Analysis of a single-server queue interacting with a fluid reservoir

We consider a single-server queueing system with Poisson arrivals in which the speed of the server depends on whether an associated fluid reservoir is empty or not. Conversely, the rate of change of the content of the reservo ir is determined by the state of the queueing system, since the reservoir f ills during idle periods and depletes during busy periods of the server. Ou r interest focuses on the stationary joint distribution of the number of cu stomers in the system and the content of the fluid reservoir, from which va rious performance measures such as the steady-state sojourn time distributi on of a customer may be obtained. We study two variants of the system. For the first, in which the fluid reservoir is infinitely large, we present an exact analysis. The variant in which the fluid reservoir is finite is analy sed approximatively through a discretization technique. The system may serv e as a mathematical model for a traffic regulation mechanism - a two-level traffic shaper - at the edge of an ATM network, regulating a very bursty so urce. We present some numerical results showing the effect of the mechanism .