Mobile-edge computation offloading (MECO) is envisioned as a promising technique 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 investigate the energy-efficient resource-management policy for asynchronous MECO systems, where the mobiles have heterogeneous input-data arrival time instants and computation deadlines. First, we consider the general case with arbitrary arrival- deadline orders. 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 obtained by using the block coordinate decent method. To gain further insights, we further study the special 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 to find the optimal scheduling order and then jointly optimize the 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.
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