Joint optimization of link scheduling and resource allocation in cooperative vehicular networks
 Qiang Zheng^{1},
 Kan Zheng^{1}Email author,
 Periklis Chatzimisios^{2} and
 Fei Liu^{3}
https://doi.org/10.1186/s1363801503924
© Zheng et al. 2015
Received: 31 August 2014
Accepted: 20 May 2015
Published: 12 June 2015
Abstract
Vehicular networks are a cornerstone of the envisioned intelligent transportation system (ITS) by enabling vehicles to communicate with each other via vehicletovehicle (V2V) communications to overcome the current and future needs for increasing traffic safety and efficiency. In this paper, we employ the knapsack problem (KP) to formulate the problem of cooperative scheduling and radio resource management in vehicular networks for nonreal time services. For the sake of maximizing sum utility (MSU) of the networks, we propose twodimensionalmultichoice knapsack problem (2DMCKP)based scheduling scheme to select the coordinator vehicles for the sink vehicle and allocate radio resource to V2V and vehicletoinfrastructure (V2I) links to solve the MSU optimization problem. Simulation results indicate that the proposed scheme significantly improves the average utility and average data rates with sustainable computational complexity. Moreover, the designed cooperative communication system achieves higher spectral efficiency and better fairness.
Keywords
1 Introduction
Vehicular networking serves as one of the most important enabling technologies in the envisioned intelligent transportation system (ITS) which mainly consists of two transmission categories, i.e., vehicletovehicle (V2V) communications which enable vehicles to communicate with each other and vehicletoinfrastructure (V2I) communications which capacitate vehicles to communicate with roadside unit [1]. Explosive growth in information technology has enabled scores of innovation applications in vehicular networks, such as realtime update of congestion, weather conditions report, multimedia services, and online games [2, 3]. In the foreseeable future, more and more vehicles will be equipped with wireless radio devices capable of V2V and V2I communications to contribute to a safer and more efficient driving experience. To satisfy the requirements of the applications in vehicular networks, intensive scholars and researchers have been constantly working for the advance of the V2I technologies. Meanwhile, extensive investigations and trials have been carried out to V2V communications resulting in the development of various standards, such as IEEE 802.11p [4] and the 1609 family of standards [5, 6].
Most of the innovation applications in vehicular networks such as mobile television, multimedia services, or security applications require high throughput and/or low delay. However, the rapid change of the topology of vehicular networks due to the mobility of the participating vehicles results in the degradation of the performance of vehicular communications and makes evident the need for more robust protocols or schemes to improve the system capacity. To eliminate the negative impact of the wireless channel fading and exploit spatial diversity, significant amount of research work has been carried out on the areas of cooperative communications and resource scheduling in cooperative vehicular networks [7–9]. The core idea of cooperative communications in vehicular networks is that when the channel between the base station (BS) and the destination is unreliable, another vehicle that encounters much better channel conditions than the BS is selected to forward the packets to the destination vehicle (DV) and, thus, a significant gain for the whole system is achieved. In [10], authors develop and analyze lowcomplexity cooperative protocol that combats fading caused by multipath propagation in wireless networks. Moreover, amplifyandforward (AF) and decodeandforward (DF) have been already developed to enhance the spectral diversity to reduce the outage probability. In [1], the authors design a new distributed cooperative relay medium access control (MAC) protocol to maximize the vehicles’ achieved system throughput and service distance by adaptively selecting among suitable transmission modes and relay nodes according the channel quality. Simulation results show that the Markovchainbased modeling outperforms existing schemes under the same networks scenarios and maximize the achieved system throughput and service distance. Crosslayer approaches for cooperative diversity networks are also investigated, combining the cooperative diversity concept with joint optimization of the physical and MAC layers [9, 11]. The network coding (NC) technique is employed to improve the performance of vehicular communications. In [12], the authors investigate the information spread problem in a joint V2I and V2V communication system, and networkcodingbased technique is used to mitigated the interference caused by relaying signal. However, little research effort has been devoted to resource allocation and relay selection for cooperative vehicular communications. A downlink resource allocation scheme for V2V2I communication system is proposed in [13]. Both an infrastructure and a vehicle can form multiple direction beams via smart antenna in order to transmit multiple data streams simultaneously. But the authors in [13] only consider the resource allocation on V2V link and V2I links and how to avoid the cochannel interference between V2I and V2V links with no regard to relay selection. In [14, 15], several relay selection and resource allocation for cooperative communication are presented. The main idea of them is that V2V communication is used to complement V2I communication. A bipartite graphbased scheduling scheme to allocate the V2I and V2V links for both 1hop and 2hop communications is proposed in [14]. The KuhnMunkres algorithm is applied to solve the problem of maximum weighted matching of the constructed bipartite graph of the vehicular networks, and simulations indicate that the proposed solution performs extremely close to the optimal one and achieves better fairness. But the radio resource are allocated equally to every link, which is not the optimal. In [16], authors take the resource allocation of V2V links into consideration when making relay selection decision. A cooperative social network and its dynamic bandwidth allocation algorithm are proposed in [17]. In [17], the authors pay more attention to upper layer social networks and the proposed scheme is divided into two step: relay selection and bandwidth allocation. However, the vehicles select the closest relay station (RS) to forward data, which is not the optimal selection and the link quality is not consideration. In addition, in the simulation, the interaction among vehicles is not taken into account. In [15], the long range (LR) transmission and short range (SR) transmission are proposed. The LR is based on LongTerm Evolution (LTE) and SR is based on IEEE 802.11p. The resource allocation in [15] only focuses on LR (LTE) links and the V2V links adopt multicast, which is suitable for delaysensitive service, for example, public safety service. An enhanced connectivity scheme is proposed in [18], in which the author proposed resource allocation algorithm for joint operation of SR V2V communications and LR LTE communications in vehicular networks. Considerable research effort that has been devoted to cooperative communication in vehicular networks have proposed a number of resource allocation schemes or relay selection schemes, respectively. However, most of them have solved part of the problems appeared in cooperative vehicular networks and the proposed schemes are usually suboptimal. In our work, we propose the optimal scheduling scheme for cooperative vehicular communications, which takes relaying selection, resource allocation on V2I links and resource allocation on V2V links into consideration.
In our paper, we consider scenarios where a vehicle equipment (VE) can enjoy service through V2I connectivity through cellular communications, such as LTE. LTE is employed to support V2I communications for following reasons, i.e, high data rate, low latency, large coverage area, high energy efficient, robust interferencecontrolled, high penetration rate, and highspeed terminal support [19, 20]. Nevertheless, several challenges lie ahead before LTE can be exploited in vehicular environments, e.g., in LTE, the VEs far away from the BS will suffer from much lower data rates due to poor radio links. To tackle this challenge, a cooperative relaying mechanism among neighboring vehicles is desired to be established for V2V communications through another OFDMAbased system [21]. Due to the limitation of V2V and V2I radio resources, the approach that we need to utilize in order to establish the V2V links and allocate the radio resources to V2I and V2V links is crucial to the performance of the vehicular network. We employ twodimensionalmultichoice knapsack problem (2DMCKP) to formulate the problem of scheduling and allocating resources to V2I and V2V links. The optimal solution is obtained through the 2DMCKP. Our approach actually enhances the total utility and achieves better fairness among VEs.

Formulation of the scheduling and allocating problem in the 2hop vehicular network;

Design of a optimal link scheduling and resources allocation scheme for vehicular networks with considerably lower computational complexity; and

Performance comparison against the maximum sum rate (MSR) and BGbased schemes of [14].
The rest of our paper is organized as follows. The system model and problem formulation are illustrated in Section 2. Multidimensionalmultichoice knapsack problembased (MDMCKP) scheduling scheme is proposed in Section 3. Simulation scenarios and numerical results are presented and analyzed in Section 4. Finally, conclusions and future research are provided in Section 5.
2 System model and problem formulation
2.1 System model
Definitions for the notations
Symbol  Description 

N  The total number of vehicles in the scenarios 
N _{ B }  The number of vehicles that directly communicate with eNB 
N _{ V }  The number of vehicles that cooperatively communicate with eNB 
K _{ B }  The number of radio resources available for direct communication 
K _{ V }  The number of radio resources available for cooperative communication 
P _{ B }  Transmit power over per bandwidth 
P _{ T }  Total transmit power of eNB 
P _{ i,j }  Transmit power for V2V link between vehicles i and j 
\({\tilde P_{T}}\)  Total transmit power of each vehicle 
N _{0}  Unilateral power spectral density of AWGN 
W  System bandwidth 
N _{ C }  The number of cells 
β  Path loss attenuation factor 
A  Binary matrix that represents the resource allocation between CVs 
B  Binary matrix that represents the resource allocation between SVs 
η _{ B,i }  Achievable data rate of the ith CV 
η _{ i,j }  Achievable data rate of the link between vehicle i and j 
n _{ i }  Radio resource allocated for the ith CV 
n _{ i,j }  Radio resource allocated for link between vehicle i and j 

The vehicles and evolved NodeB (eNB) broadcast signaling to indicate the existing of themselves via control channel periodically;

The vehicles which receive the signaling to estimate the V2V and V2I link quality and update the CSI;

Then, the vehicles upload the CSI to the scheduling center;

Based on CSI, the scheduling center schedules links, allocates radio resources and broadcasts the scheduling results via control channel.
2.1.1 2.1.1 Direct communications
where W is the basic bandwidth of one RB, n _{ i } is the number of RBs allocated to ith CV for direct communication by the scheduling center, N _{ C } is the number of cells occupying the same radio resources and only the intercell interference from the neighbor cells are taken into account, β _{ m,i } is the path loss attenuation factor from the eNB of cell m to the ith CV, P _{ m } is the transmit power over W bandwidth, i.e., \({P_{m}} = \frac {{{P_{T}}}}{{{K_{B}}}}\), P _{ T } is the total transmit power of the eNB, and N _{0} is unilateral power spectral density of the additive white Gaussian noise (AWGN).
2.1.2 2.1.2 Cooperative communication

Each SV can be assisted by only one CV at any time;

One CV can forward data to more than one SV;

The DF relaying is applied at CV.
where P _{ i,j } is the transmit power on only one RB from CV i to SV j, i.e., \({P_{i,j}} = {{{{\tilde P}_{T}}} / {{K_{V}}}}\), \({{{\tilde P}_{T}}}\) is the total transmit power over all bandwidth of V2V links.
2.2 Problem formulation
Based on the network topology, we denote that N _{ B } and N _{ V } as the number of the CV and SV. Let the binary matrix \({\textbf {A}} = {\left \{ {{a_{i,p}}{a_{i,p}} \in \left \{ {0,1} \right \}} \right \}_{{N_{B}} \times {K_{B}}}}\) represent the resource allocation between CVs, where a _{ i,p }=1 denotes that p RBs are allocated to CV i for direct communication, and a _{ i,p }=0 otherwise. The establishment of V2V links and resource allocation on CVs and SVs are indicated by another binary matrix \({\textbf {B}} = {\left \{ {{a_{i,j,p,q}}{a_{i,j,p,q}} \in \{ 0,1\}} \right \}_{{N_{B}} \times {N_{V}} \times {K_{B}} \times {K_{V}}}}\), where a _{ i,j,p,q }=1 means that SV j spends q RBs in V2V link and p RBs in V2I link assisted by CV i. Our goal is to find A and B such that the objective functions are optimal with the limited bandwidth. Many resource management methods or relayselecting mechanisms aim at maximizing throughput or spectral efficiency. However, the satisfaction of the user is not only linearly dependent on plain quality of service (QoS). Utility theory provides the reasonable methods to formulate the relationship between user experience and various QoS metrics. A utility function is used as an effective tradeoff between spectral efficiency and fairness of resource allocation. The utility function maps the performance criteria into a real number used as a metric to quantify the satisfaction [23]. From the aspect of the user, the most important factor affecting users’ satisfaction is the data rate of communication. Therefore, in this paper, the utility is assumed to be the function of data rate.
where f(∙) is the utility function of data rate. The first line in (4) is the objective function. The second and third lines in (4) account for the fact that each vehicle only has one solution to communicate with the eNB. The fourth line in (4) states the limited RBs number for V2I links, and the last line corresponds to the restrictions of RBs number used for V2V communications.
where x is the achievable data rate, R _{max} is the maximum data rate, and the parameters a and b are used for the normalization of the function [23]. The utility function is adopted for two purposes: 1) to ensure the fairness among vehicle users and 2) to represent the fact that the user satisfaction is not increasing linearly with the data rate.
3 Multidimensionalmultichoice knapsack problembased scheduling scheme
In this section, we propose a link schedulingscheme based on MDMCKP to seek the optimal solution to establish the V2V links and to distribute radio resource units to V2I and V2V links for downlink transmissions. The vehicles with poor V2I links are chosen as SVs which communicate with eNB involving both V2I and V2V links. The other vehicles with better V2I links can act as CVs to forward data to SVs. We first give a brief introduction to MDMCKP problem, followed by the proposal of the MDMCKPbased scheduling scheme.
3.1 MDMCKP problem
The MDMCKP problem is a new proposed algorithm, which integrates the 01 multidimensional knapsack problem (0–1 MDKP) and MCKP [24]. 01 MDKP and MCKP are generalization of 01 knapsack problem and special case of general 01 integer programming.
The 2DKP cannot be solved in a time bounded by a polynomial in n. However, admit a pseudopolynomial algorithm, i.e., an algorithm whose time complexity is bounded by a polynomial in n and c. In fact, it can easily be verified that the following dynamic programming recursions solve the 2DKP [24].
The time complexity of 2DKP is O(n c _{1} c _{2}).
The optimal solution is the state corresponding to f _{ r }(c). If we have \({\sum \nolimits }_{k = 1}^{r} {{{\bar w}_{k}}} > c\), the instance has no feasible solution, and we obtain f _{ r }(c)=−∞. For each l, the above computation requires O(N _{ l }c) operations, so the overall time complexity of the method is O(n c).
After the iterative process, the optimal solution is the state corresponding to f _{ r }(c _{1},c _{2}).
The parameters of the 2DMCKP example
Subset  Profit  First weight  Second weight 

First subset  (2,3,4,5)  (1,2,3,4)  (0,0,0,0) 
Second subset  (3,4,5,6)  (1,2,3,4)  (0,0,0,0) 
Third subset  (5,6,7,7)  (1,2,3,4)  (0,0,0,0) 
Fourth subset  (2,3,4,5,3,4,5,6,5,6,7,7)  (1,2,3,4,1,2,3,4,1,2,3,4)  (1,2,3,4,1,2,3,4,1,2,3,4) 
Fifth subset  (2,3,4,5,3,4,5,6,5,6,7,7)  (1,2,3,4,1,2,3,4,1,2,3,4)  (2,3,4,5,2,3,4,5,2,3,4,5) 
3.2 2DMCKPbased scheduling scheme

Construct the group of 2DMCKP.
For VE j, group G _{ j } of selections is constructed. If vehicle j is CV,$$ {G_{j}} = \left\{ {{g_{p}} = {\eta_{B,j}}\left(p \right)\left {1 \le p \le {K_{B}}} \right.} \right\}, $$(27)otherwise,$$ \begin{array}{l} {G_{j}} = \left\{ {{g_{(i  1){K_{B}}{K_{V}} + (q  1){K_{B}} + p}} = {{\tilde \eta }_{B,i,j}}\left({p,q} \right)} \right\},\;\\ \quad \quad for\;1 \le p \le {K_{B}},1 \le q \le {K_{V}},{\mathrm{1}} \le i \le {N_{B}} \end{array}. $$(28)where the set G _{ j } contains K _{ B } or K _{ B }×K _{ V }×N _{ B } elements, each of which represents the data rate corresponding to VE j, i.e., η _{ B,j }(p) and \({{{\tilde \eta }_{B,i,j}}\left ({p,q} \right)}\) are both defined in Section 2.
Based on 2DMCKP, we consider all the selections of S V _{ j } as a group and refer the K _{ B } and K _{ V } as the packet volumes. The mapping C _{1}(∙) and C _{2}(∙) is to obtain the first and second index of the solution. For CV i, the first dimension cost is p and the second dimension cost is 0, i.e., C _{1}(g _{ m })= mod (m,K _{ B }), C _{2}(g _{ m })=0. However, for SV j, the first dimension cost is p and the second dimension cost is q, i.e., \({C_{1}}\left ({{g_{m}}} \right) = \bmod \left ({m,{K_{B}}} \right),\;{C_{2}}\left ({{g_{m}}} \right) = \left \lceil {\frac {{\bmod \left ({m,{K_{B}}{K_{V}}} \right)}}{{{K_{B}}}}} \right \rceil \). The 2DMCKP aims to achieve the maximum utility of all VEs, i.e.,$$ \max \sum\limits_{i = 1;{g_{m,i}} \in {G_{i}}}^{{N_{B}} + {N_{V}}} {f\left({{g_{m,i}}} \right)}, $$(29)subjected to$$ \begin{aligned} {\sum\limits_{i = 1}^{{N_{B}}{\mathrm{+ }}{N_{V}}} {{C_{1}}\left({{g_{m,i}}} \right)} \le {K_{B}},}\\ {\sum\limits_{i = 1}^{{N_{B}}{\mathrm{+ }}{N_{V}}} {{C_{2}}\left({{g_{m,i}}} \right)} \le {K_{V}}.} \end{aligned} $$(30)Then the problem of resource management is converted to 2DMCKP.

Solution of 2DMCKP.
The solution of 2DMCKP is described in detail in Algorithm 1.

Optimization of N _{ V }.
Based on the above discussion, we can calculate the total utility of all VEs, which is determined by parameter N _{ V } in a certain optimization problem. With a relatively large N _{ V }, more SVs in poor conditions may be assisted by the CVs, and consequently increase the total utility. However, an overly large N _{ V } will limit the data rates of the V2V links, resulting in the reduction of the total utility. Furthermore, a too small N _{ V } is unable to make full use of the V2V resources, leading to waste of radio resources. In other words, the total utility is an unimodal function of N _{ V }. The optimal N _{ V } can be obtained through binary search.
Through steps 1–3, the optimal V2V links and resource allocations are obtained. The SVs may have better SVs to be forwarded data, which results in that some CV has no SV to help.
4 Performance evaluation
In this section, we evaluate the performance of the proposed 2DMCKPbased scheduling scheme via simulations. The experimental platform and considered simulation scenarios are implemented by utilizing the OPNET simulation software (version 14.5). Throughout our simulations, online oneway coupling is used, which eliminates the use of a sequential filebased process by having both simulators, traffic and communication, run in parallel [25].
4.1 Simulation configuration
Simulation parameters
Parameter  Value 

Cell radius  500 m 
VE number  10 to 100 
Traffic model  Microscopic model in [26] 
Max drive speed  126 km/h (35 m/s) 
Acceleration  2.6 m/s ^{2} 
Deceleration  −4.5 m/s ^{2} 
Length of time slot  1 ms 
Link scheduling interval  1 s 
LTE configuration (V2I link)  
Carrier frequency  2 GHz 
Bandwidth  40 MHz 
Transmit power of eNB  52 dBm for 40 MHz 
Configuration of V2V link  
Carrier frequency  5.9 GHz 
Bandwidth  5 MHz 
VE transmit power  20 dBm for 5 MHz 
Utility function for elastic service  
a  50 
b  1 
R _{max}  6000 
Path loss model  
V2I link  \(\begin {array}{l} P\left (d \right){\mathrm {= }}l{\mathrm {+ }}37.6{\log _{10}}\left ({\frac {d}{{1000}}} \right){\mathrm {,}} \\[2pt] l{\mathrm {= }}128.1{\mathrm { }}2GHz \\[2pt] \end {array}\) 
V2V link  \(P\left (d \right){\mathrm {= \textit {P}}}\left ({{d_{0}}} \right){\mathrm {+ }}10\gamma {\log _{10}}\left ({\frac {d}{{{d_{0}}}}} \right){\mathrm {+ }}{X_{\sigma } }\) 
V2I communications are based on the LTEAdvanced system. On the basis of [22], V2I communications data are transmitted via a 40MHz bandwidth at the 2GHz frequency point using 52 dBm transmit power. Nevertheless, V2V communications use another OFDMAbased system that supports three different bandwidths, i.e., 5, 10, and 20 MHz operating in the 5.8 or 5.9GHz frequency band. Four various power classes are defined in the standard, i.e., transmit power of 0, 10, 20, and 28.8 dBm. In our simulations, V2V communications use 5MHz bandwidth at 5.8GHz frequency point with transmit power at 20 dBm. Table 3 provides the path loss models of V2V and V2I links utilized in our simulations. The path loss model of V2I links is illustrated in detail in [22]. In case of V2V links, P(d) is the received signal strength at a distance d, P(d _{0}) is the received signal strength at a reference distance d _{0}, γ is the path loss exponent, and σ is the standard deviation (STD) of the zeromean Gaussian variable X _{ σ }. In the simulation, d _{0}=1,P(d _{0})=43.9,γ=2.75, and σ=5.5 [27].
4.2 Results and analysis
In this subsection, the MSR and the BGbased schemes proposed in [14] are both simulated for the purpose of performance comparison. The MSR and BGbased schemes are both subject to that one CV could forward data to at most one vehicle and the RBs are divided to all links equally.
The average data rates and data rates at 5 % CDF among different schemes
Number of VEs  Scheduling scheme  5 % CDF  Average data rate  

Data rate (kbps)  Gain (%)  Data rate (kbps)  Gain (%)  
20  MSR scheme  407  100  4386  100 
BGBased scheme  1120  275.18  4350  99.18  
2DMCKPbased scheme  1748  429.48  4552  103.79  
30  MSR scheme  348  100  3014  100 
BGBased scheme  996  286.21  2990  99.20  
2DMCKPbased scheme  1563  449.14  3110  103.19  
40  MSR scheme  296  100  2336  100 
BGBased scheme  862  291.22  2320  99.32  
2DMCKPbased scheme  1266  427.70  2430  104.02 
5 Conclusions
In this paper, the radio link scheduling and resource allocating problem for cooperative vehicular networks are formulated and a joint optimization method based on 2DMCKP algorithm is proposed. In lieu of MSR of the vehicular networks, utility theory is employed to formulate the relationship between user experience and data rate. The optimal link scheduling and resource allocating scheme obtaining the MSU of the vehicular networks is proved to be NPhard. Therefore, we propose the 2DMCKPbased scheme, which has an acceptable complexity. To verify the performance of the proposed scheme, we develop a traffic and communication simulator that is based on carfollowing and random lanechanging models. The simulation results indicate that the performance of the 2DMCKP scheme is significantly higher than one of the MSR and BGbased schemes. In addition, the 2DMCKP scheme is able to achieve better fairness among VEs than the one of MSR and BGbased schemes and considerably improves the data rate and utility of VEs under poor channel conditions. It is also shown that the 2DMCKP scheme for cooperative vehicular communications is capable of improving the throughput, as well as the spectral efficiency of vehicular networks, in comparison to the BGbased and noncooperative scheme.
In future research, we will consider the dynamic process of the arriving data packets and multiple service classifications, for example, infotainment service, traffic safety service, and traffic efficiency service. Dynamic programming theory is employed to optimize the system performance, and endtoend delay will be considered as a metric to measure the performance for different services.
Declarations
Acknowledgements
This work is funded in part by the National Science Foundation of China (No.61331009), the Fundamental Research Funds for the Central Universities (No. 2014ZD0302), and the National Key Technology R&D Program of China under Grant 2014ZX03003011–004.
Authors’ Affiliations
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