Optimality of Threshold Admission and Greedy Scheduling

We present the proof of the optimality of Threshold Admission and Greedy Scheduling (TAGS) policy under both average and deterministic settings. We first show that EDF-LMO always maintains low cost sources charging plan feasible. Then under the stochastic setting, the admission problem is formulated as a stochastic dynamic programming problem and the optimality of Threshold Admission policy is shown for identical charging demand case. For deterministic setting, we first establish an upper bound of the optimal competitive ratio by construct an adversary game. Then we show that TAGS achieves the upper bound.