Analysis of a single-server queue interacting with a fluid reservoir
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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 reservoir is determined by the state of the queueing system, since the reservoir fills during idle periods and depletes during busy periods of the server. Our interest focuses on the stationary joint distribution of the number of customers in the system and the content of the fluid reservoir, from which various performance measures such as the steady-state sojourn time distribution 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 analysed approximatively through a discretization technique. The system may serve 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 source. We present some numerical results showing the effect of the mechanism.
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- I.J.B.F. Adan and J.A.C. Resing, A two-level traffic shaper for an on-off source, in preparation.Google Scholar
- D. Anick, D. Mitra and M.M. Sondhi, Stochastic theory of a data-handling system with multiple sources, Bell System Tech. J. 61 (1982) 1871–1894.Google Scholar
- A.W. Berger and W. Whitt, The impact of a job buffer in a token-bank rate-control throttle, Stochastic Models 8 (1992) 685–717.Google Scholar
- T.S. Chihara, An Introduction to Orthogonal Polynomials (Gordon and Breach, New York, 1978).Google Scholar
- D.P. Kroese and W.R.W. Scheinhardt, A Markov-modulated fluid system with two interacting reservoirs, Memorandum No. 1365, Faculty of Mathematical Sciences, University of Twente, Enschede, The Netherlands (1997).Google Scholar
- D.P. Kroese and W.R.W. Scheinhardt, A stochastic fluid model with two interacting reservoirs, submitted.Google Scholar
- B.V. Patel and C.C. Bisdikian, On the performance behavior of ATM end-stations, in: Proc. of the 14th Annual Joint Conf. of the IEEE Computer and Communication Societies — IEEE INFOCOM '95, Boston, MA, USA (2–6 April, 1995) (IEEE Computer Soc. Press, Los Alamitos, 1995) pp. 188–196.Google Scholar
- J. Roberts, U. Mocci and J. Virtamo, eds., Broadband Network Teletraffic — Final Report of Action COST 242 (Springer, Berlin, 1996).Google Scholar
- E.A. van Doorn, A.A. Jagers and J.S.J. de Wit, A fluid reservoir regulated by a birth-death process, Stochastic Models 4 (1988) 457–472.Google Scholar
- E.A. van Doorn and W.R.W. Scheinhardt, A fluid queue driven by an infinite-state birth-death process, in: Proc. of the 15th Internat. Teletraffic Congress on Teletraffic Contributions for the Information Age, Washington, DC, USA (22–27 June, 1997), eds. V. Ramaswami and P.E. Wirth (Elsevier, Amsterdam, 1997) pp. 465–475.Google Scholar