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On the excursions of reflected local-time processes and stochastic fluid queues

Part of: Operations research and management science Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Takis Konstantopoulos ,
Andreas E. Kyprianou  and
Paavo Salminen
Takis Konstantopoulos
Affiliation:
Uppsala University, Department of Mathematics, Uppsala University, 751 06 Uppsala, Sweden. Email address: [email protected]
Andreas E. Kyprianou
Affiliation:
University of Bath, Department of Mathematical Sciences, University of Bath, Claverton Down, Bath, BA2 7AY, UK. Email address: [email protected]
Paavo Salminen
Affiliation:
Åbo Akademi, Department of Mathematics, Åbo Akademi University, Turku, FIN-20500, Finland. Email address: [email protected]
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Abstract

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In this paper we extend our previous work. We consider the local-time process L of a strong Markov process X, add negative drift to L, and reflect it à la Skorokhod to obtain a process Q. The reflection of X, together with Q, is, in some sense, a macroscopic model for a service system with two priorities. We derive an expression for the joint law of the duration of an excursion, the maximum value of the process on it, and the time between successive excursions. We work with a properly constructed stationary version of the process. Examples are also given in the paper.

Keywords

Lévy processlocal timeSkorokhod reflectionstationary process

MSC classification

Primary: 60G51: Processes with independent increments; L'evy processes 60G10: Stationary processes
Secondary: 90B15: Network models, stochastic
Type
Part 2. Lévy Processes
Information
Journal of Applied Probability , Volume 48 , Issue A: New Frontiers in Applied Probability (Journal of Applied Probability Special Volume 48A) , August 2011 , pp. 79 - 98
Copyright
Copyright © Applied Probability Trust 2011 

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