Energy Minimization of Mobile Edge Computing Networks With HARQ in the Finite Blocklength Regime

We consider a mobile edge computing (MEC) network supporting low-latency, critical offloading workloads. The task offloading from the user to the server is operated under a truncated Hybrid Automatic Repeat reQuest (HARQ) process, i.e., we consider finite retransmission attempts. Both the HARQ type-I and type-II schemes are studied. For each scheme, we first characterize the total error probability and the total energy cost, while the impact of finite blocklength (FBL) on the stochastic retransmission behavior is considered. Following the characterizations, we are interested in optimal frameworks for each considered HARQ type, where the number of potential retransmission attempts is optimized together with the duration of each transmission, while the CPU frequency at the edge node is adjusted via voltage scaling. The objective is to minimize the total energy cost with error probability threshold. We show that the resulting stochastic optimization problems can be solved by means of convex optimization. We furthermore demonstrate that sharp minima exist among the energy consumption, underlying the importance of near-optimal parameter choice in the studied scenarios. Our results underline the importance of trading off communication and computational characteristics in delay-critical MEC setups with FBL codes.