Optimal Switching On and Off the Entire Service Capacity of a Parallel Queue

TL;DR

This paper analyzes optimal control policies for a parallel queue system, demonstrating that (M, N)-policies can outperform simpler policies and providing a method to compute these policies efficiently.

Contribution

It introduces a novel (M, N)-policy framework for parallel queues and shows how to compute optimal policies using linear programming, extending previous single-server results.

Findings

(M, N)-policies can outperform (0, N)-policies in parallel queues.

Optimal policies can be computed via linear programming.

The problem reduces to a finite-state, finite-action optimization.

Abstract

This paper studies optimal switching on and o? of the entire service capacity of an M/M/Infinity queue with holding, running and switching costs where the running costs depend only on whether the system is running or not. The goal is to minimize average costs per unit time. The main result is that an average-optimal policy either always runs the system or is an (M, N)-policy defined by two thresholds M and N, such that the system is switched on upon an arrival epoch when the system size accumulates to N and is switched off upon a departure epoch when the system size decreases to M. It is shown that this optimization problem can be reduced to a problem with a finite number of states and actions, and an average-optimal policy can be computed via linear programming. An example, in which the optimal (M, N)-policy outperforms the best (0, N)-policy, is provided. Thus, unlike the case of single-server queues studied in the literature, (0, N)-policies may not be average-optimal.