 Research
 Open Access
Analysis of the scope of cooperative bandwidth sharing among mobile routers in vehicular networks
 Lai Tu^{1},
 ShihYang Lin^{2} and
 ChungMing Huang^{2}Email author
https://doi.org/10.1186/168714992014130
© Tu et al.; licensee Springer. 2014
 Received: 30 January 2014
 Accepted: 24 June 2014
 Published: 11 August 2014
Abstract
This paper investigates the optimal cooperation scope (OCS) for cooperative bandwidth sharing (CBS) in vehicular networks. An analytical model, which comprises the network model, relay schemes, cost model, and vehicular flow model, is presented. Three relay schemes based on optimal single path relay and opportunistic relay for multihop CBS are proposed and studied. The OCS is solved as the maximum physical distance or hops between the bandwidth requester and bandwidth helper in the optimal solution to maximize the CBS benefit. OCSs for different environments and with different relay schemes are given in the paper. The results indicate that the OCS is sensitive to the cost weight and may also be larger when using a proper opportunistic relaybased scheme than when using the optimal single pathbased one. The results also show that the vehicular density does not affect the optimal cooperation scope much but can result in different CBS benefit. The model and findings of the relations between OCS and the running environment revealed in this paper can be used as a reference for parameter choosing when designing the CBS system in vehicular networks.
Keywords
 Vehicular networks
 Cooperative bandwidth sharing
 Relay scheme
 Cooperation scope
 Vehicular flow model
1 Introduction
Recent advances in vehicular technologies have promoted new wireless technologies for vehicles’ internetworking [1]. In particular, the dedicated shortrange communications (DSRC) technology, which is a variant of IEEE 802.11a, is designed to operate within a frequency band (5.9 GHz) licensed solely for the purpose of vehicular communications and is being optimized for operation within the highspeed vehicular environment [2]. The DSRC technology has been studied as an intervehicle communications platform for applications like collision avoidance [3], automated highway systems [4], and passenger teleconferencing. Meanwhile, Internet access on vehicles is usually provided by some device called Mobile Router, which generally has two wireless interfaces for different purposes [5, 6]. The wireless wide area network (WWAN) interface usually uses 3G or LTE, WiFi, or modified WiFi technology to connect to the corresponding infrastructure, and the wireless local area network (WLAN) interface mostly adopts WiFi to supply local network connection on vehicle terminals.
Therefore, it is quite possible that in a future vehicle, an onboard unit (OBU) integrates all of these techniques for different purposes and works cooperatively to maximize the efficiency. In this paper, we investigate one of such issues, i.e., the optimal cooperative bandwidth sharing for mobile routers in vehicular networks. More specifically, we focus on the cooperation among nodes using WWAN and V2V wireless interfaces.
 1.
The WiFibased technologies suffer from connectivity disruptions in the vehicular environment [7, 8], while data rate of 3G or LTE degrades quite much when vehicles are moving fast or users in the cell are crowded. Thus, none of the current wireless technologies can provide perfect performance for WWAN in the vehicular environment.
 2.
Internet traffic load and pattern can be rather different from node to node. For example, Internet TV service may be provided on a bus, and some users in another car may like surfing the Internet while there happens to be no Internet traffic from a third truck.
 3.
Although DSRC supports intervehicle communication, most of its applications are limited to a specific safety or infotainment purpose; otherwise, the DSRC device is usually idle. Few studies consider DSRC as an auxiliary means to enhance general Internet access despite its communication capability, which is really some kind of waste.
As a result, we consider an approach to enable bandwidth sharing among vehicles via DSRC communications. The onboard mobile router that is short of bandwidth borrows bandwidth from one or more mobile routers in a scope whose traffic is light enough to have extra bandwidth. So the WWAN bandwidth resource has been pooled together and fully utilized by mobile routers.
While cooperation among colocated mobiles is not a new concept in mobile networks (see Section 2 for literature review), it is rarely studied in the vehicular environment. Due to the difference in the vehicular environment, pointtopoint link between two vehicles is not stable. Consequently, there may not be many collaborators in one hop range. However, if multihop cooperation is enabled, it may be a problem whether the relay cost will overwhelm the benefit from cooperation or not. So, in this paper, we are trying to answer the question: Is it worthy to use multihop bandwidth sharing for mobile routers in the vehicular environment? If the answer is positive, a further question is to be answered: How many hops will be the upper bound?
To answer the aforementioned questions, we build an analytical model that considers both networking model and vehicular flow model. We formulate the CBS problem into an optimization problem and analyze the cooperation scope (CS) in the optimal solution. A distributed algorithm to solve the CBS problem is also given as a reference for practical implementation. The results show that the optimal cooperation scope is sensitive to the cost weight and may also vary with relay schemes. The optimal cooperation scopes in different scenarios are given which can guide parameter setting in designing a CBS system. To the best of our knowledge, the work in this paper is the first attempt to model cooperative bandwidth sharing in the vehicular environment and it also gives some new findings in the CBS problem.
The rest of the paper is organized as follows: After a general review of related work in Section 2, the model details are elaborated in Section 3. Section 4 briefly introduces a distributed algorithm for practical implementation. Numeric results are given and analyzed in Section 5, followed by the conclusion in the last section.
2 Related work
Similar researches on aggregating bandwidth of multiple interfaces or mobiles’ cooperation to improve efficiency have been investigated in prior work [9–21].
To support Internet connectivity in vehicular environments, both academics and standard organizations have made their efforts on the stateoftheart network mobility (NEMO) architecture [9–11]. The NEMO Basic Support (NEMOBS) [10] and later proposed improved solutions [12, 22] provided possibility of seamless communications in vehicular environments. The Mobile IP (MIP)based solutions and their extensions are usually preferred in NEMO due to their scalability and wide adoption [11, 23, 24]. For instance, the Proxy Mobile IPv6 (PMIPv6)based NEMO (PNEMO) and fast PNEMO can achieve low traffic cost and handover latency for vehicular networks [24, 25]. To provide uninterrupted Internet connection, application of a multihoming technique in NEMO is studied in [14, 26].
BAG [15] motivated the advantages of simultaneous use of multiple interfaces and proposes a networklayer architecture that enables such use. MAR [16] makes use of the multiplicity of the wireless networks available by dynamically instantiating new channels based on traffic demand, aggregating the bandwidth and dynamically shifting load from poor quality to better quality channels.
Kandula et al. [17] focused on load balancing for more flexible and efficient allocation of resources, thereby extending the lifetime of a network. Sharma et al. [18] proposed a multipath transport protocol, based on a carefully crafted set of enhancements to TCP, that effectively utilizes the available bandwidth and diversity provided by heterogeneous, lossy wireless paths.
FatVAP [19] introduced an 802.11 driver that aggregates the bandwidth available at accessible access points (APs) and also balances their load. FatVAP challenges the fact that APs often provide highspeed wireless connectivity but access the Internet via independent, relatively lowspeed DSL or cable modem links. If we regard a mobile node with a V2V interface as an AP and an Internet application as a node in the WLAN, the scenarios considered in FatVAP are similar to ours where in both exists bandwidth unbalance.
Inspired by bridging the gap between the rangespeed dichotomy of WWAN and WLAN, Ganesh et al. [20] presented COMBINE, a system for collaborative downloading. COMBINE enables mobile devices that are within the WLAN range to pool together their WWAN links and thus significantly increases the effective speed available to them. CACBR [27] presented a contextaware community based routing for intermittently connected networks. It exploited the socialbased movement pattern and the contextawareness of nodes for efficient message delivery in delaytolerant networks.
In [28], the authors exploited the potential of smart phones in proximity cooperatively, using their resources to reduce the demand on the cellular infrastructure, through a decision framework called RACE (Resource Aware Collaborative Execution). RACE enables the use of other mobile devices in the proximity as mobile data relays.
In applications of bandwidth aggregation or bandwidth sharing, video streaming is the most common one that benefits multisourcing. In [29], the authors provided a unique solution by proposing a new multisource streaming strategy specifically tailored for nextgeneration mobile networks for delivering multimedia services to mobile users.
These works consider different aspects in cooperation coordination for collaborative communication and are mostly like bandwidth borrow schemes, and most of them focus on low mobility scenarios or onehop scenarios which are quite different in the vehicular environment.
Some other work discussed P2P cooperation in networking on public transport. Liam et al. [30] proposed a new content source selection scheme for singlehop, peertopeer based content sharing on public transport. The scheme aims to identify, among colocated peers that have relevant content, the one that has the highest chance to remain colocated long enough for data transfers to complete. However, the scenario also focused on colocated mobiles (meeting by chance) in the same vehicle.
C5 [31] introduced a collaborative content fetching scheme for groups of mobile subscribers with common characteristics. C5 employed a smallscale P2SP framework of a hybrid mobile network which considers possible concurrent mobile Internet traffic to maximize the utility of WWAN links and supports MAC layer multicast in community.
To sum up, these studies discussed the following: (i) solutions and analysis of supporting network mobility in vehicular environment [9–14], (ii) resource aggregation and allocation of multiple interfaces in mobile networks [15–17, 19], or (iii) group formation and coordination [20, 21, 28], or (iv) P2P content sharing among mobiles on one vehicle [30, 31]. Most of them focus on system implementation and scheme design. In this paper, we bring a new issue and consider the analytical model to formulate the problem.
3 System model
3.1 Target scenario and assumptions
Before we formulate the problem, we first name the elements and list some assumptions for the characteristics of the operating environment:

We assume that all mobile routers in the CBS scenario have at least three wireless interfaces: (i) WLAN as the gateway for onboard subscribers, (ii) WAVE for V2V communications, and (iii) 3G/LTE connection as the WWAN for Internet access.

A mobile router that has sufficient WWAN bandwidth (named the helper) can help the nodes that lack in WWAN bandwidth (named the requester) with its excessive bandwidth on their requests.

The cooperation scope is considered in two different representations. One is the number of hops of the transmission between the source and destination, and the other is the physical distance between the source and destination nodes. The latter is used due to the number of hops of the transmissions between two same nodes, which may vary by chance in some opportunistic routing schemes. The maximum CS in the optimal cooperative bandwidth sharing solution is considered as the optimal cooperation scope, OCS.

The cooperative bandwidth sharing can be employed between any helper and requester in a range of CS via either direct link or multihop communication. The mobile router that is involved in the traffic relay between a helper and a requester is named forwarder. Note that a helper or a requester can be a forwarder for another helperrequester pair as well. We also assume that a requester is able to find an optimal route to the helper when multihop relay is applied.

It does not matter whether mobiles in the CS are customers of the same WWAN ISP or not, but we assume that each WWAN connection uses an orthogonal channel and there is little interference in WWAN connection among mobiles, despite whether they are from the same ISP or not. We further assume that the number of mobiles in a CBS scenario does not exceed the capacity of the WWAN tower.

Any mobile node is aware of the position and velocity of any other node in its CS, which can be used to help a mobile node to find a route and estimate the cost from the requester to the helper. This is also feasible as current DSRC or WAVE protocol running in the OBU supports multichannel communication and usually reserves a dedicated broadcast channel to disseminate related information for safety applications, which usually include the vehicle’s position and velocity.
Terms and symbols
Symbols  Terms 

x _{ i }  {x_{ ij }} Rate allocation vector of node i 
e _{ i }  Available link bandwidth between node i and base station (BS) tower 
w  Available capacity of WLAN 
x _{ ii }  Flow rate of node i directly connected to BS tower 
x _{ ij }  Flow rate of node i via the link of node j to the BS tower 
 The set of the nodes in CS 
x _{i,max}  Max requirement of the traffic flow of node i 
r  A requester 
h  A helper 
f  A forwarder 
 The set of the helpers in CS 
 The set of the requesters in CS 
θ  A path $\theta \triangleq \u3008{f}_{0},{f}_{1},\dots ,{f}_{m}\u3009$, which is defined as a sequence of forwarders, each of which, e.g., f_{ i }, receives packets from its uplink node f_{i−1} and sends to its downlink node f_{i+1} 
$\mathcal{P}(h,r)$  The set of all possible paths between h and r 
c_{ h }, c_{ r }  Constant coefficients for helper cost and relay cost per unit data, respectively 
$\mathcal{\mathcal{L}}\left(\theta \right)$  The set of links that compose the path θ 
δ _{ l }  The link cost ${\delta}_{l}\triangleq \delta (i,j)\triangleq 1/p(i,j)$, which is defined as the reciprocal of the successful transmission probability between i and j 
3.2 Problem formulation
There are several requirements for the rate allocation algorithm: (i) It should allocate the bandwidth resources for all mobiles to achieve a maximum utilization of all available WWAN resources. (ii) It should allocate the resource in a fair way. (iii) Communication overhead needs to be minimized for the algorithm.
Problem formulation of the optimal bandwidth sharing among mobile nodes
$\begin{array}{cc}\underset{\mathbf{x}\ge 0}{\mathrm{max}}U\left(\mathbf{x}\right)=& \sum _{i\in \mathcal{\mathscr{H}},j\in \mathcal{R}}U\left({w}_{1}{x}_{\mathit{\text{ij}}}{w}_{2}{C}_{\mathit{\text{ij}}}\left({x}_{\mathit{\text{ij}}}\right)\right)\end{array}$  (3) 
subject to:  
$\begin{array}{lll}0\le {\sum}_{i\in \mathcal{\mathscr{H}}}{x}_{\mathit{\text{ij}}}\le {x}_{j,max}& \text{,}\phantom{\rule{2em}{0ex}}& \forall j\in \mathcal{R}\end{array}$  (4) 
$\begin{array}{ccc}{\sum}_{j\in \mathcal{R}}{x}_{\mathit{\text{ij}}}\le {c}_{i}& \text{,}\phantom{\rule{2em}{0ex}}& \forall i\in \mathcal{\mathscr{H}}\end{array}$  (5) 
$\begin{array}{lll}{\sum}_{i:j\in \mathcal{P}\left(l\right)}{x}_{\mathit{\text{ij}}}\le w& \text{,}\phantom{\rule{2em}{0ex}}& \forall l\in \mathcal{\mathcal{L}}\end{array}$  (6) 
$\begin{array}{lll}{x}_{\mathit{\text{ij}}}\ge 0& ,\phantom{\rule{2em}{0ex}}& \forall (i,j)\in \mathcal{\mathscr{H}}\times \mathcal{R}\end{array}$  (7) 
It is worthy to mention that there is another constraint that the total V2V traffic of the links in an interface range shall not exceed the capacity of the V2V communication channel, which is expressed as Equation 6. However, we assume that the capacity of the V2V communication channel is much larger than the WWAN link capacity to simplify the calculation, which means this constraint is not necessary to be considered when solving the optimization problem in Table 2. After solving the problem in Table 2, we verify whether the solution satisfies the constraint of Equation 6 or not. Thus, we can prove the rationality of the assumption.
3.3 Networking model
3.3.1 Topology
Generally speaking, a requester can borrow bandwidth from a helper for both downloading and uploading. Accordingly, the source and destination of the traffic flow among vehicles are the helper and the requester in the downloading case and the requester and the helper in the uploading case. As the uplink and downlink bandwidth in WWAN are usually considered to be independent, the analysis for the upload case and download case will be same. Therefore, we only focus on the downloading scenario in the following discussion.
To ease presentation, we number the nodes in the order of their sequence along the road, i.e., node i follows node i+1 and is followed by node i−1. Noting that the index for a node does not mean the network address nor an unchangeable identity for the node, it only represents the node’s relative order to the other nodes in a certain period. So when overtaking occurs between two vehicles, the indexes of the two nodes will accordingly change into the new ones.
3.3.2 Link model
3.3.3 Network traffic
Since a node with adequate bandwidth will not borrow bandwidth from others, nor a node lacking in bandwidth can lend its own, it is easy to understand that the cooperative bandwidth sharing will not occur if the endtoend traffic patterns of all mobile nodes are same. Therefore, the network traffic in the cooperative bandwidth sharing scenario is supposed to be unbalanced. We define three kinds of traffic patterns: (i) Idle, which means no network traffic is generated by local applications or services; (ii) Max CBR, which means the local application, e.g., streaming application, expects as much as possible bandwidth that is no more than a maximum constant bit rate (CBR); (iii) Greedy, which means the local application, e.g., file downloading, leeches as much as possible bandwidth and thus generates a bursty traffic. Each type of traffic has a certain portion of nodes to generate. We denote the portions of the nodes that generate the three kinds of traffic as r_{ I }, r_{ M }, and r_{ G } respectively, and assume r_{ I }+r_{ M }+r_{ G }=1. For Max CBR, the maximum desired bit rate can be either larger or smaller than the nodes’ WWAN bandwidth. We further assume that the desired maximum bit rates of the nodes that generate Max CBR traffic obey normal distribution with mean value of μ_{ e } and standard deviation of σ_{ e }.
3.4 The relay schemes
Three relay schemes, namely single relay, subset relay, and all relay, are considered in the CBS scenario, which is depicted in Figure 3b,c,d.
3.4.1 Single relay
In the single relay scheme, a fixed path θ between the requester and the helper will be assigned for relaying the traffic, as illustrated in Figure 3b. There will be multiple optional paths between the requester and helper, among which we define an optimal path θ_{ o } as the one with minimum link cost, as interpreted in Equation 9.
3.4.2 Subset relay
where f_{0}=h and f_{ m }=r and k represents the number of forwarders that are involved in forwarding a packet. Accordingly, we name such a subset relay scheme with value k as a ksubset relay scheme. For instance, the k value in the example depicted in Figure 3c is 2.
Therefore, the subset relay scheme opportunistically uses all paths in ${\mathcal{P}}_{k}(h,r)$, and a path θ is used only in case that any forwarder f_{ i } in the path θ is the farthest node from the previous forwarder f_{i−1} which successfully receives the packet in range of the k nearest nodes, i.e., $\theta \in {\mathcal{P}}_{k}(h,r)$ is used iff ∀f_{ i }∈θ,f_{ x }∈(f_{ i },f_{i−1}+k], f_{ i } successfully receives from f_{i−1} and f_{ x } does not.
3.4.3 All relay
The all relay scheme is a special case of the subset relay scheme where the subset of forwarders contains all the forwarders between the requester and the helper, i.e., the msubset relay scheme^{a}. The all relay scheme works almost the same as the subset relay except that there are more participants in forwarding, which is illustrated in Figure 3d.
As a result, the all relay scheme opportunistically uses all possible paths in $\mathcal{P}(h,r)$ in forwarding the traffic. Since in the all relay scheme a packet can be transmitted as near to the destination as possible during each transmission round, the scheme can result in the minimum transmission counts, which infers the minimum transmission cost. However, as too many nodes are involved during each transmission round in the all relay scheme, other costs such as computation or local maintenance of neighboring nodes may be high. Noting that the ksubset relay scheme limits the maximum transmission range in node counts for each transmission attempts, it may have lower or higher transmission cost than the optimal single relay scheme, which depends on the choice of k and the link qualities of node pairs. Therefore, a ksubset relay scheme with a proper k seems to be a tradeoff between transmission cost and other overhead, and the transmission cost in the all relay scheme can be used as a lower bound to measure the transmission cost of a certain relay scheme in analysis.
3.5 Cost model
It is important that the cost of sharing bandwidth is modeled appropriately, so that the aforementioned optimal solution can suitably reflect balance between requesters’ benefit and the expense of the helpers and the possible forwarders.
There are two principal costs that the helpers and the possible forwarders incur in helping the requester. The first cost, the socalled helper cost, is the cost of the helpers’ transferring data on the WWAN link for which the WWAN service provider extracts a fee. This fee depends on the tariff structure imposed by the service provider and may depend, in general, on factors such as the user’s service plan and the time of day. For our purposes in this paper, we assume that the WWAN tariff is known and is a uniform rate per unit data.
where $\overline{{\delta}_{\mathcal{P}}}$ denotes the mean number of transmissions of the packet of the flow x along a path θ (in the single relay scheme, $\mathcal{P}=\left\{\theta \right\}$), or a path set (in the opportunistic relay schemes).
where p_{ θ } is the probability that path θ is used, p(f_{i+1},f_{ i }) denotes the probability that f_{i+1} successfully receives from f_{ i } in the j th retransmission, ${\stackrel{\u0304}{p}}_{{f}_{i+1}}$ denotes the probability that no farther node than f_{i+1} receives from f_{ i } in the j th retransmission, and ${\stackrel{\u0304}{p}}_{k}^{(j1)}$ represents that none of the k nearest nodes from f_{ i } receives from f_{ i } for first j−1 transmission attempts.
Therefore, with known topology and the successful transmission probabilities of any two node pairs, the cost of a flow from the helper to the requester in different relay schemes can be figured out.
3.6 Vehicular flow model
In order to investigate the OCS, vehicular traffic needs to be modeled so that the intervals between vehicles and the link property can be estimated. We consider a microscopic model of the road traffic. More specifically, we consider a carfollowing model [34] with N vehicles for a singleline traffic flow on a circular road, where very vehicle in the system follows one vehicle and is followed by another vehicle in the system.
where V^{max} and a are positive constants [37]. The choice of V imposes a driving law, and we assume that this law is the same for all N drivers. The difference ${d}_{i}\triangleq {y}_{i+1}{y}_{i},i=1,\dots ,N$ is called headway of the i th vehicle, which will be also used in the link quality calculation as depicted in Equation 8.
where $s\in \mathbb{R}$ is an arbitrary phase shift.
Therefore, given an initial condition [y^{0},z^{0}] and the network traffic patterns for vehicular nodes, the parameters of the problem formulation depicted in Table 2 can be determined by using numerical calculation. We can then solve the optimal bandwidth sharing problem and find the features of the number of hops in the optimal solution. Thus, we can recommend the OCS for cooperative bandwidth sharing.
4 Distributed algorithm
For practical consideration, the problem depicted in Table 2 needs to be solved in a distributed way to achieve optimal cooperative bandwidth sharing. Thus, we briefly introduce the distributed algorithm in this section.
where λ, which includes α,β, is the Lagrange multiplier vector, and ${L}_{\mathit{\text{ij}}}\left({x}_{\mathit{\text{ij}}},{\mathit{\lambda}}_{\mathit{\text{ij}}}\right)={a}^{{\omega}_{\mathit{\text{ij}}}{x}_{\mathit{\text{ij}}}}\left({\alpha}_{j}+{\beta}_{i}\right){x}_{\mathit{\text{ij}}}$ is the Lagrangian to be maximized by the local source node i for each sourcedestination pair i→j.
which is unique due to the strict concavity of the object function.
where t is the iteration index, δ(t) is a sufficiently small positive step size, and [ ·]^{+} denotes the projection onto the nonnegative orthant.
5 Results analysis
Parameters and settings in the numeric analysis
Parameters  Values 

Portion of nodes with different traffic (r_{ I },r_{ M },r_{ G },)  0.1 to 0.9, default r_{ I }=0.5,r_{ M }=r_{ G }=0.25 
WLAN data rate (Mbps)  54 
WWAN link rate (Kbps)  1,024 
Relay schemes  Optimal single relay, ksubset relay (default k=3), all relay 
Vehicular density (ρ, vehicles per kilometer)  5 to 20, default ρ=10 
5.1 Network traffic patterns
We also fixed r_{ I } and tune the portions r_{ M } and r_{ G }. See Figure 7b,c. We have the same conclusion that the background traffic is not important to the cooperative scope, except the extreme case that most nodes are greedy, which can be excluded from considerations in designing the CBS system. Therefore, these results hint that we can exclude the background traffic from the considerations of deciding the CS when designing a multihop CBS scheme, which also means that a fixed CS can be applied despite of the dynamics of background traffic.
5.2 Relay schemes
As is mentioned in Section 3.4, the all relay scheme reflects the lower bound of the transmission cost, which is proved true in both cases from Figure 8a,b. Meanwhile, for a ksubset relay scheme, the transmission cost will decrease and approach the results of the all relay as k increases.
When comparing the ksubset relay scheme with the optimal single relay scheme, we can find difference in the high node density scenario and the low node density scenario. In the illustrated result of a low node density scenario depicted in Figure 8b, the transmission cost in a ksubset relay scheme (k>1) is lower than that in the optimal single relay scheme. While in the high node density scenario result depicted in Figure 8a, the transmission cost in a ksubset relay scheme is lower than only when k is large enough. It is because the ksubset relay scheme may limit the maximum transmission range for each transmission attempt even if the link quality is good enough to transmit the packet to the destination. Therefore, the results depicted in Figure 8a,b can be explained as the node density affects the link qualities between nodes and the ksubset relay scheme’s limitation. On the contrary, the ksubset relay scheme can show its predominance of multiple opportunistic relay paths over a single relay scheme when the link quality is not promising.
5.3 Cost weights
5.4 Vehicular flow
6 Conclusion
In this paper, we have proposed an analytical model that tries to reveal the optimal cooperation scope for cooperative bandwidth sharing in vehicular networks. Four components of the model, which are the network model, relay schemes, cost model, and vehicular flow model, are studied. The optimal cooperation scope is solved as the maximum physical distance or hops between the requester and the helper in the optimal solution to maximize the CBS benefit. The results show that the optimal cooperation scope is sensitive to the cost weight and may also vary with different relay schemes. The vehicular density does not affect the optimal cooperation scope much but can result in different CBS benefit. The model and findings of the relations between optimal CS and the running environment revealed in this paper can be used as a reference for parameter choosing when designing the CBS system in vehicular networks.
Endnotes
^{a} Note that the single relay scheme is not a 1subset relay.
^{b} OCS in the number of hops with the ksubset relay scheme is ignored as the hops may vary in an opportunistic relay scheme.
Declarations
Acknowledgements
The research is supported by the National Science Council of the Republic of China under Grant No. NSC 1022221E006009 and National Science Fund of China (Grant No. 61202303).
Authors’ Affiliations
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