  Mobile-edge computation offloading (MECO) is an emerging technology for
enhancing mobiles' computation capabilities and prolonging their battery lives,
by offloading intensive computation from mobiles to nearby servers such as base
stations. In this paper, we study the energy-efficient resource-management
policy for the asynchronous MECO system, where the mobiles have heterogeneous
input-data arrival time instants and computation deadlines. First, we consider
the general case with arbitrary arrival-deadline orders. Based on the monomial
energy-consumption model for data transmission, an optimization problem is
formulated to minimize the total mobile-energy consumption under the
time-sharing and computation-deadline constraints. The optimal
resource-management policy for data partitioning (for offloading and local
computing) and time division (for transmissions) is shown to be computed by
using the block coordinate decent method. To gain further insights, we study
the optimal resource-management design for two special cases. First, consider
the case of identical arrival-deadline orders, i.e., a mobile with input data
arriving earlier also needs to complete computation earlier. The optimization
problem is reduced to two sequential problems corresponding to the optimal
scheduling order and joint data-partitioning and time-division given the
optimal order. It is found that the optimal time-division policy tends to
balance the defined effective computing power among offloading mobiles via time
sharing. Furthermore, this solution approach is extended to the case of reverse
arrival-deadline orders. The corresponding time-division policy is derived by a
proposed transformation-and-scheduling approach, which first determines the
total offloading duration and data size for each mobile in the transformation
phase and then specifies the offloading intervals for each mobile in the
scheduling phase.
