IPA for flow-control fluid queues with delays

This paper concerns the application of Infinitesimal Perturbation Analysis (IPA) to a fluid queue with flow control. The control law restricts the inflow rate to the queue by an amount that is proportional to the loss rate, and the control signal incurs a delay. The performance measure consists of a weighted sum of the loss volume and cumulative workload, and it is treated as a function of the buffer limit. The IPA derivative is derived, and its use in optimization is demonstrated via a simulation example. Published results on IPA for flow-control systems assume that the control signal is instantaneous, and the main contribution of this paper is in a technique for analysis of a system with delayed control. The derivation of the IPA derivative for the loss volume is presented in detail, and analogous results for the cumulative workload are highlighted.