Optimal Control of Single-Stage Hybrid Systems with Poisson Arrivals and Deterministic Service Times

Abstract—We tackle an optimal control problem for a single-stage hybrid system with Poisson arrivals and determin-istic service times. In our setting, not only that the optimization problem is non-convex and non-differentiable, but also future arrival times are unknown at the times of decision. We propose a state-dependent service times policy where the state is defined as the system size. These service times are determined iteratively by a steepest descent algorithm whose derivative in-formation is supplied by an infinitesimal perturbation analysis derivative estimator. We also propose an improved receding horizon controller with zero-length time window that utilizes the interarrival time distribution information available from the observed arrivals. Performances of these methods are compared to the optimal performance obtained from the Forward Decompositon Algorithm for which all future arrival times are known. It is also shown that the utilization of the observed interarrival time distribution information improves the performance of the receding horizon controller with zero-length time window