Continuous feedback fluid queues

Authors:
Werner Scheinhardt;Nicky Van Foreest;Michel Mandjes
Affiliations:
Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands and Center for Mathematics and Computer Science (CWI), P.O. Box 94079, 1090 GB Amsterdam, T ...;Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands;Department of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands and Center for Mathematics and Computer Science (CWI), P.O. Box 94079, 1090 GB Amsterdam, T ...
Venue:
Operations Research Letters
Year:
2005

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Abstract

We investigate a fluid queue with feedback from the (finite) buffer to the background process. The latter behaves as a continuous-time Markov chain, but the generator (and traffic rates) depend continuously on the current buffer level. We derive the Kolmogorov equations, and, for two-state background processes, the explicit stationary distribution.