Nash equilibrium and social optimization of a task offloading strategy with real-time virtual machine repair in an edge computing system.

In order to relieve the pressure of the local devices, some tasks need to be offloaded to the edge computing system. In order to guarantee the service level of the edge computing system, virtual machines (VMs) deployed in the edge server should be as active as possible. For light load application scenarios such as smart home, to meet the quality of service of tasks while coping with occasional VM failures, we propose a task offloading strategy with real-time VM repair in an edge computing system. Accordingly, we establish a repairable queueing model with multiple servers and VM-dependent failure rates. By using quasi-birth-death process and matrix-geometric solution method, we give the average latency of tasks in steady state. Considering that the number of tasks and the VM state are fully unobservable, we construct profit functions to study the Nash equilibrium arrival rate of tasks and the socially optimal arrival rate of tasks. In order to maximize the social profit, we present a pricing policy for tasks in the edge computing system with the proposed strategy. [ABSTRACT FROM AUTHOR]