Perturbation Analysis and Optimization of Stochastic Flow Networks

Abstract

We consider a stochastic fluid model of a network consisting of several single-class nodes in tandem and perform perturbation analysis for the node queue contents and associated event times with respect to a threshold parameter at the first node. We then derive infinitesimal perturbation analysis (IPA) derivative estimators for loss and buffer occupancy performance metrics with respect to this parameter and show that these estimators are unbiased. We also show that the estimators depend only on data directly observable from a sample path of the actual underlying discrete event system, without any knowledge of the stochastic characteristics of the random processes involved. This renders them computable in online environments and easily implementable for network management and optimization. This is illustrated by combining the IPA estimators with standard gradient based stochastic optimization methods and providing simulation examples.