  The recent drastic increase in mobile data traffic has pushed the mobile edge
computing systems to the limit of their capacity. A promising solution to this
problem is the task migration provided by unmanned aerial vehicles (UAV). Key
factors to be taken into account in the design of UAV offloading schemes must
include the number of tasks waiting in the system as well as their
corresponding deadlines. An appropriate system cost which is used as an
objective function to be minimized comprises two parts. First, an offloading
cost which can be interpreted as the cost of using computational resources at
the UAV. Second, a penalty cost due to potential task expiration. In order to
minimize the expected (time average) cost over a time horizon, we formulate a
Dynamic Programming (DP) equation and analyze it to describe properties of a
candidate optimal offloading policy. The DP equation suffers from the
well-known "Curse of Dimensionality" that makes computations intractable,
especially when the state space is infinite. In order to reduce the
computational burden, we identify three important properties of the optimal
policy. Based on these properties, we show that it suffices to evaluate the DP
equation on a finite subset of the state space only. We then show that the
optimal task offloading decision associated with a state can be inferred from
the decision taken at its "adjacent" states, further reducing the computational
load. Finally, we provide numerical results to evaluate the influence of
different parameters on the system performance as well as verify the
theoretical results.
