilyobtained as |M| = N . On the other hand, the number of thedestination vehicles using the V2V links is |MV | = L.

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 1, NO. 1, MARCH 2013 4

With the given spanning tree T, the total achievable down-link data rate of the network for all the VEs can be computedwith the knowledge of the weight of each edge as follows

W = WB +WV =∑

eB,i∈MB

w (eB,i)+∑

ei,j∈MV

w (ei,j). (8)

Apparently, different topologies of T result in differentsums of rate. In other words, by properly selecting the edgeset M of T, the maximum sum rate (MSR) can be obtainedfor the network. Then, the problem can be formulated into thefollowing optimization function

M = arg maxM⊂E

{W} (9)

= arg maxM⊂E

∑eB,i∈MB

w (eB,i)+∑

ei,j∈MV

w (ei,j)

.

To the best of our knowledge, the optimal solution toproblem (9) can only be found via exhaustive search. Inthe network with N VEs, there are N edges in EB , andN (N − 1) /2 edges in EV . We can calculate the number ofenumerations as follows:

• First, we choose n VEs as destination vehicles from theN vehicles, which receive data with 2-hop communica-tions. The amount of possible combinations is Cn

N . Thenumber of destination vehicles is smaller than that ofrelay vehicles because one relay vehicle can forward to nomore than one destination vehicle, i.e., 0 < n ≤ ⌊N/2⌋;

• Then, we select n relay vehicles from the rest N − nVEs to help the n destination vehicles. The number ofpermutation is An

N−n;• For each 0 < n ≤ ⌊N/2⌋, the number of enumeration is

CnNAn

N−n.Hence, to compare all the possibilities, the number of enumer-ations is

⌊N/2⌋∑n=1

CnNA

nN−n =

⌊N/2⌋∑n=1

N !

n! (N − 2n)!, (10)

which is overwhelmingly large resulting in a nondeterministicpolynomial (NP) time complexity. When there are a largenumber of vehicles in the network, a massive number ofalternative radio links for V2V communications make suchsearch unacceptable due to intractable computational com-plexity. Therefore, we propose a low-complexity schedulingscheme to arrange the 2-hop links in vehicular networks inthe following section.

III. BIPARTITE GRAPH-BASED SCHEDULING SCHEME

In view of the high computational complexity of solvingthe optimization problem of (9) with exhaustive search, wepropose a graph-based scheduling scheme for a suboptimalsolution. Firstly, either 1-hop or 2-hop communications areselected for each VE according to its channel quality. Thevehicles with a poor V2I channel link are chosen as the 2-hop destination vehicles. The other vehicles with a betterradio link to the BS can be used as relays to assist in theselected destination vehicles. Then, we solve the maximum

weighted matching (MWM) problem of the Bipartite Graph(BG), consisting of two disjoint vertex sets of the relayvehicles and destination vehicles with their adjacent edges.The proposed scheme is described in detail in the followingpart.

A. Construction of the weighted bipartite graph

Since the VEs close to the BS have the V2I links with agood channel quality, they usually establish direct communi-cations with the BS and are able to help forward the data forother VEs. Meanwhile, in order to improve the achievable datarate, those VEs far from the BS under poor channel conditionsmay communicate with the BS via 2-hop communications. Wedenote NB and NV as the number of the VEs with 1-hop and2-hop communication, respectively. We choose NV VEs withthe worst channel conditions as the destination vehicles, andthe rest NB = N −NV as 1-hop VEs, of which NV are usedas the relay vehicles to help the selected destination vehicles.Since the 1-hop VEs may or may not help another VE, wehave NB ≥ NV , equally, 0 ≤ NV ≤ ⌊N/2⌋. Now we need todetermine which VEs are suitable to act as the relay vehiclesto help which destination vehicles.

A weighted bipartite graph G′ = (U′,E′) is constructed onthe basis of G = (U,E), where the vertexes are divided intotwo disjoint subsets. One subset of UV is the set of the VEsselected to be 2-hop destination vehicles, whereas the othersubset UB is the set of VEs with 1-hop communications. It isevident that U′ = UB

∪UV and UB

∩UV = ∅. Thus, the

V2I link set is MB = {eB,i|ui ∈ UB}, where MB ⊂ EB .Then, we can readily obtain the relationship as

|MB | = |UB | = NB = N −NV . (11)

The edges with one endpoint in UB and the other one inUV comprise the set of possible V2V links, denoted by

E′V = {ei,j |ui ∈ UB , ui ∈ UV } , (12)

which is a subset of EV , i.e., E′V ⊂ EV . Fig. 3(a) gives

an example of G′ in a network with 8 VEs. VE u2, u3 andu7 are selected as destination vehicles while the others are1-hop VEs which may help them by 2-hop communications.Thus, there are NV = 3 destination vehicles, and L = 3 V2Vlinks should be established. The next stage is to solve for theoptimal V2V links, namely, the maximum weighted matchingof the bipartite graph G′.

B. Solving Maximum weighted matching (MWM)

A match of G′ is denoted by MV and defined as follows.• MV ⊆ E′

V .• If ei,j ∈ MV , ∀ei,x=j /∈ MV ∧ ∀ey =i,j /∈ MV .Hance, MV is a subset of the edges in G′, and no two edges

in MV share identical end points, as shown in Fig. 3(b). Eachvertex in UB has no more than one connected node in UV .Every edge in E′

V is associated with a weight w (ei,j). Withthe following optimization objective function

WV =∑

ei,j∈MV

w (ei,j), (13)

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 1, NO. 1, MARCH 2013 5

1u

,i je

BU

VU

3u

5u

7u

6u

8u

4u

2u

1u

,i je

BU

VU

3u

5u

7u

6u

8u

4u

2u

( ), ,B V V

¢ ¢=G U U E V V¢ÍM E

Fig. 3. An exemplary bipartite graph and its matching in an 8-VE network.

1u

,i je

BU

VU

3u

5u

7u

6u

8u

4u

2u

1u

,i je

BU

V

+U

3u

5u

7u

6u

8u

4u

2u

9u

10u

Fig. 4. An example of the expansion of an asymmetric bipartite graph in an8-VE network.

MWM satisfies that

WV = max∑

ei,j∈MV

w (ei,j), (14)

MV =argmaxMV

{WV } = argMV

{WV = WV

}. (15)

We then employ the Kuhn-Munkres (KM) algorithm tosolve the MWM problem of the given bipartite graph G′ [21].For G′ = (UB ,UV ,E

′V ), if the cardinalities of UB and

UV are identical, i.e., NB = NV , the bipartite graph issymmetric, or asymmetric otherwise. The KM algorithm canbe applied directly in a symmetric graph [21]. However, thenumber of the 1-hop users is usually larger than that of 2-hopones. Thus, we can expand an asymmetric bipartite graph withadditional NB−NV nodes, so as to construct a symmetric one.Additional vertexes are added to set UV which has a smallernumber of nodes. The added vertex set is denoted by U+

V ,in which the nodes are connected to those in UB with zeroweight. Fig. 4 gives an example of the extended graph, whereu9 and u10 are two added nodes.

It has been proven that the KM algorithm can alwaysachieve MWM for bipartite graphs [21]. Next, the optimalsolution to the radio link scheduling problem that can besolved by the KM algorithm described in Appendix I. Anexample is also illustrated in Fig. 5.

C. Optimization of NV

From the previous two parts, one can obtain the V2I radiolinks and the optimal V2V links based on the separation ofthe V2I and V2V vehicles. Consequently, we can calculate the

1u,i je

BU

V

+U

3u 5u

7u

6u

4u

2u

8u

RV DV 2 3 4 5

3 2 0 2W

0 3 3 4

1 6 0 6

=

é ùê úê úê úê úë û

(a) Matrix

0 0 0 0

5 2 3 4 5

3 3 2 0 2

4 0 3 3 4

6 1 6 0 6

é ùê úê úê úê úë û

(b) Step 1.

1st iteratiion

0 0 0 0

5 3 2 1 0

C 3 0 1 3 1

4 4 1 1 0

6 5 0 6 0

=

é ùê úê úê úê úë û

(c) Step 2.

1st iteration

0 0 0 0

5 3 2 1 0

3 0 1 3 1

4 4 1 1 0

6 5 0 6 0

é ùê úê úê úê úë û

(d) Step 3.

1st iteration

2 1 0 0

0 1 2 3

3 0 0 0

5 0 6 1

é ùê úê úê úê úë û

(f) Optimal

assignment

0 0 0 1

4 2 3 4 5 X

3 3 2 0 2

3 0 3 3 4 X

6 1 6 0 6

Y

é ùê úê úê úê úë û

(e) Step 4.

1st iteration

Fig. 5. An example of the KM algorithm for the bipartite graph in an 8-VEnetwork.

data rate of each part as follows

WB =∑

eB,i∈UB

w (eB,i), (16)

WV =∑

ei,j∈MV

w (ei,j). (17)

Then, the throughput of the entire network is given by

W = WB + WV . (18)

W is determined by parameter NV in a certain optimizationproblem. In other words, given diverse values of NV , i.e.,the different amounts of destination vehicles, the optimizedresults obtained from stage 1 and 2 may not be identical. Thus,in order to achieve the optimal data rate in the network, anappropriate NV is desired to be found.

When there are only few vehicles with a poor channelquality to be aided by others, i.e., small NV , the benefit ofcooperative relaying is not very obvious due to the inefficientuse of the out-of-band radio resources in V2V links. On theother hand, if there are too many vehicles that need help,i.e., large NV , the amount of resources in V2V links to eachvehicle has to be reduced. Thus, the achievable rate of avehicle with 2-hop communications is limited by its V2V link.Therefore, in the given application scenario, there exists anoptimal NV in the proposed scheme, which represents a goodtrade-off between these two effects .

The BG-based scheme proposed above requires much lesscomputational costs. In order to obtain optimal results fora vehicular downlink network, the BG-based scheme canachieve an O(N3 logN) running time, which is of polynomialcomplexity. The complexity of the KM algorithm is O(N3),while that of the optimization procedure of NV is O(logN)with binary search or golden section search [22].

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TABLE ISIMULATION PARAMETERS

Parameter ValueCell radius 500 mVE number 10 to 100

Vehicle model Microscopic model in [25]Max drive peed 126 km/h (35 m/s)

Acceleration 2.6 m/s2

Deceleration -4.5 m/s2

Link scheduling interval 1 sTTI 1ms

Thermal Noise Density -174 dB/HzLTE-Advanced configuration (V2I link)

Carrier frequency 2 GHzBandwidth 40 MHz

Transmit power of BS 52 dBm for 40 MHzDSRC configuration (V2V link)

Carrier frequency 5.9 GHzBandwidth 5 MHz

VE transmit power 20 dBm for 5 MHz

IV. SIMULATION AND NUMERICAL RESULTS

In this section, simulation results are presented to evaluatethe performance of the proposed BG-based scheduling scheme.

A. Simulation configurationThe main parameters and configurations of the network

in our simulations are listed in Table I. In our simulations,vehicles move around an intersection, each direction of whichis a 500 meters long highway. As illustrated in Fig. 6, theintersection is located at the center of the cell and a traffic lightmodel is presented in the intersection to regulate traffic flows.The highway has five 3.5 meters wide lanes, three of whichenter into the intersection and two leave out of it. According tothe microscopic traffic model in [25], two dynamical processesof car-following and lane-changing are considered. The car-following theory is based on the assumption that the motionof a vehicle is governed exclusively by the motion of itspreceding vehicle, the features of which are continuous inspace, discrete in time and accident-free. The random lane-changing model is adopted in our simulations, according towhich vehicles can change to adjacent co-directional lanesrandomly.

The V2I communications use the LTE-Advanced system,which transmits data via a 40 HMz bandwidth at the 2 GHzfrequency with 52 dBm transmit power [23]. The V2V com-munications use the WLAN 802.11p protocol, which supportsthe use of WLAN in the vehicle environment [24]. We adopta 5 MHz bandwidth at the 5.9 GHz frequency with 20 dBmtransmit power. Table II gives the path loss models of V2Vand V2I links used in the simulation. The path loss model ofV2I link is illustrated in detail in [23]. In case of V2V links,βi,j (di,j) is the pass loss attenuation factor at distance di,j ,βi,j (d0) is the pass loss attenuation factor at reference distanced0, γ is the path loss exponent, and σ is the standard deviationof the zero-mean Gaussian variable Xσ∼CN (0, σ). In thesimulation, d0=1,βi,j (d0)=43.9,γ=2.75, and σ= 5.5 [27].

B. Results and discussionsThe performance of the network with exhaustive search for

the MSR is also evaluated for comparative purposes, i.e., the

Destination Vehicle

Vehicle Equipment

Relay Vehicle

Traffic light

V2V link

V2I link

eNB

Fig. 6. Illustration of the simulation scenario in an intersection.

TABLE IIPATH LOSS MODEL

Link type Path loss model

V2I link [23] βB,i

(dB,i

)=l+37.6log10

(dB,i

1000

),

l=128.1−2GHz

V2V link [27] βi,j (di,j)=βi,j (d0)+10γlog10

(di,jd0

)+Xσ

optimal solution to problem (9). Since the optimization ofthe MSR is known to be an NP problem, the number of thevehicles (N ) is set to no more than 40, so as to make exhaus-tive search possible in our simulations with the help of pre-processing. As we know, when two vehicles are far from eachother, there is almost no possibility of cooperative relayingbetween them. Therefore, before the exhaustive search, theV2V links of the vehicles, whose distance is more than 500m, are excluded in the link set. The performances of the MSRalgorithm with or without such pre-processing are comparedwith N = 20, which shows little difference. Then, for the casesof N = 30 and N = 40, we directly apply this pre-processingin order to obtain the performance of the MSR algorithm.

Fig. 7 presents the cumulative distribution functions (CDFs)of the data rates with the MSR and BG-based schemes undervarious numbers of vehicles. It is shown that the data ratesof the BG-based scheme are close to those of the optimal so-lution. In addition, the proposed scheme effectively decreasesthe distribution at the low-rate area, reducing the number ofthe VEs suffering from low speed transmission. For example,it can be seen that in Fig. 7 the CDF curves of MSR are higherthan that of the BG-based scheme at about 500 kbps, i.e., avery low date rate level. It means that there are more userssuffering from the low-speed transmission.

There usually exists some degree of inaccuracy in linkestimation, which may affect the performance of the V2Vnetworks. The SNR inaccuracy is modeled as a random

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 1, NO. 1, MARCH 2013 7

0 1000 2000 3000 4000 5000 60000.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

40 VEs

30 VEs

CD

F

Data rate (kbps)

MSR

BG-based

20 VEs

Fig. 7. CDFs of the data rate with the MSR and BG-based schemes.

0 1000 2000 3000 4000 5000 60000.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

20 VEs

CD

F

Data rate (kbps)

MSR (ideal)

BG-based (ideal)

BG-based (∆=0.5)

BG-based (∆=2)

Fig. 8. CDFs of the data rate with the MSR and BG-based schemes withinaccurate SNRs.

variance with a Gaussian distribution, which has zero meanand a variance of ∆ for each link. Thus, the inaccurate SNRis used for calculating the link weights. Fig. 8 shows the daterate CDF of the BG-based scheme either with the ideal SNRor inaccurate SNR. The variance ∆ is set to 0.5 or 2. It can beseen that the proposed BG-based scheme has good toleranceto the inaccuracy in SNR estimation, i.e., the results withinaccurate SNRs are very close to those under ideal channelestimation. For instance, the average date rates are 4412 kbpsand 4387 kbps in the cases of ∆ = 0.5 and ∆ = 2, whileit is 4429 kbps under perfect channel estimation without theCER. Nevertheless, with a relatively serious CER, it can befound that there are more low-rate VEs, since they cannot becorrectly selected to be relayed.

To better demonstrate the performance difference, Fig. 9plots the average throughout and the data rates at the 5% CDFwith the MSR and BG-based schemes. Compared with theMSR scheme, there is only a slight performance loss in termsof the average data rate, but a considerable improvement on

20 30 400

1000

2000

3000

4000

5000

184.85%221.68%187.77%

0.88%

0.81%

0.83%

Data

rate

(k

bp

s)

Number of VE

MSR: average data rate

BG-based: average data rate

MSR: 5% CDF data rate

BG-based: 5% CDF data rate

Fig. 9. The average data rates and the data rates at 5% CDF with the MSRand BG-based schemes.

the data rate at the 5% CDF, when using the proposed BG-based scheme. This is due to the helping-worst mechanism ofour proposed scheme, which always chooses the VEs underpoor channel condition as the destination vehicles with 2-hopcommunications. The comparison shown in Fig. 9 impliesthat the proposed scheme performs better in fairness thanthe MSR one. Moreover, the proposed scheme has a lowercomputational complexity of O(N3 logN), which is muchmore practical than solving the NP problem for the objectiveof the MSR.

We also simulate the vehicular network without V2V co-operation, i.e., only using the V2I links of the LTE-Advancedsystem. As shown in Fig. 10, the proposed BG-based cooper-ative scheme results in a remarkable improvement in through-put compared to other schemes. The non-cooperative systemachieves a lower data rate than the BG-based cooperative one,by using only 40 MHz bandwidth without the additional 5MHz out-of-band frequency of DSRC. When there are moreVEs in the network, the average data rate decreases due to thereduction in the number of radio resource obtained by eachVE.

To compare the non-cooperative system and BG-basedcooperative system in fairness, we compute their spectralefficiency (SE) as shown in Fig. 11. The SE is relatively higherwhen the VE amount is around 40. When vehicles on the roadare sparser, their locations change rapidly with faster motion,resulting in bad channel conditions and a lower SE. Wheneverthere are too many vehicles passing through the intersection,traffic congestion may not only occur on the road but alsoin the wireless network, which consequently reduces the datarate. In addition, under the assumption of light traffic, the radioresources of DSRC, i.e., the V2V links, are not fully used,since there are not always appropriate relay vehicles availableto help the destination vehicles, resulting in the waste of theout-of-band resources. However, cooperative communicationscan achieve a higher SE when there are more VEs in thenetwork.

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10 20 30 40 50 60 70 80 90 1000

1000

2000

3000

4000

5000

6000

7000

8000

9000

Av

era

ge d

ata

rate

(k

bp

s)

Number of VEs

Non-cooperation

BG-based cooperation

Fig. 10. The average data rate obtained by the non-cooperative and BG-basedcooperative system under various VE numbers.

10 20 30 40 50 60 70 80 90 1001.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2

Sp

ectr

al

eff

icie

ncy

(b

it/s

/Hz)

VE number

Non-cooperation

BG-based cooperation

Fig. 11. The spectral efficiency obtained by the non-cooperative system andBG-based cooperative system under various VE numbers.

Finally, Fig. 12 plots the average number of destinationvehicles NV , while there are various numbers of VEs. Thisvalue represents the number of allocated V2V links underdifferent levels of traffic on the road. With an increasingamount of the VEs, there are more destination vehicles thatare selected to adopt 2-hop communications to enhance theoverall throughput, attributed to the better channel quality ofthe V2V links due to nearer distances and potentially moreappropriate VEs that can be used as the relay vehicles.

V. CONCLUSION AND FUTURE WORKS

The radio scheduling problem in the 2-hop communicationsfor vehicular networks is formulated and solved by a graph-based scheme proposed in this paper. Due to the channelvariation and mobility of VEs, the 2-hop network topology istime-varying, which can be modeled as a spanning tree basedon the V2I and V2V links by using graph theory. The com-putational complexity of solving the optimal tree structure is

10 20 30 40 50 60 70 80 90 1000

5

10

15

20

25

30

35

40

Av

era

ge n

um

ber

of

DV

s

Nnumber of VEs

Fig. 12. Average destination vehicle number in the BG-based cooperativesystem under various VE numbers.

analyzed and proved to be NP hard for practical networks. Asa result, we propose a bipartite graph (BG)-based schedulingscheme, which has low complexity. The performance of theBG-based scheme is found close to that of the optimal MSRscheme. Moreover, the proposed scheme is able to achievebetter fairness among VEs, and can considerably enhancethe date rate of the VEs with poor channel conditions. It isalso shown that cooperative communications are capable ofimproving the throughput, as well as the spectral efficiencyof vehicular networks, in comparison to the scheme withoutcooperation especially under a relatively high traffic load. Forfuture work, the traffic impact on radio resource schedulingwill be investigated, where the user arrival or departure processwill be taken into account.

APPENDIX IKUHN-MUNKRES ALGORITHM FOR SOLVING MWM

PROBLEM

Step 0: Adjacency matrix initialization.We establish a matrix W = [w (ei,j)], which contains all

the weights as illustrated in Fig. 5 (a).Step 1: Label initialization.This algorithm starts with the following labels of each

vertex.

s (ui) =

{max

ei,j∈E′V

w (ei,j) , ui ∈ UB

0, ui ∈ U+V

In Fig. 5 (b), the numbers written at the left and the top ofthe matrix represent the values of s (ui).

Step 2: Calculate excess matrix C.We calculate the excess matrix C as follows.

ci,j = s(ui) + s(uj)− w (ei,j) .

The obtained C is shown in Fig. 5 (c).Step 3: Finding subgraph G′

s.

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 1, NO. 1, MARCH 2013 9

We find the subgraph G′s that includes vertexes ui and

uj satisfying ci,j = 0 and the corresponding edge ei,j .Then, we could get a maximum matching M′ in G′

s, whichcontains the underline edges in Fig. 5 (d). In this example,the maximum matching is e1,8,e3,2 and e6,5. If the foundmaximum matching, M′, is a perfect one with NB edges, weobtain the optimal assignment and the algorithm terminates.

Step 4: Adjustment of labels.Let set Q be a vertex cover of subgraph G′

s, and X =UB ∩Q and Y = U+

V ∩Q. The vertex set Q is a vertex setof G′

s which contains at least one endpoint of each edge. Inthis example, Q is chosen to be the nodes corresponding toRV u1 and u4, and DV u8. Now find

ε = min{ci,j |ui ∈ UB −X, uj ∈ U+V −Y}.

Then, the labels of the vertexes are adjusted according to

s (ui) =

s (ui)− ε, ui ∈ UB −X,s (ui) + ε, ui ∈ Y,s (ui) , others.

Go to Step 2.

REFERENCES

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[2] Pavle Belanovi, Danilo Valerio, Alexander Paier, Thomas Zemen, FabioRicciato, and Christoph F. Mecklenbrauker , “On Wireless Links forVehicle-to-Infrastructure Communications,” IEEE Trans. Vehicular Tech-nology, vol. 59, no.1, pp. 269-282, Jan. 2010.

[3] Christoph Sommer, Armin Schmidt, Yi Chen, Reinhard German, Wolf-gang Koch, and Falko Dressler, “On the feasibility of UMTS-basedTraffic Information Systems,” Ad Hoc Networks, vol. 8, no. 5, pp. 506-517, Jul. 2010.

[4] J. B. Kenney, “Dedicated Short-Range Communications (DSRC) Stan-dards in the United States,” Proceeding of the IEEE, vol. 99, no. 7, pp.1162-1182, Jul. 2011.

[5] M. H. Ahmed, I. Syed, and H. Yanikomeroglu, “On the Performanceof Time Division Multiple Access-Based Multihop Fixed Cellular Net-works with Respect to Available Frequency Carriers,” IET Commun.,vol. 2, no. 9, pp. 1196-1204, Oct. 2008.

[6] K. Zheng, Y. Wang, L. Lei, and W. Wang, “Cross-layer queuinganalysis on multihop relaying networks with adaptive modulation andcoding,” IET Communications, vol. 4, no. 3, pp. 295-302, Feb. 2010.

[7] J. N. Laneman, D. Tse, and G. W. Wornell, “Cooperative Diversityin Wireless Networks: Efficient Protocols and Outage Behavior,” IEEETrans. Inform. Theory, vol. 50, no. 12, pp. 3062-3080, Dec. 2004.

[8] H. Ilhan, I. Altunbas, and M. B. I. Uysal, “Cooperative Diversity forRelay-Assisted Inter-Vehicular Communication,” in Proc. IEEE VTSVehicular Technology Conference, 2008, pp. 605-609.

[9] J. Zhang, Q. Zhang, and W. Jia, “VC-MAC: A Cooperative MACProtocol in Vehicular Networks,” IEEE Trans. Vehicular Technology,vol. 58, no. 3, pp. 1561-1571, Mar. 2009.

[10] L. Zhou, B. Geller, B. Zheng and J. B. I. Cui, “Cross-Layer Designfor Scheduling in Cooperative VANETs,” in Proc. 9th InternationalConference on Intelligent Transport Systems Telecommunications, 2009,pp. 505-509.

[11] Y. Bi, L. X. Cai, X. S. Shen, and H. Zhao, “Efficient and ReliableBroadcast in Intervehicle Communication Networks: A Cross-LayerApproach,” IEEE Trans. Vehicular Technology, vol. 59, no. 5, pp. 2404-2417, Jun. 2010.

[12] Ting Zhou, Hamid Sharif, Michael Hempel, Puttipong Mahasukhon, WeiWang, and Tao Ma, “A Novel Adaptive Distributed Cooperative RelayingMAC Protocol for Vehicular Networks,” IEEE J. Sel. Areas Commun.,vol.29, no. 1, pp. 72-82, Jan. 2011.

[13] I. Krikidis, J. Thompson, and N. Goertz, “A Cross-layer Approach forCooperative Networks,” IEEE Trans. Vehicular Technology, vol. 57, no.5, pp. 3257-3263, Sep. 2008.

[14] Z. Ding, and K. K. Leung, “Cross-Layer Routing Using CooperativeTransmission in Vehicular Ad-hoc Networks,” IEEE J. Sel. Areas Com-mun., vol. 29, no. 3, pp. 571-581, Mar. 2011.

[15] B. Sikdar, “Comparison of Broadcasting Schemes for Infrastructure toVehicular Communications,” IEEE Transactions on Intelligent Trans-portation Systems, vol. 13, no.2, pp. 492 - 502, 2012.

[16] K. Zheng, B. Fan, Z. Ma, X. Shen, G. Liu, and W. Wang, “Multihopcellular networks toward LTE-advanced,” IEEE Vehicular TechnologyMagazine, vol. 4, no. 3, pp. 40-47, Sept. 2009.

[17] J. Janssen, K. Kilakos, and O. Marcotte, “Fixed Preference ChannelAssignment for Cellular Telephone Systems,” IEEE Trans. VehicularTechnology, vol. 48, no. 2, pp. 533-541, Mar. 1999.

[18] Y. Chen, N. Han, S. H. Shon, and J. M. Kim, “Dynamic Frequency Al-location Based on Graph Coloring and Local Bargaining for Multi-CellWRAN System,” in Proc. Asia-Pacific Conference on Communications,2006, pp.1-5.

[19] Y. Chang, Z. Tao, J. Zhang, and C. C. J. B. Kuo, “A Graph-based Ap-proach to Multi-cell OFDMA downlink Resource Allocation,” in Proc.IEEE Global Telecommunications Conference (Globecomm), 2008, pp.1-6.

[20] K. Zheng, Y. Wang, C. Lin, X. Shen, and J. Wang, “Graph-BasedInterference Coordination Scheme in Orthogonal Frequency-DivisionMultiplexing Access Femtocell Networks,” IET Commun., vol. 5, no.17, pp. 2533-2541, Nov. 2011.

[21] H. W. Kuhn, “The Hungarian Method for the Assignment Problem,”Naval Research Logistic Quarterly, vol. 2, pp. 83-97, 1955.

[22] D. Knuth, The Art of Computer Programming, vol. 3, Addison-WesleyProfessional, Boston, Mar. 2011.

[23] 3GPP TR 36.814, V9.0.0, “Further Advancements for E-UTRA, PhysicalLayer Aspects,” Mar. 2010. [Online]. Available: http://www.3gpp.org

[24] IEEE 802.11p-2010, “Wireless LAN Medium Access Control (MAC)and Physical Layer (PHY) Specifications Amendment 6: Wireless Ac-cess in Vehicular Environments,” IEEE Standards Association, 2010.

[25] S. Krauß, “Microscopic Modelling of Traffic Flow: Investigation ofCollision Free Vehicle Dynamics,” DLR, Mar. 1998. [Online]. Available:http://e-archive.informatik.uni-koeln.de/319/

[26] 3GPP TS 36.211, V10.4.0, “Technical Specification Group Radio AccessNetwork,” Dec. 2011.

[27] L. Cheng, B. Henty, D. Stancil, F. Bai, and P. Mudalige, “AFully Mobile, GPS Enabled, Vehicle-to-Vehicle Measurement Platformfor Characterization of the 5.9 GHz DSRC Channel,” in Proc. IEEEAntennas and Propagation Society International Symposium, 2007, pp.1847-1850.

Kan Zheng (SM’09) received the B.S., M.S.and Ph.D degree from Beijing University of Post-s&Telecommunications (BUPT), China, in 1996,2000 and 2005, respectively, where he is currentlyassociate professor. He worked as a researcher in thecompanies including Siemens, Orange Labs R&D(Beijing), China. His current research interests liein the field of wireless communications, with em-phasis on heterogeneous networks and M2M/V2Vnetworks.

Fei Liu received his B.S. degree from the Schoolof Information and Communication Engineering,Beijing University&Posts and Telecommunications(BUPT), China, in 2010. He is currently a candidatefor M.S. in the Key Lab of Universal WirelessCommunications, Ministry of Education, BUPT. Hisresearch interests include performance analysis ofwireless networks, resource allocation and schedul-ing algorithm.

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 1, NO. 1, MARCH 2013 10

Qiang Zheng received his B.S. degree from Collegeof Computer Science and Technology, ShandongUniversity of Technology (SDUT), China, in 2010.He is currently a candidate for PhD in the Key Labof Universal Wireless Communications, Ministryof Education, BUPT. His research interests includeradio resource allocation in vehicular networks.

Wei Xiang (SM’10) received the B.Eng. and M.Eng.degrees, both in electronic engineering, from theUniversity of Electronic Science and Technology ofChina, Chengdu, China, in 1997 and 2000, respec-tively, and the Ph.D. degree in telecommunication-s engineering from the University of South Aus-tralia, Adelaide, Australia, in 2004. Since January2004, he has been with the Faculty of Engineeringand Surveying, University of Southern Queensland,Toowoomba, Australia, where he was first an As-sociate Lecturer in Computer Systems Engineering

from 2004 to 2006, then a Lecturer from 2007 to 2008, and currentlyholds a faculty post of associate professor. He received the Best PaperAward at 2011 IEEE WCNC. His research interests are in the broad areaof communications and information theory, particularly coding and signalprocessing for multimedia communications systems.

Wenbo Wang (M’94) received his B.S., M.S.,and Ph.D degree from Beijing University of Post-s&Telecommunications (BUPT), China, in 1986,1989, and 1992 respectively.

He is currently a professor and dean of graduateschool of BUPT. His research interests include signalprocessing, mobile communications and wireless ad-hoc network.