A Unified Approach to Infinitesimal Perturbation Analysis in Stochastic Flow Models: The Single-Stage Case

This paper develops an abstract framework for Infinitesimal Perturbation Analysis (IPA) in the setting of stochastic flow models, and it applies it to several problems arising in the study of flow control in single-server fluid-flow queues. The framework is based on a switched-mode hybrid-system paradigm, and especially on the interplay between its discrete-event dynamics and continuous-time dynamics. It is quite general, and most of the formulas obtained to-date for IPA on single-server queues can be derived from it as simple corollaries. Additional new results can be derived as well, and the paper demonstrates it by considering a queue with loss-rate-based flow control. The main contribution of the paper is in the proposed framework and its apparent broad scope. Its possible extension to a general class of fluid-flow queueing networks appears likely, and will be pointed out as a direction for future research.