On An Equivalence Between Loss Rates And Cycle Maxima In Queues And Dams

Authors:
René/ Bekker;Bert Zwart
Affiliations:
CWI, 1090 GB Amsterdam, The Netherlands, and, Department of Mathematics & Computer Science, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands, E-mail: rbekker@win.tue.nl/ zwar ...;CWI, 1090 GB Amsterdam, The Netherlands, and, Department of Mathematics & Computer Science, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands, E-mail: rbekker@win.tue.nl/ zwar ...
Venue:
Probability in the Engineering and Informational Sciences
Year:
2005

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Abstract

We consider the loss probability of a customer in a single-server queue with finite buffer and partial rejection and show that it can be identified with the tail distribution of the cycle maximum of the associated infinite-buffer queue. This equivalence is shown to hold for the GI/G/1 queue and for dams with state-dependent release rates. To prove this equivalence, we use a duality for stochastically monotone recursions, developed by Asmussen and Sigman (1996). As an application, we obtain several exact and asymptotic results for the loss probability and extend Takács' formula for the cycle maximum in the M/G/1 queue to dams with variable release rate.