The Surrogate Estimation Approach for Sensitivity Analysis in Queueing Networks

Abstract

The construction of good gradient estimators, known as sensitivity, analysis, has recently been the subject of many studies. Gradient estimators may be used to optimize the performance of stochastic processes. In this paper we propose a method for sensitivity estimation that can be used for the optimization of stochastic discrete, event dynamic systems (DEDS). Most of the current, methods for gradient estimation have limited applicability for complex problems. The surrogate estimation approach that we propose uses the system's dynamics and heuristic relations in the parameters to construct the desired gradient estimators using local sensitivity estimators. We present an example of routing in an open data network. Some of the most successful methods for gradient estimation-such as the IPA method-cannot be applied directly and other methods are in-appropriate for real time operation. We show how the estimation of the gradient, of the stationary average sojourn time with respect to the routing probabilities can be decomposed in terms of local sensitivities. Each node needs to estimate the derivatives of the average queue length with respect to its own arrival rate. The computation is thus distributed and the estimation of the local sensitivities is a much simpler problem, suited for IPA. The amount of calculations required for our approach is proportional to the number of nodes in the network. Those required for direct estimation grow with the number of nodes, the number of outgoing links and the number of destinations. Our simulations indicate that, surrogate estimation is very efficient, even when some of the required assumptions for IPA estimation are not satisfied.