Fluid Queues Driven by a Discouraged Arrivals Queue

We consider a fluid queue driven by a discouraged arrivals queue and obtain explicit expressions for the stationary distribution function of the buffer content in terms of confluent hypergeometric functions. We compare it with a fluid queue driven by an infinite server queue. Numerical results are presented to compare the behaviour of the buffer content distributions for both these models. 1. Introduction. Stochastic fluid flow models are increasingly used in the performance analysis of communication and manufacturing models. Recent measurements have revealed that in high-speed telecommunication networks, like the ATM-based broadband ISDN, traffic conditions exhibit long-range dependence and burstiness over a wide range of time scales. Fluid models characterize such traffic as a continuous stream with a parameterized flow rate. Fluid queue models, where the fluid rates are controlled by state-dependent rates, have been studied in the literature. van Doorn and Scheinhardt [3] analyse the content of the buffer which receives and releases fluid flows at rates which are determined by the state of an infinite birth-death process evolving in the background. Lam and Lee [7] investigate a fluid flow model with linear adaptive service rates. Lenin and Parthasarathy [9] provide closed form expressions for the eigenvalues and eigenvectors for fluid queues driven by an M/M/1/N queue. Resnick and Samorodnitsky [12] have obtained the steady-state distribution of the buffer content for M/G/∞ input fluid queues using large deviation approach. In this paper, we obtain explicit expressions for the stationary distribution function of the buffer content for fluid processes driven by two distinct queue-ing models, namely, discouraged arrivals queue and infinite server queue, respectively. Both these models have the same steady-state probabilities. We show that the buffer content distributions of fluid queues modulated by the two models vary considerably as depicted in the graph. The discouraged arrivals single-server queueing system is useful to model a computing facility that is solely dedicated to batch-job processing (see [11]). The well-known infinite server queue is often used to analyze open loop statistical multiplexing of data connections on an ATM network (see [6]).