Perturbation analysis of stochastic flow systems with multiplicative feedback

This paper uses stochastic flow models (SFMs) for control and optimization (rather than performance analysis) of queueing systems with multiplicative feedback. Unlike earlier work based on additive feedback, the multiplicative feedback scheme considered here requires minimal state information and bypasses the problem of delayed state information. Using infinitesimal perturbation analysis (IPA), we derive gradient estimators for loss and workload related performance metrics with respect to a feedback gain parameter, in contrast to previous work where threshold parameters were considered. The unbiasedness of these estimators is also established.