Partial Replication for Delay-Optimal Distributed Edge Computing

The ever-increasing scale and more stringent latency requirements of mobile computing tasks have driven the recent development of distributed edge computing. In distributed edge computing, a large-scale computing task is partitioned into multiple small subtasks and executed in parallel on multiple edge nodes (ENs) to reduce computation delay. In early works of this area, the computation results of the subtasks are often transmitted back in a non-cooperative manner, which may lead to suboptimal downlink communication delay. Replicated edge computing can alleviate this issue by replicating the computing task over multiple ENs to enable cooperative transmission in the downlink. However, this will inevitably entail multi-fold increase of computation costs. To bridge the gap between the conventional distributed edge computing and the replicated edge computing, a novel partial replication based distributed edge computing scheme is proposed in this work. In particular, by judiciously determining the portion of task to be replicated at the ENs, the proposed scheme can harvest cooperative transmission gains while avoiding excessive computational replication costs. Accordingly, a partial replication based delay minimization problem is formulated. By leveraging the generic alternating optimization framework, this problem can be divided into two subproblems of power allocation and task partitioning. Through analysis, a semi-closed form solution is derived for the former non-convex subproblem, while the latter subproblem turns out to be linear. Simulation results are presented to corroborate the effectiveness of the proposed scheme.