Sensitivity analysis of loss volume in stochastic fluid systems with flow control

This paper concerns infinitesimal perturbation analysis (IPA) for fluid queues with finite buffers, where input fluid in excess of buffer capacity is turned away and considered lost. In particular, it considers the loss-volume (and hence average loss rate) performance measure with respect to the buffer sizes. Most previous results pertained to open- loop systems, but recently there has been a mounting interest in feedback control, and especially in workload-based flow control systems. This paper considers an alternative flow- control mechanism whereby the inflow rate is restricted by an amount that is proportional to the loss rate. It first discusses a single-server queue, and then it analyzes a two-queue tandem network, while pointing out possible extensions to more general- topology networks and other performance functions. The main results are comprised of recursive algorithms for computing the IPA derivatives in nonparametric and model-free forms.