  This letter investigates a cache-enabled multiuser mobile edge computing
(MEC) system with dynamic task arrivals, taking into account the impact of
proactive cache placement on the system's overall energy consumption. We
consider that an access point (AP) schedules a wireless device (WD) to offload
computational tasks while executing the tasks of a finite library in the
\emph{task caching} phase, such that the nearby WDs with the same task request
arriving later can directly download the task results in the \emph{task arrival
and execution} phase. We aim for minimizing the system's weighted-sum energy
over a finite-time horizon, by jointly optimizing the task caching decision and
the MEC execution of the AP, and local computing as well as task offloading of
the WDs at each time slot, subject to caching capacity, task causality, and
completion deadline constraints. The formulated design problem is a
mixed-integer nonlinear program. Under the assumption of fully predicable task
arrivals, we first propose a branch-and-bound (BnB) based method to obtain the
optimal offline solution. Next, we propose two low-complexity schemes based on
convex relaxation and task-popularity, respectively. Finally, numerical results
show the benefit of the proposed schemes over existing benchmark schemes.
