Gradient Estimation for Queues with Non-identical Servers

Abstract

We consider a single-queue system with multiple servers that are non-identical. Our interest is in applying the technique of perturbation analysis to estimate derivatives of mean steady- state system time. Because infinitesimal perturbation analysis yields biased estimates for this problem, we apply smoothed perturbation analysis to get unbiased estimators. In the most general cases, the estimators require additional simulation, so we propose an approximation to eliminate this. For two servers, we give an analytical proof of unbiasedness in steady state for the Markovian case. We provide simulation results for both Markovian and non-Markovian examples, and compare the performance with regenerative likelihood ratio estimators.