To overcome devices limitations in performing computation-intense applications, mobile edge computing (MEC) enables users to offload tasks to proximal MEC servers for faster task computation. However, current MEC system design is based on average-based metrics, which fails to account for the ultra-reliable low-latency requirements in mission-critical applications. To tackle this, this paper proposes a new system design, where probabilistic and statistical constraints are imposed on task queue lengths, by applying extreme value theory. The aim is to minimize users power consumption while trading off the allocated resources for local computation and task offloading. Due to wireless channel dynamics, users are re-associated to MEC servers in order to offload tasks using higher rates or accessing proximal servers. In this regard, a user-server association policy is proposed, taking into account the channel quality as well as the servers computation capabilities and workloads. By marrying tools from Lyapunov optimization and matching theory, a two-timescale mechanism is proposed, where a user-server association is solved in the long timescale while a dynamic task offloading and resource allocation policy is executed in the short timescale. Simulation results corroborate the effectiveness of the proposed approach by guaranteeing highly-reliable task computation and lower delay performance, compared to several baselines.
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