# Minimum-Cost Offloading for Collaborative Task Execution of MEC-Assisted Platooning
## 2 Related Work  
There are a number of concepts that are closely related to MEC, for instance, mobile cloudlet systems, and MEC is considered to be the natural evolution of previous mobile cloud services (e.g., cloudlet) [13; 14; 15]. MEC provides a promising solution to the challenge for the development of mobile platforms and extends the capabilities of vehicle terminals, by providing additional computing, storage, and bandwidth resources in an on-demand manner [7]. MEC aims to further reduce delay, improve network operation efficiency, and promote service distribution capability, so as to improve the end-user experiences. Some of the proposed solutions can be applied to MEC scenarios. For example, an optimized structure for offloading a single mobile device to multiple MEC servers was proposed [16]. By jointly optimizing the task allocation decision and the Central Process Unit (CPU) frequency of the mobile device, the task execution delay and the energy consumption of the mobile device were minimized, but it only considered a single offloading architecture and could not achieve the multilayer tasks offloading. In addition, a game method could be used to solve the multi-user distributed computing offloading problem in multi-channel wireless interference environment, and provided users with computing resources by MEC at the edge of wireless access network [12]. However, the research did not consider the division of the application tasks, which were not flexible for execution of tasks. Some people considered offloading decision from the point of view of the servers, set the price for the unit resource provided to each vehicle user, and used the gain function of task offloaded to maximize the profit of the vehicular edge computing server [17], which increased the purchase cost of the vehicle user that was contrary to the interests of consumers. The authors of Reference [18] proposed an offloading algorithm minimized the completion time of the tasks. Some tasks were executed locally, and the other part were offloaded to the cloud. This algorithm could not be deployed directly to the realistic scenario, because reducing the completion time would result in too much processing cost. The authors of Reference [19] proposed a collaborative task execution strategy between the end-user and the cloud, which accomplished the tasks with minimum energy consumption within the application deadline. Its simulation results had proved that the collaborative task execution could significantly reduce the energy consumption on the mobile device, thus prolonged the lifetime of devices. The authors of Reference [20] used a directed graph to represent the code blocks and proposed a relatively genetic algorithm to determine how to offload the code blocks among multiple nodes. In Reference [21] the authors proposed an adaptive recedinghorizon offloading strategy, which could minimize the estimating cost of offloading among multiple devices and meet the time constraints of the tasks. At present, there are lack of researches on tasks offloading in platoon, most of which are about connectivity [22; 23] and communication strategy [24] of the network in which the platoon is located, but no consideration has been given to how to offload the tasks in the platoon. Due to the stability and predictability of platoon on the road [25], platoon members can also provide stable computing resources to users for a certain period of time, so as to obtain better computing performance and save the cost. In order to have a deeper understanding of the offloading decision strategy, a simple task model is considered. Each task is executed one after another, forming a linear topology [19]. The task model is transformed into a constrained shortest path problem in directed acyclic graph. We deal with this problem under the path loss model and use Lagrange aggregation cost algorithm to obtain an approximate solution of the constrained problem.