Decomposable score function estimators for sensitivity analysis and optimization of queueing networks

Abstract

This paper surveys some recent results and presents some new results on the so-called decomposable and truncated score functions (DSF and TSF) estimators for performance evaluation, sensitivity analysis and optimization of open non-Markovian (non-product) queueing networks. The idea behind the TSF estimators is based on truncation of the score function process, while the idea behind the DSF estimators is to decompose the queueing network into smaller units, calledmodules, such that each module contains several connected queues, and then approximate the unknown quantities by treating these modules as if they were completely independent. In other words, in the DSF estimators we use frequently occurrentlocal regenerative cycles at eachindividual module instead oftrue but seldom occurrentglobal ones of theentire system. Although the local cycles at each module interact with their neighbors, our numerical studies show that typically the contribution from the neighbors is quite small and thus DSF estimators approximate the unknown quantities rather well, in the sense that their bias is reasonably small and the variance is much smaller than that of the standard score function estimators. Both DSF and TSF estimators were implemented in a simulation package, called thequeueing network stabilizer and optimizer (QNSO). This package is suitable for performance evaluation, sensitivity analysis and optimization of general open non-Markovian queueing networks with respect to the parameter vector of an exponential family of distributions.