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A fluid queue with a finite buffer and subexponential input

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  01 July 2016

A. P. Zwart
A. P. Zwart*
Affiliation:
Eindhoven University of Technology
*
∗ Postal address: Eindhoven University of Technology, Department of Mathematics and Computing Science, PO Box 513, 5600 MB Eindhoven, The Netherlands. Email address: zwart@win.tue.nl
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Abstract

We consider a fluid model similar to that of Kella and Whitt [32], but with a buffer having finite capacity K. The connections between the infinite buffer fluid model and the G/G/1 queue established by Kella and Whitt are extended to the finite buffer case: it is shown that the stationary distribution of the buffer content is related to the stationary distribution of the finite dam. We also derive a number of new results for the latter model. In particular, an asymptotic expansion for the loss fraction is given for the case of subexponential service times. The stationary buffer content distribution of the fluid model is also related to that of the corresponding model with infinite buffer size, by showing that the two corresponding probability measures are proportional on [0,K) if the silence periods are exponentially distributed. These results are applied to obtain large buffer asymptotics for the loss fraction and the mean buffer content when the fluid queue is fed by N On-Off sources with subexponential on-periods. The asymptotic results show a significant influence of heavy-tailed input characteristics on the performance of the fluid queue.

Keywords

On-Off processesfinite buffersfluid queuesloss fractionsproportionality of probability measuresregenerative processesregular variationsubexponentialityTauberian theorems

MSC classification

Primary: 60K25: Queueing theory 90B22: Queues and service

Information

Type
General Applied Probability
Information
Advances in Applied Probability , Volume 32 , Issue 1 , March 2000 , pp. 221 - 243
Copyright
Copyright © Applied Probability Trust 2000 

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