A Game Theoretic Approach to Computation Offloading Strategy Optimization for Non-cooperative Users in Mobile Edge Computing

Computation offloading from a user equipment (UE, also called mobile user, mobile subscriber, or mobile device) to a mobile edge cloud (MEC) provides an effective way to virtualize an ordinary smart mobile device (e.g., smartphone, tablet, handheld computer, wearable device, and personal digital assistant) into a formidable equipment, which is able to provide more and stronger functionalities than that of a laptop or a desktop computer. It is conceivable that there can be several MECs with different processing capabilities in a geographic area, and each MEC many serve many UEs with endless sequences of computation tasks, various application characteristics, and diversified communication requirements and bandwidths. Furthermore, the mobile users are competitive and selfish, which means that computation offloading strategy optimization needs to be carried out for each individual mobile user to optimize the performance of only his applications. In this paper, we conduct a mathematical study of computation offloading strategy optimization for non-cooperative users in mobile edge computing by using a game theoretic approach. The main contributions of this paper can be summarized as follows. We establish an M/G/1 queueing model to characterize multiple heterogeneous UEs and MECs, so that the average response time of all offloadable and non-offloadable tasks generated on a UE can be calculated analytically and the optimal computation offloading strategy of a UE can be defined rigorously. We construct a non-cooperative game framework for a mobile edge computing environment, in which each player (i.e., a UE) can selfishly minimize his payoff by choosing an appropriate strategy in his strategy space. We prove the existence of the Nash equilibrium of the above game. We develop algorithms to find the Nash equilibrium, including an algorithm to find the best response of a mobile user and an iterative algorithm to find the Nash equilibrium. We demonstrate numerical examples and data of our game, including numerical data for the Nash equilibrium and numerical data for the convergence of the Nash equilibrium. To the best of the author's knowledge, this is the first paper that effectively investigates computation offloading strategy optimization for multiple, heterogeneous, and competitive mobile users and multiple heterogeneous mobile edge clouds by using a non-cooperative game approach. Hence, the paper makes noticeable contributions towards the understanding of a competing mobile edge computing environment and its stabilization.