# A Swarming Approach to Optimize the One-Hop Delay in Smart Driving Inter-Platoon Communications
## 3 System Model  
For a multi-platoon, the backbone vehicles in platoons periodically transmit packets with vehicles' kinematics information between them through inter-platoon communications, and then a backbone vehicle in a platoon forwards the packets to its platoon members through intra-platoon communications to keep a platoon formation. In this paper, we focus on the inter-platoon communications. In this section, we introduce the inter-platoon communications model.  
Considering a multi-platoon which is moving in a highway. Similar with [7], we assume that the inter-platoon spacing is not larger than the communication range of a backbone vehicle to guarantee the communication between the leader vehicle of a platoon and the tail vehicle of the preceding platoon. Moreover, the inter-platoon spacing is not smaller than the difference between the communication range of a backbone vehicle and the platoon length to avoid the collision between the leader (tail) vehicle in a platoon and the leader (tail) vehicle in the preceding platoon. In this case, there are one or two neighboring backbone vehicles within the communication range of a backbone vehicle. Specifically, the number of neighbor backbone vehicles is 1 for the first or last backbone vehicle of the multi-platoon and 2 for other backbone vehicles. Let \(n\) be the number of backbone vehicles in the multi-platoon. We label these backbone vehicles by 1, 2,..., \(n-1\), \(n\). For the inter-platoon communications, the backbone vehicles use the same transceiver to communicate with each other through multi-hop communications. The data traffic is saturated, i.e., a backbone vehicle always has packets to transmit. Let \(a\) be the probability that backbone vehicle \(i\) is the destination of backbone vehicle \(i+1\)'s packets, where \(1\leq i<n-1\). Hence, the probability that backbone vehicle \(i+2\) is the destination of backbone vehicle \(i+1\)'s packet is \(1-a\). The inter-platoon communications model is illustrated in Figure 2.  
For the inter-platoon communications, backbone vehicles adopt the IEEE 802.11 DCF mechanism to access a CCH. When a backbone vehicle has a packet to transmit, it randomly selects an integer from [0, \(W_{k}-1\)] as the value of the back-off counter, here \(k\) denotes the number of the packet retransmission and \(W_{k}\) is the minimum contention window size when the packet is retransmitted for \(k\) times. If the channel is detected to be idle, the value of the back-off counter would be decremented by one. Otherwise, the value of the back-off counter would be frozen until the channel keeps idle during a distributed inter-frame spacing (DIFS) period. Once the value of the back-off counter is decremented to 0, the backbone vehicle would transmit the packet. Afterwards, if the backbone vehicle does not receive an acknowledge (ACK) message after a short inter-frame space (SIFS) period, it would select an integer from [0, \(W_{k+1}-1\)] randomly as the value of the back-off counter and initiate a new back-off procedure, in which \(W_{k+1}+1=2W_{k}\). If the number of retransmissions reaches a retransmission limit, the backbone vehicles would drop this packet. In addition, to avoid the capture effect, a backbone vehicle should wait a random back-off value between two consecutive packet transmissions according to the back-off counter.