  In mobile computation offloading (MCO), mobile devices (MDs) can choose to
either execute tasks locally or to have them executed on a remote edge server
(ES). This paper addresses the problem of assigning both the wireless
communication bandwidth needed, along with the ES capacity that is used for the
task execution, so that task completion time constraints are satisfied. The
objective is to obtain these allocations so that the average power consumption
of the mobile devices is minimized, subject to a cost budget constraint. The
paper includes contributions for both soft and hard task completion deadline
constraints. The problems are first formulated as mixed integer nonlinear
programs (MINLPs). Approximate solutions are then obtained by decomposing the
problems into a collection of convex subproblems that can be efficiently
solved. Results are presented that demonstrate the quality of the proposed
solutions, which can achieve near optimum performance over a wide range of
system parameters.
