Bias properties of infinitesimal perturbation analysis for multi-server queues

Infinitesimal perturbation analysis (IPA) gives biased estimates for multi-server queues when the service time distributions of the servers are not equal. The authors analytically calculate the bias for IPA gradient estimators of mean steady-state system time (with respect to parameters in the inter-arrival or service time distributions) in a two-server Markovian queue where reversibility holds. Because it is believed that the applicability of IPA is in general distribution-independent, it is conjectured that the order of biases with respect to nonidenticality may be applicable to more general distributions. This would mean that IPA is relatively insensitive to small deviations from the equal server case