Queueing networks with a single shared server: Light and heavy traf c M.A.A. Boon Department of Mathematics and Computer Science Eindhoven University of Technology P.O. Box 513, 5600MB Eindhoven, The Netherlands R.D. van der Mei Centre for Mathematics and Computer Science (CWI) Department of Probability and Stochastic Networks 1098 SJ Amsterdam, The Netherlands E.M.M. Winands Department of Mathematics, Section Stochastics VU University De Boelelaan 1081a, 1081HV Amsterdam, The Netherlands marko@win.tue.nl ABSTRACT mei@cwi.nl emm.winands@few.vu.nl We study a queueing network with a single shared server, that serves the queues in a cyclic order according to the gated service discipline. External customers arrive at the queues according to independent Poisson processes. After completing service, a customer either leaves the system or is routed to another queue. This model is very generic and nds many applications in computer systems, communication networks, manufacturing systems and robotics. Special cases of the introduced network include well-known polling models and tandem queues. We derive exact limits of the mean delays under both heavy-tra c and light-tra c conditions. By interpolating between these asymptotic regimes, we develop simple closed-form approximations for the mean delays for arbitrary loads. Categories and Subject Descriptors G.3 [Mathematics of Computing]: Probability and
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