## 3 Preliminaries  
This paper focuses on the problem of V2V-based computation task offloading in Vehicular Edge Computing networks, as shown in the right part of Figure 1. When a UV has a computation task that needs to be offloaded to other vehicles, the UV will firstly multicast this offloading requirement message to all neighboring vehicles, asking for their cooperation. Upon receiving the request, a neighboring vehicle determines the proper price it wants to charge for providing help with the computation task, according to the fuzzy logic-based pricing strategy. It then responds to the UV with the price. After receiving all responses from the neighboring vehicles, the UV makes the optimal offloading decision based on the Max-Min fairness-oriented approach and acknowledges the appropriate proportions of the computation task to be unloaded to each SV. The negotiation process is similar to the famous \"Three-Way Handshake\" and the exchanged messages can be contained in beacons so that the overhead is negligible. Denote the UV as \(u_{0}\), and the potential SVs set as \(\boldsymbol{SV}=\{sv_{1},sv_{2},\ldots,sv_{K}\}\). The computation task of \(u_{0}\) is defined as \(T_{0}=\left\{D_{0},G_{0},T_{0}^{max}\right\}\), where \(D_{0}\) represents the size of the task, \(G_{0}\) is the number of CPU cycles required to process 1-bit data of the task, and \(T_{0}^{max}\) is the maximum acceptable completion delay of the task. The task can be divided into several sub-tasks of any size to enable synchronous processing on multiple SVs. To obtain a microscopic vehicle movement model closer to the real high-speed scene, this paper adopts the car-following model in [27] as the mobility model. Time is slotted. At the beginning of each time slot \(\Delta t\), a vehicle \(v_{i}\) updates its speed and then maintains this speed throughout the time slot. The update of \(v_{i}\)'s speed at time \((t+\Delta t)\) can be expressed as follows:  
\[v_{i}(t+\Delta t)=v_{i}(t)+\delta_{i}(t)\cdot a\cdot\Delta t, \tag{1}\]  
where \(v_{i}(t)\) denotes the speed of \(v_{i}\) at time \(t\), \(\delta_{i}(t)\in[-1,1]\) is a random adjusting parameter for acceleration or deceleration at time \(t\), and \(a\) is the acceleration constant. The minimum and maximum allowable speeds of a vehicle are denoted as \(v_{min}\) and \(v_{max}\), and the safety distance and the following distance between any two vehicles are denoted as \(L_{safe}\) and \(L_{follow}\), respectively. The microscopic mobility of a vehicle is constrained by its speed and distance according to Formula (2) as follows:  
\[v_{i}(t+\Delta t)= \begin{cases}v_{min},&\text{if}\quad v_{i}(t+\Delta t)<v_{ min}\\ v_{max},&\text{if}\quad v_{i}(t+\Delta t)>v_{max}\\ v_{i}(t)+a\cdot\Delta t,&\text{if}\quad L_{i,i+1}(t)>L_{follow}\\ v_{i}(t)-a\cdot\Delta t,&\text{if}\quad L_{i,i+1}(t)<L_{safe}\end{cases} , \tag{2}\]  
where \(L_{i,i+1}(t)\) is the distance between two consecutive vehicles \(v_{i}\) and \(v_{i+1}\) at time \(t\). It is noted that Formula (2) is defined according to the actual driving conditions of vehicles. The safety distance is the minimum driving distance between vehicles, which depends on the real-time speeds of the vehicles. It can ensure that the rear vehicle has enough distance to brake in case of emergency, and reduces the incidence of chain traffic accidents. The following distance is the maximum driving distance between vehicles, which can save more space for other vehicles behind. The V2V communications among vehicles are assumed to comply with IEEE 802.11p standards [28], the data transmission rate between any two vehicles can be calculated as follows:  
\[R=B\cdot log_{2}\left(1+\frac{P_{up}\cdot h}{\sigma^{2}}\right), \tag{3}\]  
where \(B\) is the channel bandwidth, \(P_{up}\) is the transmission power of a vehicle, \(h\) is the channel gain and \(\sigma^{2}\) is the noise power. The symbols used in this paper are listed in Table 1.