Queueing Systems

Abstract

In this chapter, we present various examples from queueing, the application area that has served as the main focus of perturbation analysis and other gradient estimation techniques. We concentrate on various examples related to a single queue, as even for this simple queueing system, there are many problems where IPA does not suffice, either because the sample performance measure is discontinuous or because the system itself has “discontinuities” (e.g., does not satisfy the commuting condition), or both. We consider the following variations:

• discontinuous performance measures;

• finite capacity;

• priority classes;

• second derivatives for multiple servers;

• non-identical multiple servers;

• routing (admission) probability;

• other threshold-based parameters.