  The mobile edge computing framework offers the opportunity to reduce the
energy that devices must expend to complete computational tasks. The extent of
that energy reduction depends on the nature of the tasks, and on the choice of
the multiple access scheme. In this paper, we first address the uplink
communication resource allocation for offloading systems that exploit the full
capabilities of the multiple access channel (FullMA). For indivisible tasks we
provide a closed-form optimal solution of the energy minimization problem when
a given set of users with different latency constraints are offloading, and a
tailored greedy search algorithm for finding a good set of offloading users.
For divisible tasks we develop a low-complexity algorithm to find a stationary
solution. To highlight the impact of the choice of multiple access scheme, we
also consider the TDMA scheme, which, in general, cannot exploit the full
capabilities of the channel, and we develop low-complexity optimal resource
allocation algorithms for indivisible and divisible tasks under that scheme.
The energy reduction facilitated by FullMA is illustrated in our numerical
experiments. Further, those results show that the proposed algorithms
outperform existing algorithms in terms of energy consumption and computational
cost.
