  Mobile-edge computing (MEC) has recently emerged as a prominent technology to
liberate mobile devices from computationally intensive workloads, by offloading
them to the proximate MEC server. To make offloading effective, the radio and
computational resources need to be dynamically managed, to cope with the
time-varying computation demands and wireless fading channels. In this paper,
we develop an online joint radio and computational resource management
algorithm for multi-user MEC systems, with the objective as minimizing the
long-term average weighted sum power consumption of the mobile devices and the
MEC server, subject to a task buffer stability constraint. Specifically, at
each time slot, the optimal CPU-cycle frequencies of the mobile devices are
obtained in closed forms, and the optimal transmit power and bandwidth
allocation for computation offloading are determined with the Gauss-Seidel
method; while for the MEC server, both the optimal frequencies of the CPU cores
and the optimal MEC server scheduling decision are derived in closed forms.
Besides, a delay-improved mechanism is proposed to reduce the execution delay.
Rigorous performance analysis is conducted for the proposed algorithm and its
delay-improved version, indicating that the weighted sum power consumption and
execution delay obey an $\left[O\left(1\slash V\right),O\left(V\right)\right]$
tradeoff with $V$ as a control parameter. Simulation results are provided to
validate the theoretical analysis and demonstrate the impacts of various
parameters.
