A TANDEM FLUID QUEUE WITH GRADUAL INPUT

Authors:
Werner R. W. Scheinhardt;Bert Zwart
Affiliations:
Faculty of Mathematical Sciences, University of Twente, Enschede, The Netherlands, E-mail: werner@math.utwente.nl, and CWI, Amsterdam, The Netherlands;Department of Mathematics & Computing Science, Eindhoven University of Technology, Eindhoven, The Netherlands, E-mail: zwart@win.tue.nl
Venue:
Probability in the Engineering and Informational Sciences
Year:
2002

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Abstract

For a two-node tandem fluid model with gradual input, we compute the joint steady-state buffer-content distribution. Our proof exploits martingale methods developed by Kella and Whitt. For the case of finite buffers, we use an insightful sample-path argument to extend an earlier proportionality result of Zwart to the network case.