  Mobile Edge Computing (MEC) has attracted significant research efforts in the
recent years. However, these works consider mostly the computation resources
located at the cloud centers and wireless access nodes, ignoring the
possibility of utilizing server-empowered relays to improve the performance. In
this paper, we study stochastic relay-assisted MEC in systems with discrete
transmission time-line and block fading wireless channels. In order to clearly
identify and inspect the fundamental affecting factors, we investigate the
building block of this architecture, namely a hierarchical network consisting
of a source, a buffer-and-server-aided relay and another higher-level computing
node. We provide a framework to take into account the effects of the fading
channels, the task arrival dynamics as well as the queuing delays in both the
transmission and computation buffers, which facilitates the derivation of the
expression for the Average Response Time (ART). Based on that and the system
average power consumption in each slot, we introduce the concept of Average
Response Energy (ARE) as a novel metric to capture the energy efficiency in MEC
while considering the stochastic nature of the system parameters. Accordingly,
we propose two offloading schemes with their respective problem formulations,
namely the Minimum ART (MART) and the Minimum ARE (MARE) schemes, to optimize
the transmission power and task assignment probability while keeping the system
queues stable. We demonstrate the difference of the formulated problems with
the relevant problem in a recent work, analyze the properties of the problems
and noting them, we propose effective solution methods. Using extensive
simulations, we validate the presented analysis and show the effectiveness of
the proposed schemes in comparison with various baseline methods adapting
existing approaches.
