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Finding the Conjugate of Markov Fluid Processes

Published online by Cambridge University Press:  27 July 2009

Michel Mandjes  and
Ad Ridder
Michel Mandjes
Affiliation:
Department of Econometrics, Vrije Universiteit Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands
Ad Ridder
Affiliation:
Department of Econometrics, Vrije Universiteit Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands
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Abstract

This paper addresses characteristics of finite-buffer Markov-modulated fluid processes, particularly those related to their deviant behavior. Our aim in this paper is to find rough asymptotics for the probability of a loss cycle. Apart from that, we derive some properties of the fluid process in case of the buffer contents reaching a high level (a process we call the conjugate of the original process). Our main goal is to obtain practicable methods to find the rate matrix of this conjugate process. For this purpose we use large deviations techniques, but we consider the governing eigensystem, as well, and we discuss the relation between these two approaches. We extend the analysis to the multiple source case. Finally, we use the obtained results in simulation. We examine variance reduction by importance sampling in a multiple source example. The new statistical law of the fluid process is based on the conjugate rate matrices.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 9 , Issue 2 , April 1995 , pp. 297 - 315
Copyright
Copyright © Cambridge University Press 1995

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