This paper proposes a novel algorithmic solution for dynamic computation offloading, aimed at reducing the energy consumption of a mobile network endowed with multi-access edge computing. The dynamic evolution of the system is modeled through three queues: a local queue at the user side, a computation queue at the edge server, and a queue of results at the network access point. The optimization problem is cast as the minimization of the long-term average energy consumption of the whole system, comprising user devices, servers, and access points. Quality of service constraints for end users are imposed in terms of probability that the textit{sum of the queues} exceeds a given threshold. A suitable weighting parameter can be tuned to drive the system toward a user-centric, a network-centric, or a hybrid solution. Exploiting stochastic optimization tools, the problem is solved thanks to a dynamic optimization algorithm, based on the solution of deterministic convex problems in each time slot. The algorithm does not assume any knowledge on the task input and output random sizes and the radio channel statistics. Several numerical results illustrate the advantages of the proposed method. © 2019 IEEE.