# A Swarming Approach to Optimize the One-Hop Delay in Smart Driving Inter-Platoon Communications
## 2 Related Work  
This section introduces the relevant works. At first, the related works about the multi-platoon are surveyed; then, some related works that focus on the platoon without considering the impact of the multi-platoon are reviewed. Only several works mainly focused on the performance of the multi-platoon. In [7], [PERSON] et al. proposed a performance evaluation model considering the hidden terminal problem in a multi-platoon. They evaluated the performance in terms of throughput and packet delay from two aspects, i.e., the intra-platoon communications and inter-platoon communications. It has shown that the one-hopdelay of the inter-platoon communications are unbalanced and relatively long. This inspired us to optimize the one-hop delay of inter-platoon communications. In [8], [PERSON] and [PERSON] proposed a multi-platooning leaders positioning strategy and an algorithm to maintain a constant inter-platoon spacing and attain high traffic capacity. In [10], [PERSON] et al. presented a sub-channel allocation scheme by jointly considering the broadcast services and device-to-device (D2D) communications. This scheme reduced the end-to-end delay and increased the successful delivery ratio in a multi-platoon. In [11], [PERSON] et al. proposed a cooperative adaptive cruise control (CACC) strategy to achieve string stability in heterogeneous platoons and formulated a framework to evaluate the stability of the platoons. In [12], [PERSON] et al. proposed a hybrid safety message transmission protocol for multi-platoon which can overcome the low delivery ratio of safety application by adopting visible light communications (VLC). This protocol kept the advantage of 802.11p while guaranteeing the stability of a platoon and the security of inter-vehicle communications. In [13], [PERSON] et al. considered the sequential mode and simultaneous mode of dynamic scheduling when using the cellular vehicle-to-everything (C-V2X) communication technology, and proposed a resource allocation algorithm. The results have demonstrated that the simultaneous mode can reduce the data latency in high-density platoon scenarios. Many works designed approaches to enhance the performance of the platoon without considering the impact of the multi-platoon. In [14], [PERSON] and [PERSON] proposed a two-layer control system including a set-point optimization layer and a vehicle tracking control layer for platooning application. In the set-point optimization layer, [PERSON]'s minimum principle (PMP) was used to calculate the optimal speed set-point. In the vehicle tracking control layer, the string stability of vehicles for the platoons was guaranteed through a set of distributed sliding-mode controllers. In [15], [PERSON] et al. proposed a dynamic platoon dispersion model which can be used to predict the evolution of traffic signal flows. The dynamic model considered the time-zone length, the percentages of turning, traffic flows and so on. In [16], [PERSON] et al. proposed a platoon-based driving protocol which is called platoon-to-vehicle (P2V) based on game theory for video transmission with high quality of experience (QoE) support. The protocol combined some vehicles based on direction, speed and distance into a platoon. P2V improved the connectivity between these vehicles in a certain platoon and decreased the ratio of packet loss. In [17], [PERSON] et al. proposed a long-term evolution (LTE) system to support the additional V2V communication for data transmission in a platoon scenario. In [18], [PERSON] et al. proposed a delay-based and string stability spacing policy to determine the desired inter-vehicle spacing and enable all vehicles track the same path and velocity. In [19], [PERSON] et al. proposed an approach which formulated an optimal combination problem to solve the coordination of a large platoon and ensure low consumption of fuel. In [20], [PERSON] et al. established a two-level system to detect the fault of the vehicle platoon. The system detected both system failure and component element failure. In [21], [PERSON] et al.