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Asymptotic analysis of a fluid model modulated by an M/M/1 queue

Part of: Special processes Markov processes Asymptotic theory

Published online by Cambridge University Press:  01 July 2016

Charles Knessl  and
Diego Ernesto Dominici
Charles Knessl*
Affiliation:
University of Illinois at Chicago
Diego Ernesto Dominici*
Affiliation:
State University of New York at New Paltz
*
∗ Postal address: Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago (M/C 249), 851 South Morgan Street, Chicago, IL 60607-7045, USA. Email address: [email protected]
∗∗ Postal address: Department of Mathematics, State University of New York at New Paltz, 1 Hawk Dr. Suite 9, New Paltz, NY 12561-2443, USA. Email address: [email protected]
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Abstract

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We analyze asymptotically a differential-difference equation that arises in a Markov-modulated fluid model. We use singular perturbation methods to analyze the problem with appropriate scalings of the two state variables. In particular, the ray method and asymptotic matching are used.

Keywords

Fluid queueasymptoticsM/M/1 queueray method

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60J25: Continuous-time Markov processes on general state spaces 34E10: Perturbations, asymptotics
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 40 , Issue 3 , September 2008 , pp. 856 - 881
Copyright
Copyright © Applied Probability Trust 2008 

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