  Task offloading provides a promising way to enhance the capability of the
mobile terminal (also called terminal user) that is distributed on network edge
and communicates edge clouds with wireless. Generally, there are multiple edge
cloud nodes with distinct processing capability in a geographic area, which can
offer computing service for various terminal users. Furthermore, the terminal
users are competitive and selfish, i.e., each user takes into account only
maximizing her own profit, while conducting task offloading strategies. In this
paper, we focus on the resource management optimization for edge clouds, and
formulate the problem of resource competition among terminal users as a
non-cooperative game, in which the terminal user who acts as the player always
pursues the minimization of the expected response time for her tasks by
optimizing allocation strategies. We present the utility function of the user
with queuing theory, and then prove the existence of Nash equilibrium for the
formulated game. Using the concept of Nash bargaining solution to calculate the
optimal task offloading scheme for the user, we propose a distributed task
offloading algorithm with low computation complexity. The results of simulated
experiments demonstrate that our method can quickly reach the Nash equilibrium
point, and deliver satisfying performance at the expected response time of the
user's tasks.
