Dynamic Safety-Stocks for Asymptotic Optimality in Stochastic Networks

Abstract

This paper concerns control of stochastic networks using state-dependent safety-stocks. Three examples are considered: a pair of tandem queues; a simple routing model; and the Dai-Wang re-entrant line. In each case, a single policy is proposed that is independent of network load ρ•. The following conclusions are obtained for the controlled network in each case, where the finite constant K0 is independent of load: The policy is fluid-scale asymptotically optimal, and satisfies the bound 2 $$ eta_ast \le \eta \le \eta_\ast + K_0 \log(\eta_\ast),\quad 0 \le \rho_\bullet \le 1, $$ where η* is the optimal steady-state cost. These results are based on the construction of an approximate solution to the average-cost dynamic programming equations using a perturbation of the value function for an associated fluid model. Moreover, a new technique is introduced to obtain fluid-scale asymptotic optimality for general networks modeled in discrete time. The proposed policy is myopic with respect to a perturbation of the value function for the fluid model.