Mobile Edge Computing (MEC) has evolved into a key technology that can leverage resources of computing, storage and network deployed at the proximity of the Mobile Devices (MDs). How to offload delay-sensitive and energy-constraint tasks is of research importance. In this paper, considering time-correlated traffic and Virtual Machine (VM) repair, we come up with a method to evaluate the task offloading scheme in a MEC system. Applying a Markovian Arrival Process (MAP) to describe the task arrivals in a MEC system, the local computing offloading and the MEC offloading are modeled as a MAP/M/1 queue and a MAP/M/N/N+K queue with VM repair, respectively. By exploiting the matrix-geometric solution approach and the Gauss–Seidel approach, we give the average delay, the energy consumption level and computation resource availability. Next, we provide numerical results to investigate the influence of the offload rate on the response performance and the energy efficiency with different correlation coefficients and the influence of the repair rate and the service rate of a VM on the availability. In addition, an improved Sine and Cosine Algorithm (SCA) is developed to acquire the optimal offload rate with a delay-energy tradeoff.

移动边缘计算 (MEC) 已发展成为一项关键技术，可以利用部署在移动设备 (MD) 附近的计算、存储和网络资源。如何卸载延迟敏感和能量约束的任务具有重要的研究意义。在本文中，考虑到时间相关流量和虚拟机 (VM) 修复，我们提出了一种评估 MEC 系统中任务卸载方案的方法。应用马尔可夫到达过程（MAP）来描述MEC系统中的任务到达，将本地计算卸载和MEC卸载建模为MAP/M/1队列和MAP/M/ N / N + K分别与 VM 修复一起排队。通过利用矩阵几何求解方法和 Gauss-Seidel 方法，我们给出了平均延迟、能耗水平和计算资源可用性。接下来，我们提供数值结果来研究不同相关系数下卸载率对响应性能和能源效率的影响，以及修复率和虚拟机服务率对可用性的影响。此外，还开发了一种改进的正弦余弦算法 (SCA)，以通过延迟能量权衡获得最佳卸载率。