# Task Offloading Based on Lyapunov Optimization for MEC-Assisted Vehicular Platooning Networks
## 1 Introduction  
In several typical application scenarios under the fifth-generation (5G) cellular networks, the huge number of intelligent vehicles (2.8 billion) will be a question worth pondering by 2020 [1]. In the 3 rd Generation Partnership Project Technical (3 GPP) Report [2], 27 use cases of vehicle-to-everything (V2X)were proposed to intend to help drivers in avoiding or mitigating rear-end vehicle collisions in the forward path of travel. Different V2X scenarios require the transport of V2X messages with different performance requirements for the 3 GPP system. The Technical Specification [3] specifies service requirements to enhance 3 GPP support for V2X scenarios in five areas and vehicle platooning is one of the areas. Platooning, as a vehicular traffic management strategy, is a key step for autonomous driving in intelligent transportation systems (ITS). In general, the platooning consists of two types of members: one is the leader (commander) and the other is the member of platooning (including the relay vehicle and tail vehicle) [4]. Vehicles in platooning run on the same driveway, and the distances between vehicles are approximately the same. In platooning, vehicles use virtual strings to connect adjacent vehicles and control them by updating real-time motion data (such as the driving distance between vehicles and speed). Most vehicle-related tasks, such as automatic drive, 3D navigation, voice processing, traffic information system, etc, are typically computation-intensive tasks that require more computing resources and energy to process [5].  
Generally, vehicles have limited computing resources and battery lifetime, bringing great challenges at effectively addressing these computation-intensive mobile applications. A solutionbased on cloud computing is proposed by the academic community, where the computation data are transmitted to a remote cloud center for execution [6]. However, if such typical computation-intensive tasks are transferred to a remote cloud center, the transmission delay may not be able to meet the requirement of ultra-low delay for vehicular applications and services. The European Telecommunications Standards Institute (ETSI) has proposed a promising paradigm-mobile edge computing (MEC) [7; 8], which is an advanced technology to support multiple applications and services that requires ultra-low latency. In an MEC-assisted vehicular network, a mobile application can be executed on the vehicle itself (local execution) or offloaded to an MEC server (edge execution) for processing. Because of the short distance between an MEC server and a vehicle, the MEC paradigm provides high bandwidth, low latency, and computational agility in computation offloading [9].  
In this paper, we consider a platooning with an MEC-assisted server to execute computing tasks of vehicle terminals. An optimal offloading decision is investigated among the members of the platooning and MEC server to minimize the average total energy consumption at each time within the tasks' execution deadlines. Mathematically, the classical Lyapunov algorithm is adopted to simplify the research objective. Then, a sub-optimal solution of the simplified problem is obtained by a greedy algorithm. The simulation results show that the proposed algorithm can effectively reduce the energy consumption of task execution and greatly improve the offloading efficiency of vehicles compared with the shortest queue waiting time algorithm and the full offloading to an MEC algorithm.  
The rest of this paper is organized as follows. We review related work in Section 2. In Section 3, we present the system model. In Section 4, we describe the formulation of our optimization problem. A solution is provided in Section 5. Section 6 shows the simulation results, and Section 7 concludes the paper.