Optimal Wireless Service Within Average Delay

Service provision over wireless networks is a key performance criterion, yet an onerous task due to the stochastic nature of channels, transmission overhead, and service delay requirements. This paper considers services differentiated by preference without benefit or penalty for early or delayed completion, instead a benefit exists for maintaining the average delay of completed services below a predefined limit. The average delay is constrained at each network instance via joint optimization of probing order and transmission decisions, resulting in a nonlinear expanding-then-collapsing optimization constraint. A permutation in the transmission order does not impact the sum delay but can impact the average delay. Therefore, finding the optimal order is paramount for proper service provision. A particular greedy ordering is shown to reduce the set of feasible solutions without losing global optimality. Practical solutions are proposed via stochastic programming formulation and an optimal stopping strategy that does not use a priori knowledge. The stopping strategy results in a set of thresholds, which can be practically computed a priori and implemented in a decentralized manner. Simulations show that our proposed Dantzig inspired stopping strategy achieves near optimal sum service value with higher throughput than a stochastic programming formulation.