# Cooperative Bargain for the Autonomous Separation of Traffic Flows in Smart Reversible Lanes

Authors: Guangbing Xiao; Haibo Zhang; Ning Sun; Yong Chen; Jiamin Shi; Yong Zhang
Journal: Complexity
 (2019)

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## Abstract

Spacer bars in the smart reversible lanes make periodically broadcast of messages to share their local observed traffic information with each other. This aims to help other spacer bars acquire the global traffic information and make consistent movement when separating the flows. However, radio interference and vehicles in the traffic may degrade the qualities of wireless communication links and cause frequent message losses in the broadcast. Existing solutions tend to use data forwarding to enhance the message dissemination, which may cause imbalanced load in the spacer bars. For instance, the nodes close to the sink have to forward more messages, whereas the ones far away from the sink have fewer messages for forwarding. The unbalanced distribution of network load has a high risk of blocking the wireless communication links and yield inconsistent movement in the reversible lanes. In this paper, we propose a Cooperative Bargain (CoB) scheme where each spacer bar carries some received messages to help other spacer bars recover their lost messages. Since the spacer bars can only acquire the local information, we formulate a cooperative bargain game to negotiate how to allocate the task of message recovery with a balanced network load until a consensus is achieved. CoB is evaluated with the real-world Wi-Fi communication traces in Isti/rural. Simulation results show that CoB can recover an average of 98.6% messages within 100 milliseconds in a 50-node network. CoB does not require the global network information but it can still achieve a comparable performance to other broadcast schemes.


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## Body

## 1. Introduction

The rapidly growing demand on congestion-free driving makes the smart traffic control a critical functionality in intelligent transportation systems (ITSs) [1, 2]. To make full utilization of road resources, the smart reversible lanes are deployed on roads to reduce directional traffic congestion in rush hours. The smart reversible lanes monitor traffic environment and work as movable centre dividers to separate traffic flows from different directions, aiming to increase the traffic capacity in the peak direction by borrowing some unused lanes from off-peak direction. As shown in Figure 1, a smart reversible lane is composed of several spacer bars that are connected with longitudinal barriers. There are two categories of spacer bars in a smart reversible lane, i.e., active spacer bars and passive spacer bars. The active spacer bar is equipped with a radio transceiver, integrated sensors (e.g., video camera and ultrasonic unit), and a step motor. The radio transceiver is used for wireless communications, and the integrated sensors are used for monitoring the traffic environment. The step motor is installed on the base and powered by batteries to drive the spacer bar forward or backward. In contrast, the passive spacer bar has no radio transceiver, integrated sensors, or step motor. It is mechanically connected with the adjacent spacer bars and moves passively when dragged by others.Figure 1
(a) The mechanical structure of an active spacer bar. (b) A smart reversible lane where the spacer bars are connected with longitudinal barriers.
(a)
(b)Considering the hardware investment and maintenance cost, the number of active spacer bars are limited and they are sparely distributed in the smart reversible lane. These active spacer bars form a backbone and drive the smart reversible lane forward or backward when separating the traffic flows. Each active spacer bar monitors the local traffic conditions, e.g., the volume of traffic flow and average vehicle speed, and then decides to move forward, backward, or stand still. Since the active spacer bars are distributed in a decentralized environment, they can only observe the local traffic information. This may yield dispute in the moving decisions and cause inconsistent movement of spacer bars as well as mechanical damages to the reversible lanes [3]. To eliminate the dispute in the moving decisions, the active spacer bars broadcast some messages to exchange their local observed traffic information with others and negotiate how to move the reversible lane consistently. However, the empirical studies in [4] have shown that, even in rural areas, the radio jamming and multiple-path interference can decrease the packet delivery ratio (PDR) by 50%. Put it in another way, not all the active spacer bars can receive the messages. Since each message contains the local observed traffic information, the frequent message losses will cause inconsistent movement of the spacer bars and mechanical damages to the reversible lanes.A straightforward approach to address this issue isdata forwarding. Take a line network for example. The node forwards its received messages to the next node until they are successfully delivered to the sink. However, it will cause unbalanced load in the network, e.g., the nodes that are close to the sink have more messages to forward, whereas the nodes that are far away from the sink have few messages to forward [5]. In [6], a flooding-based scheme is proposed where each node forwards all received messages to help other nodes recover their lost ones. However, the fast expense of message duplications will increase the communication overhead and chock the communication channels with a high risk of broadcast storms. Another frequently used method is cooperative broadcasting, where the task of message delivery is offloaded to each node regarding its local resources, e.g., the quality of communication links and the remaining energy in the battery. Based on this key idea, a number of cooperative broadcasting schemes are proposed with different metrics for the task offloading, e.g., the geolocation-based schemes [7], the energy-based schemes [8, 9], and the neighborhood-based schemes [10, 11]. Note that most of these schemes require the global information for central administration and task offloading, which is challenging in wireless networks due to the unstable qualities of communication links.In this paper, we develop a Cooperative Bargain (CoB) scheme to improve the message delivery ratio (MDR) in the broadcast. CoB only uses the local information at the active spacer bars but can reduce most disputes in the moving decisions and avoid inconsistent movements in the smart reversible lanes. Each active spacer bar carries some received messages to help others recover their lost messages. Since the messages are carried in each active spacer bar’s broadcast, no extra retransmission is needed, yielding high MDRs with small communication overhead and short time delay. Besides, a decentralized cooperative bargain game is formulated to offload the task of message recovery regarding each active spacer bar’s local resource [12]. The active spacer bars keep on negotiating with each other on which messages to carry until a consensus is achieved, so that they can make consistent movement in the reversible lanes.The rest of this paper is organized as below. Section2 reviews some related works on the reliable broadcast in wireless networks. Section 3 describes the system model and formulates the procedure of cooperative broadcast as an integral optimization problem. In Section 4, a cooperative bargain game is formulated to offload the task of message recovery. Section 5 proves that the achieved consensus in the cooperative bargain game is an optimal solution based on the theory of Nash equilibrium. Section 6 presents the simulation results where CoB is compared with some other broadcast schemes, and Section 7 concludes the whole paper.


## 2. Related Work

There have been active research studies on the reliable broadcast in wireless networks, but few can be applied to the wireless communications in smart reversible lanes. The reasons are twofold: (1) the signal jams and multiple-path interference in the traffic may degrade the qualities of wireless communication links between the spacer bars, causing frequent message losses in the broadcast of messages [13, 14] and (2) the active spacer bar can only obtain incomplete network topology and local traffic information, which may yield inconsistent moving actions and mechanical damages to reversible lanes [15]. Existing solutions can be divided into two categories, i.e., cooperative broadcast and noncooperative broadcast, depending on whether the nodes cooperate with others during the message recovery.Flooding is a widely used noncooperative broadcast solution, where each node forwards all received messages through all outgoing channels to improve the broadcast reliability [16]. To reduce the communication overhead resulting from excessive duplications in the broadcast, some variants of flooding are proposed. As shown in [17], Dash et al. proposed a hop-controlled flooding to restrict the number of hops when forwarding the received messages. It describes a novel hop-count update procedure using a history database called Info-Base. Current hop-count update procedure reduces the hop count at each routing node. However, the inherent redundant duplication in the flooding-based schemes remains unchanged and the nodes still suffer from the high risk of broadcast storms. In [18], Byeon et al. proposed an opportunistic flooding-based scheme where the duplication of messages is strictly limited. Depending on the contribution level for the entire network, the proposed technique enhances transmission efficiency through priority adjustment and the removal of needless relay nodes. However, it is prone to blind spots or redundant overlaps if the parameter p is not well designated, as it highly depends on the broadcast environment and application scenarios.The greedy-based scheme is a typical noncooperative solution for reliable dissemination of messages, where each node tries to recover the lost messages individually with little or seldom cooperation with others [19]. Xiao et al. [20] proposed a greedy-based piggybacking scheme to recover Cooperative Awareness Messages (CAMs) in the vehicular networks. Each vehicle broadcasts a request list to inform others which CAMs it has lost, and the CAM with maximum request-times will be selected for piggybacking first. However, the vehicles act too much greedy and little cooperation can be observed in the recovery of lost messages, which may cause redundant piggybacking and a low MDR with long time delay and large communication overhead. In [21], Xu et al. formed a noncooperative game for distributed wireless sensor networks to control the topology for energy saving and network load balancing. A price function is developed to calculate the reward for forwarding messages and the penalty for declining messages in the broadcast. Since all the nodes tend to maximize the reward, both the MDR and the network lifetime can be enhanced when a Nash equilibrium is achieved. However, Nash equilibrium is not sufficient to guarantee a global optimal solution. A simple example is the prisoner’s dilemma in the game theory.Recently, much attention has been paid to the cooperative broadcast, where the message recovery is offloaded to the nodes in a cooperative manner [22, 23]. For instance, a cooperative beacon broadcast scheme is proposed in [24] to provide the vehicles with more traffic information when driving on roads. Each vehicle selects w neighbors and piggybacks their awareness messages in the periodical beacon broadcast. It aims to improve the driving safety via the exchange of traffic information as it can provide sufficient traffic awareness when driving on roads. The drawback is that each vehicle has to dynamically maintain the geographic information of all its neighboring vehicles, which will consume a lot of network resources and introduce large communication overhead in the networks. A cooperative volunteer-based broadcast is studied in [25], where each vehicle exchanges its routing table with others to explore hidden neighbors in the non-line of sight (NLOS) area. The vehicles that have reliable links to the hidden neighbors will be selected as forwarders to retransmit the messages. Similarly, this scheme assumes that all nodes can obtain the global network information when offloading the task of message recovery, which is quite challenging for the active spacer bars in smart reversible lanes [26, 27].This paper provides a novel cooperative broadcast scheme called CoB to improve MDR in the broadcast of messages, aiming to eliminate the bias and making consistent movements in reversible lanes. Besides, a cooperative bargain game is formulated to negotiate the recovery strategies and moving decisions in all nodes until a consensus is achieved. Therefore, the task of message recovery can be offloaded to the nodes regarding their local resources, which is proved to be a global optimal solution to the cooperative recovery problem. Since the messages can be delivered reliably and efficiently, the spacer bars will acquire the same traffic information and thus move consistently to separate the traffic flows.


## 3. System Model and Problem Statement

Consider a smart reversible lane withN active spacer bars. Each active spacer bar is equipped with a radio transceiver for transmitting and receiving messages, and the radio transceivers have the same transmission range of r meters. A stepping motor is installed on the base of each active spacer bar to move it forward or backward for separating the traffic flows. We model the smart reversible lane as a line network G=N,L. The vertices in N=ni∣i≤N,i∈ℤ+ represent the active spacer bars, which is referred to as node(s) in the rest of this paper. The edges in L=lij∣i,j≤N,i,j∈ℤ+,i≠j denote the wireless communication links between the active spacer bars.Time is synchronized within a consensus-based synchronization method. Each node uses the carrier sense multiple access/collision detection (CSMA/CD) scheme to access the channels for broadcasting, which can achieve a high utilization of channel resources which do not require the central administration to schedule the nodes for broadcasting [28]. Once the local traffic conditions have changed (e.g., the vehicle density has changed by 0.1 vehicle/m and the shockware speed has changed by 2 vehicle/s), the node will broadcast a message to inform other nodes of the up-to-date local traffic information [29]. Thereby, the nodes will acquire more traffic information to make consistent movement in the reversible lanes when separating the traffic flows. The messages received by node ni are cached in its receiving buffer Fi. Each message is associated with a time-to-live (TTL) of δ ms and will be discarded when the TTL expires.However, not all the nodes can receive the messages due to the fragile communication links, which may cause inconsistent movements in the reversible lanes when separating the traffic flows. To address this issue, each node carries some received messages when it is scheduled for broadcasting and helps other nodes recover their lost messages. Letsit be node ni’s task in the message recovery, and the combination of each node’s task in the message recovery, Sit=s1t,s2t,…,sNt is defined as the joint recovery strategy in the broadcast. Suppose Mj is the set of messages generated by node nj in the broadcast, and NiMj,St is the number of messages in Mj that are received by node ni under the joint recovery strategy St. Then, node ni’s message reception ratio (MRR) regarding node nj’s messages, denoted by rijSt=NiMj,St/Mj, is defined as the ratio between the number of messages received by node ni and the total number of messages in Mj. Thereby, we can convert the process of cooperative broadcasting in the reversible lane into an integral optimization problem as shown in the following equation:(1)max∑ni∈N∑nj∈NrijStN2.Equation (1) indicates that the joint recovery strategy St should be capable of maximizing the average MRR for all the nodes in the broadcast. It aims to find an optimal joint recovery strategy St∗ that can maximize the MRR in the broadcast, so that they can acquire the same messages and make consistent movement when separating the traffic flows.


## 4. Cooperative Bargaining

In this section, we formulate a cooperative bargain game to allocate the task of cooperative recovery regarding each node’s local resources, and then propose a Cooperative Bargain scheme to maximize the objection function in 1.


### 4.1. Game Formulation

To achieve a consensus in the recovery of lost messages, each nodeni generates a bargain proposal Bit and exchanges it with other nodes for negotiation. The bargain proposal contains a recommending strategy Rit and a bidding strategy Pit. The recommending strategy Rit=ri1t,ri2t,…,riNt is a set of recommendations generated by node ni, and it indicates which message node ni expects other nodes to carry. The bidding strategy Pit=pi1t,pi2t,…,piNt is a set of bidding prices offered by node ni corresponding to each recommendation in Rit. The higher bidding price the node ni offers, the higher priority the recommended message will be piggybacked first.After generating a bargain proposal, each node will receive a reward, depending on how much its bargain proposal deviates from other nodes’ bargain proposals. The bargain proposal with less deviation will yield more rewards and vice versa. To maximize the rewards, the nodes will negotiate with each other to update their bargain proposal until a consensus is achieved. The deviations of bargain proposals are referred to asbargain bias in the rest of this paper, and the definition is presented as below:Definition 1.
Consider two bargain proposals generated by nodeni and nj at time t, respectively, i.e., Bit=Rit,Pit and Bjt=Rjt,Pjt. The bargain bias of Bit against Bjt, denoted by θijt as shown in equation (3), indicates how much node ni’s bargain proposal deviates from node nj’s bargain proposal:(2)θijt=Pjt−Pit⋅1T+Rjt−Rit⋅diagPit⋅Rjt−RitT.
According to Definition 1, if nodesni and nj have generated the same bargain proposal, e.g., they have made the same recommending strategy and offered the same bidding prices, the bargain bias is calculated as 0; otherwise, the bargain bias is nonzero. To make consistent movement in the reversible lanes, the nodes should eliminate the bargain bias and enforce all the bargain proposals converge to a consensus. The challenge is that the nodes can only acquire the local information, and it is difficult to compare the bargain proposal with all the other nodes in the decentralized environment. To address this issue, we connect all the nodes into a virtual ring and divide them into several overlapped groups. Each group is composed of three nodes, e.g., a heading node, a central node, and an ending node, and the group overlaps with a preceding group and a succeeding group, respectively. Put it in another way, the heading node in the current group is the ending node of its preceding group, whereas the ending node is the heading node of its succeeding group. For example, consider a set of N nodes in Figure 2. If N is an odd number, the nodes can be divided as, n1,n3,n5,n3,n5,n7,…,nN−4,nN−2,nN,nN−2,nN,nN−1,nN,nN−1,nN−3,…,n4,n2,n1,n2,n1,n3. If the number of nodes N is even, the nodes can be divided as n1,n3,n5,n3,n5,n7,…,nm−5,nm−3,nm−1,nm−3,nm−1,nm,nm−1,nm,nm−2,…,n4,n2,n1,n2,n1,n3. Since each group overlaps with its preceding group and the succeeding group, the central node only has to compare its bargain proposal inside of the group because the preceding node and the successive node will carry on comparing the bargain proposal with other nodes in the overlapped groups. Thereby, the bargain proposals will be compared among all the nodes group by group along the virtual ring until a consensus is achieved.Figure 2
Dividing all nodes into groups for the comparison of bargain proposals. (a) The division of groups when the number of nodesN is odd. (b) The division of groups when the number of nodes N is even.
(a)
(b)Definition 2.
Consider a group with three nodesni,nj,andnk in the cooperative bargain game. Bjt is the bargain proposal generated by the central node nj. It will receive a reward wBit, which is defined as the difference between the bargain bias θijt and θjkt in the following equation:(3)wBit=θijt−θjkt=Pit−Pjt⋅1T+Rit−Rjt⋅diagPit⋅Rit−RjtT−Pjt−Pkt⋅1T−Rjt−Rkt⋅diagPjt⋅Rjt−RktT.
As shown in equation (3), if the bargain bias between nodes ni and nj is less than the bargain bias between nodes nj and nk, node ni will receive a positive reward wBit>0 as a bonus for its bargain proposal; otherwise, node ni will receive a negative reward wBit<0 as a penalty for its bargain proposal. Since each node aims to maximize the rewards, the bargain bias will be eliminated ultimately. However, eliminating the bargain bias does not mean the messages have been recovered successfully, e.g., the nodes may achieve a consensus that no one piggybacks any message. The nodes will not receive any penalty but they fail to recover the lost messages in the broadcast. To solve this problem, we combine the reward with MRR and form a utility function as shown in equation (4).Definition 3.
For each nodeni in the cooperative bargain game, the utility function, denoted by uBit=Rit,Pit, is defined as the sum of MRR following its recommending strategy Rit and the reward for its bargain proposal wBit:(4)uBit=∑nj∈NrijRitN2+wBit.
For each node in the cooperative bargain, it keeps on updating the bargain proposal to eliminate the bargain bias and maximize the utility function. According to the definition of Nash equilibrium in [30], all the bargain proposals will converge to a consensus, which is referred to as balance point in the Nash equilibrium. When the balance point is achieved, none of the nodes is willing to change its bargain proposal as the utility function has been maximized according to the node’s local information.


### 4.2. Cooperative Bargain

In this subsection, a Cooperative Bargain (CoB) scheme is proposed to maximize the utility function in equation (4). The key ideas of CoB can be described as follows:(1)
For each message in the broadcast, nodeni generates a set of recommendations to indicate which node it expects to carry the message. Considering all the messages in the broadcast, the combination of node ni’s recommendations to each other node, i.e., Rit=ri1t,ri2t,…,riNt, is defined as its recommending strategy.(2)
For each recommendation inRit, node ni offers a bidding price. The higher bidding price it offers, the higher priority the recommended message is expected to be carried first. The set of bidding prices offered by node ni, denoted by Pit=pi1t,pi2t,…,piNt, is defined as its bidding strategy.(3)
The combination of piggybacking strategy and bidding strategy, i.e.,Bit=Rit,Pit, is defined as node ni’s bargain proposal. Node ni compares the bargain proposal with the heading node and ending node in the group, and it calculates the reward wBit regarding the bargain bias between them.(4)
The nodeni keeps on adjusting its bargain proposal to maximize the utility function until a consensus is achieved.A key issue in CoB is how to generate and update the bargain proposals. If the nodes know the qualities of wireless communication links, they will recommend the one with a good link to piggyback the messages. Meanwhile, the bidding price can be offered regarding how many nodes have lost the message. The more nodes that have lost the message, the higher bidding price will be offered for recommending other nodes to carry it for recovery. To address this issue, we develop the following two principles for generating and updating the bargain proposals.Principle 1.
The nodes with fewer stable communication links should be recommended for recovering the messages first.
The nodes with more stable communication links tend to have more options when carrying the messages for recovery. If these nodes are recommended for recovery first, they may choose to carry some messages that can also be recovered by other nodes, but fail to carry the messages that can only be recovered by themselves.Principle 2.
If the bargain proposal is different from that of others, the node should(1)
Choose the mainstreamed one as the new bargain proposal if it can recover the message with fewer forwarders, shorter time delays, or higher success probability(2)
Remain the bargain proposal unchanged if the mainstreamed one fails to recover one or more messages
Since the nodes can only acquire the local information, they may generate different bargain proposals for the message recovery. To eliminate the bargain bias, each node should update its bargain proposal to achieve a consensus. Note that some nodes have already achieved a local consensus (e.g., the mainstreamed bargain proposal can be regarded as a local consensus), and they have a higher probability to make an optimal bargain proposal as they have acquired more information via exchanging the bargain proposals. Therefore, if a node has generated a bargain proposal that is different from the mainstream one, it should update its bargain proposal to coincide with the mainstreamed one. However, it might be possible that the node has detected a lost message which fails to be detected by the nodes with the mainstreamed bargain proposals. Therefore, the node should check whether the mainstreamed bargain proposal can recover all the messages. If the mainstreamed bargain proposal fails to recover one or more messages, the node should remain its bargain proposal unchanged on recovering these messages, and thus the other nodes will be informed that the mainstreamed bargain proposal failed to recover all the messages.
The pseudocode of CoB is given in Algorithm1, where each node ni exchanges its bargain proposal with other nodes for comparison and updating until a consensus is achieved. Upon broadcasting a packet, each node ni will infer the lost messages and qualities of wireless communication links in the broadcast. Then, it will generate a bargain proposal based on the inferred information to maximize the utility function. Upon receiving a packet from another node nj, node ni will check each piggybacked message in the packet and cache it in the receiving buffer Fi. The node nj’s bargain proposal in the received packet will be used to update node ni’s bargain proposal if it is different from the mainstreamed one.Algorithm 1:CoB at each node ni.
//Upon broadcasting a packet:
Infer the qualities of wireless communication links and the lost messages in the broadcast;;
for each lost message in the broadcastdo
Recommend the node with the fewest stable communication links to piggyback the message
ifthe recommendation is different from the mainstreamed onethen
Rank all the received recommendations on piggybacking this message, and choose the top-ranked one as the new recommendation;
Broadcast a packet with the bargain proposal to inform other nodes of nodeni’s recommendations
//Upon receiving a packet from nodenj:
foreach piggybacked message in the received packetdo
ifthere is no such a message in the receiving buffer Fi then
Cache it in the receiving bufferFi.
else
Keep the one that has the latest time stamp.
Cache nodenj’s bargain proposal for comparison;


## 4.1. Game Formulation

To achieve a consensus in the recovery of lost messages, each nodeni generates a bargain proposal Bit and exchanges it with other nodes for negotiation. The bargain proposal contains a recommending strategy Rit and a bidding strategy Pit. The recommending strategy Rit=ri1t,ri2t,…,riNt is a set of recommendations generated by node ni, and it indicates which message node ni expects other nodes to carry. The bidding strategy Pit=pi1t,pi2t,…,piNt is a set of bidding prices offered by node ni corresponding to each recommendation in Rit. The higher bidding price the node ni offers, the higher priority the recommended message will be piggybacked first.After generating a bargain proposal, each node will receive a reward, depending on how much its bargain proposal deviates from other nodes’ bargain proposals. The bargain proposal with less deviation will yield more rewards and vice versa. To maximize the rewards, the nodes will negotiate with each other to update their bargain proposal until a consensus is achieved. The deviations of bargain proposals are referred to asbargain bias in the rest of this paper, and the definition is presented as below:Definition 1.
Consider two bargain proposals generated by nodeni and nj at time t, respectively, i.e., Bit=Rit,Pit and Bjt=Rjt,Pjt. The bargain bias of Bit against Bjt, denoted by θijt as shown in equation (3), indicates how much node ni’s bargain proposal deviates from node nj’s bargain proposal:(2)θijt=Pjt−Pit⋅1T+Rjt−Rit⋅diagPit⋅Rjt−RitT.
According to Definition 1, if nodesni and nj have generated the same bargain proposal, e.g., they have made the same recommending strategy and offered the same bidding prices, the bargain bias is calculated as 0; otherwise, the bargain bias is nonzero. To make consistent movement in the reversible lanes, the nodes should eliminate the bargain bias and enforce all the bargain proposals converge to a consensus. The challenge is that the nodes can only acquire the local information, and it is difficult to compare the bargain proposal with all the other nodes in the decentralized environment. To address this issue, we connect all the nodes into a virtual ring and divide them into several overlapped groups. Each group is composed of three nodes, e.g., a heading node, a central node, and an ending node, and the group overlaps with a preceding group and a succeeding group, respectively. Put it in another way, the heading node in the current group is the ending node of its preceding group, whereas the ending node is the heading node of its succeeding group. For example, consider a set of N nodes in Figure 2. If N is an odd number, the nodes can be divided as, n1,n3,n5,n3,n5,n7,…,nN−4,nN−2,nN,nN−2,nN,nN−1,nN,nN−1,nN−3,…,n4,n2,n1,n2,n1,n3. If the number of nodes N is even, the nodes can be divided as n1,n3,n5,n3,n5,n7,…,nm−5,nm−3,nm−1,nm−3,nm−1,nm,nm−1,nm,nm−2,…,n4,n2,n1,n2,n1,n3. Since each group overlaps with its preceding group and the succeeding group, the central node only has to compare its bargain proposal inside of the group because the preceding node and the successive node will carry on comparing the bargain proposal with other nodes in the overlapped groups. Thereby, the bargain proposals will be compared among all the nodes group by group along the virtual ring until a consensus is achieved.Figure 2
Dividing all nodes into groups for the comparison of bargain proposals. (a) The division of groups when the number of nodesN is odd. (b) The division of groups when the number of nodes N is even.
(a)
(b)Definition 2.
Consider a group with three nodesni,nj,andnk in the cooperative bargain game. Bjt is the bargain proposal generated by the central node nj. It will receive a reward wBit, which is defined as the difference between the bargain bias θijt and θjkt in the following equation:(3)wBit=θijt−θjkt=Pit−Pjt⋅1T+Rit−Rjt⋅diagPit⋅Rit−RjtT−Pjt−Pkt⋅1T−Rjt−Rkt⋅diagPjt⋅Rjt−RktT.
As shown in equation (3), if the bargain bias between nodes ni and nj is less than the bargain bias between nodes nj and nk, node ni will receive a positive reward wBit>0 as a bonus for its bargain proposal; otherwise, node ni will receive a negative reward wBit<0 as a penalty for its bargain proposal. Since each node aims to maximize the rewards, the bargain bias will be eliminated ultimately. However, eliminating the bargain bias does not mean the messages have been recovered successfully, e.g., the nodes may achieve a consensus that no one piggybacks any message. The nodes will not receive any penalty but they fail to recover the lost messages in the broadcast. To solve this problem, we combine the reward with MRR and form a utility function as shown in equation (4).Definition 3.
For each nodeni in the cooperative bargain game, the utility function, denoted by uBit=Rit,Pit, is defined as the sum of MRR following its recommending strategy Rit and the reward for its bargain proposal wBit:(4)uBit=∑nj∈NrijRitN2+wBit.
For each node in the cooperative bargain, it keeps on updating the bargain proposal to eliminate the bargain bias and maximize the utility function. According to the definition of Nash equilibrium in [30], all the bargain proposals will converge to a consensus, which is referred to as balance point in the Nash equilibrium. When the balance point is achieved, none of the nodes is willing to change its bargain proposal as the utility function has been maximized according to the node’s local information.


## 4.2. Cooperative Bargain

In this subsection, a Cooperative Bargain (CoB) scheme is proposed to maximize the utility function in equation (4). The key ideas of CoB can be described as follows:(1)
For each message in the broadcast, nodeni generates a set of recommendations to indicate which node it expects to carry the message. Considering all the messages in the broadcast, the combination of node ni’s recommendations to each other node, i.e., Rit=ri1t,ri2t,…,riNt, is defined as its recommending strategy.(2)
For each recommendation inRit, node ni offers a bidding price. The higher bidding price it offers, the higher priority the recommended message is expected to be carried first. The set of bidding prices offered by node ni, denoted by Pit=pi1t,pi2t,…,piNt, is defined as its bidding strategy.(3)
The combination of piggybacking strategy and bidding strategy, i.e.,Bit=Rit,Pit, is defined as node ni’s bargain proposal. Node ni compares the bargain proposal with the heading node and ending node in the group, and it calculates the reward wBit regarding the bargain bias between them.(4)
The nodeni keeps on adjusting its bargain proposal to maximize the utility function until a consensus is achieved.A key issue in CoB is how to generate and update the bargain proposals. If the nodes know the qualities of wireless communication links, they will recommend the one with a good link to piggyback the messages. Meanwhile, the bidding price can be offered regarding how many nodes have lost the message. The more nodes that have lost the message, the higher bidding price will be offered for recommending other nodes to carry it for recovery. To address this issue, we develop the following two principles for generating and updating the bargain proposals.Principle 1.
The nodes with fewer stable communication links should be recommended for recovering the messages first.
The nodes with more stable communication links tend to have more options when carrying the messages for recovery. If these nodes are recommended for recovery first, they may choose to carry some messages that can also be recovered by other nodes, but fail to carry the messages that can only be recovered by themselves.Principle 2.
If the bargain proposal is different from that of others, the node should(1)
Choose the mainstreamed one as the new bargain proposal if it can recover the message with fewer forwarders, shorter time delays, or higher success probability(2)
Remain the bargain proposal unchanged if the mainstreamed one fails to recover one or more messages
Since the nodes can only acquire the local information, they may generate different bargain proposals for the message recovery. To eliminate the bargain bias, each node should update its bargain proposal to achieve a consensus. Note that some nodes have already achieved a local consensus (e.g., the mainstreamed bargain proposal can be regarded as a local consensus), and they have a higher probability to make an optimal bargain proposal as they have acquired more information via exchanging the bargain proposals. Therefore, if a node has generated a bargain proposal that is different from the mainstream one, it should update its bargain proposal to coincide with the mainstreamed one. However, it might be possible that the node has detected a lost message which fails to be detected by the nodes with the mainstreamed bargain proposals. Therefore, the node should check whether the mainstreamed bargain proposal can recover all the messages. If the mainstreamed bargain proposal fails to recover one or more messages, the node should remain its bargain proposal unchanged on recovering these messages, and thus the other nodes will be informed that the mainstreamed bargain proposal failed to recover all the messages.
The pseudocode of CoB is given in Algorithm1, where each node ni exchanges its bargain proposal with other nodes for comparison and updating until a consensus is achieved. Upon broadcasting a packet, each node ni will infer the lost messages and qualities of wireless communication links in the broadcast. Then, it will generate a bargain proposal based on the inferred information to maximize the utility function. Upon receiving a packet from another node nj, node ni will check each piggybacked message in the packet and cache it in the receiving buffer Fi. The node nj’s bargain proposal in the received packet will be used to update node ni’s bargain proposal if it is different from the mainstreamed one.Algorithm 1:CoB at each node ni.
//Upon broadcasting a packet:
Infer the qualities of wireless communication links and the lost messages in the broadcast;;
for each lost message in the broadcastdo
Recommend the node with the fewest stable communication links to piggyback the message
ifthe recommendation is different from the mainstreamed onethen
Rank all the received recommendations on piggybacking this message, and choose the top-ranked one as the new recommendation;
Broadcast a packet with the bargain proposal to inform other nodes of nodeni’s recommendations
//Upon receiving a packet from nodenj:
foreach piggybacked message in the received packetdo
ifthere is no such a message in the receiving buffer Fi then
Cache it in the receiving bufferFi.
else
Keep the one that has the latest time stamp.
Cache nodenj’s bargain proposal for comparison;


## 5. Theoretical Analysis

In CoB, each node generates bargain proposals based on its local information and then exchanges them with other nodes for negotiation and updating so that the bargain bias can be eliminated. In this section, we prove that the achieved consensus in CoB is Nash equilibrium (NE), and the bargain proposal at the NE is an optimal solution for the cooperative recovery of lost messages in the broadcast.Theorem 1.
If a consensus is achieved in the cooperative bargain game, the combination of each node’s bargain proposal is a Nash equilibrium to the objection function in equation (1).Proof.
Supposeℝt=R1t,R2t,…,RNt is the set of recommending strategies generated by all the nodes at time t and Pt=P1t,P2t,…,PNt is the set of bidding prices corresponding to each recommending strategy in Rt. Denote the achieved consensus by BPt∗=Bit∗=Rit∗,Pit∗∣ni∈N. Define ℝt∗=R1t∗,R2t∗,…,RNt∗ and Pt∗=P1t∗,P2t∗,…,PNt∗ as the joint recommended strategies and bidding prices at the consensus, respectively. According to the definition of Nash equilibrium, the achieved consensus BPt∗ is a balance point where no node tends to change its bargain proposal or bidding price unilaterally, where each node’s utility function has been locally maximized. Considering the group division in Figure 2 and the definition of rewards in equation (3), the sum of rewards at each node is zero as shown in the following equation:(5)∑ni∈NwBit∗=θ13t−θ35t+θ35t−θ57t+⋯+θ42t−θ21t+θ21t−θ13t=0.
By substituting equation (5) into the utility function in equation (4), we can convert the objection function into the following equation:(6)∑ni∈N∑nj∈NrijRit∗N2=∑ni∈NuBit∗−wBit∗=∑ni∈NuBit∗−∑ni∈NwBit∗=∑ni∈NuBit∗.
Since each node’s utility function achieves a Nash equilibrium atBPt∗=Rit∗,Pit∗∣ni∈N, the object function in equation (1) will also achieve a Nash equilibrium at BPt∗=Rit∗,Pit∗∣ni∈N based on the equivalence relationship as shown in equation (6).
Theorem 1 proves that the achieved consensus is a Nash equilibrium in the cooperative bargain game. However, it does not mean that the achieved Nash equilibrium is the optimal bargain proposal. In other words, maximizinguBit∗ locally at each node is not equivalent to maximizing ∑ni∈NuBit∗ globally. The following Theorem 2 proves that the Nash equilibrium achieved in the cooperative bargain game is an optimal solution to the objective function in equation (1).Theorem 2.
The combination of each node’s bargain proposal at the achieved consensus in the cooperative bargain game is an optimal solution to the objective function in equation (1).Proof.
Consider a bargain proposalBPt=Bit=Rit∗,Pit∣ni∈N in the cooperative bargain game. It cannot yield a higher value in the object function than the one at the Nash equilibrium, i.e., BPt∗=Bit∗=Rit∗,Pit∗∣ni∈N. Therefore, we can have the following inequality:(7)∑ni∈NuBit≤∑ni∈NuBit∗,Bit=Rit∗,Pit,Bit∗=Rit∗,Pit∗,BPt=B1t∗,B2t∗,…,Bit,…,BN−1t∗,BNt∗,BPt∗=B1t∗,B2t∗,…,Bit∗,…,BN−1t∗,BNt∗.
Since the utility functionuBit is strictly monotone decreasing of wBti, we can have the following inequality:(8)∀ni∈N,wBit≤wBit∗.
Suppose nodeni is the heading nodes in the group ni,nj,andnk, and then we can rewrite Inequality (8) into Inequality (9) based on the definition of wBit:(9)Pit−Pit∗+Rit−Rjt∗TdiagPit−Pit∗Rit−Rjt∗≤0.
Since Inequality (9) stands up for all bidding prices, we can have Inequality (10) by substituting Pit=2Pit∗ and Pit=0 into Inequality (9), respectively:(10)Pit∗+Rit−Rjt∗TdiagPit∗Rit−Rjt∗=0.
Substitute equation (10) into equation (3), and the reward of node ni at the Nash equilibrium is calculated as follows:(11)wBit∗=Pkt∗−Pjt∗1T.
Consider the definition of the Nash equilibrium again, and we can have another inequality (12) as below:(12)∑ni∈NuBit′≤∑ni∈NuBit∗,Bit′=Rit′,Pit′,Bit∗=Rit∗,Pit∗,BPt=B1t∗,B2t∗,…,Bit′,…,BN−1t∗,BNt∗,BPt∗=B1t∗,B2t∗,…,Bit∗,…,BN−1t∗,BNt∗.
By substituting Inequality (11) into Inequality (12), we can have the following inequality:(13)∑ni∈N∑nj∈NrijRit′N2+Pit′−Pjt∗−Pjt∗−Pkt∗⋅1T+Rit′−Rjt∗⋅diagPit′⋅Rit′−Rjt∗T,−Rjt∗−Rkt∗⋅diagPjt∗⋅Rjt∗−Rkt∗T≤∑ni∈N∑nj∈NrijRit∗N2+Pkt∗−Pjt∗1T.
Since Inequality (13) holds for all values of Pit′, we can obtain Inequality 14 by setting Pit′ = 0 in Inequality (13):(14)∑ni∈N∑nj∈NrijRit′N2≤∑ni∈N∑nj∈NrijRit∗N2.
Putting it in another way, Inequality (14) can be transformed into equation (15) as follows:(15)Rit∗=argmax∑ni∈N∑nj∈NrijRitN2,s.t.Bit∗=Rit∗,Pit∗.
Therefore, we prove thatBit∗ is the optimal solution in the feasible solution space of equation (1), where the objective function reaches the maximum value at the achieved consensus. Putting it in another way, the Nash equilibrium Bit∗=Rit∗,Pit∗ is the optimal solution to the cooperative piggybacking problem in equation (1).


## 6. Simulations

### 6.1. Simulation Setup

In this section, we evaluate CoB with some real-world Wi-Fi communication data traces in the Isti/rural dataset. It is compared with the following broadcast schemes in terms of MDR, time delay, and communication overhead:(1)
Probabilistic Flooding (PF). Each node forwards its received messages with a predefined probability (say p = 50% in our simulation) to improve MDR in the broadcast.(2)
Retransmission-Based Recovery (RR). The node carries a request list in its message to inform others which one it has lost. The source node, i.e., the one that generated this message, will make the retransmission until it is received by all the nodes.(3)
Greedy Recovery (GR). Each node carries a request list in its packets. It also carries some messages to help other nodes recover their lost ones. The more the nodes request for recovering a message, the higher priority it will be carried for recovery first.(4)
Centralized Recovery (CR). Assume there exists a central node that can obtain the global information in the network. The central node develops the recovery strategy by using the global information and then disseminates it to the other nodes. These nodes recover the lost messages following the strategy developed by the central node.Isti/rural contains a set of real-world communication data traces which records the link qualities within a Wi-Fi network. Each node in the Wi-Fi network is equipped with a CNet CNWLC-811 IEEE 802.11b PCMCIA wireless card and a standard driver in the ad hoc mode. Fragmentation, RTS/CTS, retransmissions, and dynamic rate switching are disabled and each message is only broadcast once. This helps to sample the link qualities quickly and accurately compared to the setup where retransmission is enabled after each message loss. For each data trace in the Isti/rural, it records the status of message delivery (which can be regarded as the link qualities) in the broadcast, where the distance between the sending node and the receiving node is set as a fixed value. If a message can be received successfully, the link quality is marked as “1”; otherwise, it is marked as “0”. Isti/rural is composed of a number of such data traces by varying the distance between the sending node and the receiving node with a difference of every 20 meters, starting from 40 to 300 meters. In our simulations, we set the gap between two adjacent spacer bars as 20 meters. For each wireless communication link in the broadcast, we allocate it with a unique data trace in the Isti/rural, where the gap between the two spacer bars along the wireless communication link is equal to the distance between the sending node and the receiving node in the data trace. If the wireless communication link is reliable, i.e., the status of message delivery in the allocated data trace is marked as “1,” the simulator will deliver the message to the receiving node; otherwise, the simulator will discard the message. The TTL of messages is set as 100 milliseconds, and the nodes can carry at most two messages in each transmission.


### 6.2. Broadcast Reliability

As shown in equation (1), we calculate the MDR for each node in the broadcast, and define the average value of each message’s MDR as the broadcast reliability. Figure 3(a) illustrates the MDR of different broadcast schemes when the number of nodes varies from 5 to 30. Since CP assumes all the nodes can acquire the global information, it has the highest MDR compared with other broadcast schemes. Note that the proposed CoB can achieve a comparable MDR to CP, only using each node’s local information for the recovery of lost messages. Moreover, when the number of nodes increases, the MDRs of CoB and CP are basically unchanged. It indicates that both schemes are stable and robust, which are little impacted by the number of nodes. GP follows behind CoB with an average MDR of 96%, and it decreases slightly when the number of nodes increases. This mainly results from the greedy recovery of lost messages in GP, as the messages that are lost by more nodes will be carried with higher priority, which can benefit more nodes in the recovery of lost messages. PF has a lower MDR (around 92%) when the number of nodes is small, and it drops to 85% when the number of nodes increases to 30, as the redundant forwarding of messages may cause frequent data collisions and yield a high risk of overloading the communication channels in the broadcast. DR has the lowest MDR which drops significantly when the number of nodes increases from 5 to 30.Figure 3
The performance evaluations on cooperative bargain. (a) Broadcast reliability. (b) Network load balancing. (c) Message delivery delay. (d) Recovery accuracy.
(a)
(b)
(c)
(d)


### 6.3. Network Load Balancing

LetNi be the number of messages transmitted by vehicle vi in the broadcast, and N¯ is the average number of transmitted messages at each node in the broadcast. Then, we define the degree of network load balancing (DNLB) as ∑i=1NPΨi2/N⋅∑i=1NPΨi2. If the nodes have transmitted the same number of messages in the broadcast, DNLB is maximized as 1. If one node has transmitted all the messages, whereas the other nodes have transmitted no messages, DNLB is minimized as 1/n. As shown in Figure 3(b), CoB has a high DNLB which decreases slightly when the number of nodes increases. This results from the negotiation for eliminating the bias among the nodes where the task of message recovery is allocated regarding each node’s local information. CP has a similar high DNLB as it assumes the central node can acquire the global information and thus make optimal recovery strategy with balanced network load. GP has the lowest DNLB as the nodes always tend to carry the same message for recovery, i.e., the one that is requested by most nodes, which will cause imbalanced network load in the nodes.


### 6.4. Delay of Message Delivery

We define the delay of message delivery (DMD) as the time interval between the instant when a message is generated and the instant when it is delivered or recovered at all the receiving nodes. Figure3(c) shows the cumulative distribution function (CDF) of DMDs when the number of node is set as 30. CoB and CP have the shortest DMD in the recovery of lost messages, which are always smaller than 15 milliseconds. GP fails to recover all lost messages, and the CDF climbs to 0.98 when the TTL expires. PF only recovers 85% lost messages at the end of TTL, as all the nodes forward their received packets which will cause severe data collisions in the broadcast. DR has the worst performance which only recovers 80% lost messages. This is because the success probability of message recovery highly depends on the qualities of wireless communication links, and retransmission helps little in the recovery of lost messages if the qualities of wireless communication links remain unstable.Another factor that may impact the DMD is the network size, i.e., the number of nodes in the network. When the number of nodes is small, the nodes tend to have a low probability of data collisions when accessing the communication channel for broadcasting messages. In contrast, when the number of nodes increases, the nodes suffer from a high probability of data collisions when accessing the communication channel for broadcasting. This will also deteriorate the success probability in the recovery of lost messages and yield a long time delay in DMDs. As shown in Figure3(d), the DMDs for recovering lost messages within a 5-node network are averagely shorter than 20 ms, whereas the DMDs for recovering lost messages within a 30-node network rise to 75 ms. The DMDs increase when the number of nodes increases, but CoB can still recover most messages before the TTLs expire.


### 6.5. Recovery Accuracy

We define the recovery accuracy as the average number of transmitted messages for each received message, that is, the ratio between the total number of transmitted messages and the number of successfully received messages. As shown in Table1, fewer messages are transmitted in CoB compared to that of CP. This is because the nodes in CoB work in a decentralized environment and they only use the local information to make cooperative piggybacking. In contrast, the central node in CP has to acquire the global information via exchanging messages with all the other nodes. After developing the optimal recovery strategy, the central nodes have to communicate with the other nodes again to disseminate the developed optimal recovery strategy, which will yield a large communication overhead in the broadcast. GP has transmitted more messages in the broadcast, and the number of transmitted packets increases when the network size becomes large. SP and PF have the worst performance in terms of network load, where 475 and 1157 packets are transmitted in each broadcast period, respectively, which may cause a high risk of data collisions in the broadcast.Table 1
The average number of transmitted packets for each successfully received message.
Number of nodes
4
6
8
10
12
14
CBP
63
72
87
98
106
125
CP
87
111
125
169
234
271
GP
91
113
134
150
150
150
SP
181
285
337
377
436
475
PF
237
359
525
692
949
1157


## 6.1. Simulation Setup

In this section, we evaluate CoB with some real-world Wi-Fi communication data traces in the Isti/rural dataset. It is compared with the following broadcast schemes in terms of MDR, time delay, and communication overhead:(1)
Probabilistic Flooding (PF). Each node forwards its received messages with a predefined probability (say p = 50% in our simulation) to improve MDR in the broadcast.(2)
Retransmission-Based Recovery (RR). The node carries a request list in its message to inform others which one it has lost. The source node, i.e., the one that generated this message, will make the retransmission until it is received by all the nodes.(3)
Greedy Recovery (GR). Each node carries a request list in its packets. It also carries some messages to help other nodes recover their lost ones. The more the nodes request for recovering a message, the higher priority it will be carried for recovery first.(4)
Centralized Recovery (CR). Assume there exists a central node that can obtain the global information in the network. The central node develops the recovery strategy by using the global information and then disseminates it to the other nodes. These nodes recover the lost messages following the strategy developed by the central node.Isti/rural contains a set of real-world communication data traces which records the link qualities within a Wi-Fi network. Each node in the Wi-Fi network is equipped with a CNet CNWLC-811 IEEE 802.11b PCMCIA wireless card and a standard driver in the ad hoc mode. Fragmentation, RTS/CTS, retransmissions, and dynamic rate switching are disabled and each message is only broadcast once. This helps to sample the link qualities quickly and accurately compared to the setup where retransmission is enabled after each message loss. For each data trace in the Isti/rural, it records the status of message delivery (which can be regarded as the link qualities) in the broadcast, where the distance between the sending node and the receiving node is set as a fixed value. If a message can be received successfully, the link quality is marked as “1”; otherwise, it is marked as “0”. Isti/rural is composed of a number of such data traces by varying the distance between the sending node and the receiving node with a difference of every 20 meters, starting from 40 to 300 meters. In our simulations, we set the gap between two adjacent spacer bars as 20 meters. For each wireless communication link in the broadcast, we allocate it with a unique data trace in the Isti/rural, where the gap between the two spacer bars along the wireless communication link is equal to the distance between the sending node and the receiving node in the data trace. If the wireless communication link is reliable, i.e., the status of message delivery in the allocated data trace is marked as “1,” the simulator will deliver the message to the receiving node; otherwise, the simulator will discard the message. The TTL of messages is set as 100 milliseconds, and the nodes can carry at most two messages in each transmission.


## 6.2. Broadcast Reliability

As shown in equation (1), we calculate the MDR for each node in the broadcast, and define the average value of each message’s MDR as the broadcast reliability. Figure 3(a) illustrates the MDR of different broadcast schemes when the number of nodes varies from 5 to 30. Since CP assumes all the nodes can acquire the global information, it has the highest MDR compared with other broadcast schemes. Note that the proposed CoB can achieve a comparable MDR to CP, only using each node’s local information for the recovery of lost messages. Moreover, when the number of nodes increases, the MDRs of CoB and CP are basically unchanged. It indicates that both schemes are stable and robust, which are little impacted by the number of nodes. GP follows behind CoB with an average MDR of 96%, and it decreases slightly when the number of nodes increases. This mainly results from the greedy recovery of lost messages in GP, as the messages that are lost by more nodes will be carried with higher priority, which can benefit more nodes in the recovery of lost messages. PF has a lower MDR (around 92%) when the number of nodes is small, and it drops to 85% when the number of nodes increases to 30, as the redundant forwarding of messages may cause frequent data collisions and yield a high risk of overloading the communication channels in the broadcast. DR has the lowest MDR which drops significantly when the number of nodes increases from 5 to 30.Figure 3
The performance evaluations on cooperative bargain. (a) Broadcast reliability. (b) Network load balancing. (c) Message delivery delay. (d) Recovery accuracy.
(a)
(b)
(c)
(d)


## 6.3. Network Load Balancing

LetNi be the number of messages transmitted by vehicle vi in the broadcast, and N¯ is the average number of transmitted messages at each node in the broadcast. Then, we define the degree of network load balancing (DNLB) as ∑i=1NPΨi2/N⋅∑i=1NPΨi2. If the nodes have transmitted the same number of messages in the broadcast, DNLB is maximized as 1. If one node has transmitted all the messages, whereas the other nodes have transmitted no messages, DNLB is minimized as 1/n. As shown in Figure 3(b), CoB has a high DNLB which decreases slightly when the number of nodes increases. This results from the negotiation for eliminating the bias among the nodes where the task of message recovery is allocated regarding each node’s local information. CP has a similar high DNLB as it assumes the central node can acquire the global information and thus make optimal recovery strategy with balanced network load. GP has the lowest DNLB as the nodes always tend to carry the same message for recovery, i.e., the one that is requested by most nodes, which will cause imbalanced network load in the nodes.


## 6.4. Delay of Message Delivery

We define the delay of message delivery (DMD) as the time interval between the instant when a message is generated and the instant when it is delivered or recovered at all the receiving nodes. Figure3(c) shows the cumulative distribution function (CDF) of DMDs when the number of node is set as 30. CoB and CP have the shortest DMD in the recovery of lost messages, which are always smaller than 15 milliseconds. GP fails to recover all lost messages, and the CDF climbs to 0.98 when the TTL expires. PF only recovers 85% lost messages at the end of TTL, as all the nodes forward their received packets which will cause severe data collisions in the broadcast. DR has the worst performance which only recovers 80% lost messages. This is because the success probability of message recovery highly depends on the qualities of wireless communication links, and retransmission helps little in the recovery of lost messages if the qualities of wireless communication links remain unstable.Another factor that may impact the DMD is the network size, i.e., the number of nodes in the network. When the number of nodes is small, the nodes tend to have a low probability of data collisions when accessing the communication channel for broadcasting messages. In contrast, when the number of nodes increases, the nodes suffer from a high probability of data collisions when accessing the communication channel for broadcasting. This will also deteriorate the success probability in the recovery of lost messages and yield a long time delay in DMDs. As shown in Figure3(d), the DMDs for recovering lost messages within a 5-node network are averagely shorter than 20 ms, whereas the DMDs for recovering lost messages within a 30-node network rise to 75 ms. The DMDs increase when the number of nodes increases, but CoB can still recover most messages before the TTLs expire.


## 6.5. Recovery Accuracy

We define the recovery accuracy as the average number of transmitted messages for each received message, that is, the ratio between the total number of transmitted messages and the number of successfully received messages. As shown in Table1, fewer messages are transmitted in CoB compared to that of CP. This is because the nodes in CoB work in a decentralized environment and they only use the local information to make cooperative piggybacking. In contrast, the central node in CP has to acquire the global information via exchanging messages with all the other nodes. After developing the optimal recovery strategy, the central nodes have to communicate with the other nodes again to disseminate the developed optimal recovery strategy, which will yield a large communication overhead in the broadcast. GP has transmitted more messages in the broadcast, and the number of transmitted packets increases when the network size becomes large. SP and PF have the worst performance in terms of network load, where 475 and 1157 packets are transmitted in each broadcast period, respectively, which may cause a high risk of data collisions in the broadcast.Table 1
The average number of transmitted packets for each successfully received message.
Number of nodes
4
6
8
10
12
14
CBP
63
72
87
98
106
125
CP
87
111
125
169
234
271
GP
91
113
134
150
150
150
SP
181
285
337
377
436
475
PF
237
359
525
692
949
1157


## 7. Conclusion

This paper proposes a decentralized Cooperative Bargain scheme, namely CoB, to improve the broadcast reliability when disseminating messages in the reversible lanes. It aims to drive the spacer bars make consistent movement for the autonomous separation of traffic flows. To achieve this target, each active spacer bar is allowed to carry some received messages to help others recover the lost ones. Besides, a cooperative bargain game is formulated to allocate the task of message recovery regarding each spacer bar’s local information. Each active spacer bar keeps on negotiating with others and updating its recovery strategy until a consensus is achieved, which is proved to be an optimal solution to the recovery of lost messages. Our future work is to improve the convergence speed, that is, minimizing the process of negotiation in the recovery of lost messages, and extend the proposed scheme to other ad hoc networks.



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*Source: 2893732-2019-10-30.xml*