# Task Offloading Based on Lyapunov Optimization for MEC-Assisted Vehicular Platooning Networks
## 3 System Model
### Task Offloading Model  
Figure 1 depicts the task offloading scenario in this paper, where vehicle-to-vehicle (V2V) communication is adopted between vehicles, and vehicle-to-infrastructure (V2I) communication is adopted between vehicle and base station (BS) [25; 26]. A cellular network can provide sufficiently stable/reliable wireless communication for V2V and V2I communication. In three application scenarios under the 5G cellular network, URLLC (Ultra-Reliable and Low Latency Communications) not only guarantees ultra-low transmission delay, but also guarantees ultra-reliability transmission [27]. Without loss of generality, it is assumed that the entire platooning is covered by a cellular network, and all PMs and MEC can directly communicate in pairs. There are \(M\) PMs in the platooning. Starting from the driving direction of the platooning, the first member is defined as 1, and then the serial numbers of other PMs increase consecutively. An MEC server is deployed with a BS via wired connection [28; 29; 30; 31]. If a vehicle sends information to an MEC server, it first should send information to BS through V2I, and then forward to the MEC server through wired transmission.  
Figure 2 illustrates the task offloading system model. The task requester in platooning is denoted as \(m\in\{1,2,...,M\}\), and the computation node of the task is denoted as \(k\in\{0,1,...,M\}\), in which 0 represents the MEC server. \(B_{m,k}\) is the transmission rate between PM \(m\) and computation node \(k\). When \(m=k\), the task is executed at the local \(m\). Due to the fast transmission rate of wired transmission and the co-existing deployment between the BS and MEC server, the wired transmission time is ignored in this paper [28].  
All vehicles in platooning will generate a computation task in each time interval, that is, all PMs are task requesters. Notice that there are a total of \(M\) PMs in platooning. Thus, each PM has a total of  
Figure 1: Task offloading scenario.  
Figure 2: Task offloading system model.  
\(M+1\) computation nodes, namely \(M\) PMs and an MEC server. In addition, the time of offloading task is discretized, and time \(t\) is to represent the execution slot of the task. Then, the offloading member should transfer the offloading tasks to other PMs or the MEC server for execution through V2V or V2I. The task offloading queue model is shown in Figure 3, where \(Q_{k}(t)\in\{Q_{0}(t),Q_{1}(t),...,Q_{M}(t)\}\) represents the length of task queue \(k\) at time \(t\). The task load arrived at PM \(m\) in time \(t\) is \(A_{m}(t)\), which is expressed by the number of CPU cycles required to execute the task. \(A_{m}(t)\in\{A_{1}(t),A_{2}(t),...,A_{M}(t)\}\) follows Poisson distribution with mean \(\Omega\{A_{m}(t)\}=\lambda_{m}\), and satisfies independent identical distribution. \(b_{k}(t)\in\{b_{0}(t),b_{1}(t),...,b_{M}(t)\}\) represents the task computation workload that arrives at queue \(k\) after offloading decision at time \(t\). For instance, when PM 1 and PM 2 decide to offload the task to MEC server at time \(t\), \(b_{0}(t)=A_{1}(t)+A_{2}(t)\) can be obtained. Each vehicle can provide a certain amount of computation resources [28; 32; 33], and \(f_{k}\in\{f_{0},f_{1},...,f_{M}\}\) represents the computation capacity (i.e., CPU cycles per second) provided by the computation node \(k\) in each time interval.