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September 2013 Factorization identities for reflected processes, with applications
Brian H. Fralix, Johan S. H. van Leeuwaarden, Onno J. Boxma
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J. Appl. Probab. 50(3): 632-653 (September 2013). DOI: 10.1239/jap/1378401227

Abstract

We derive factorization identities for a class of preemptive-resume queueing systems, with batch arrivals and catastrophes that, whenever they occur, eliminate multiple customers present in the system. These processes are quite general, as they can be used to approximate Lévy processes, diffusion processes, and certain types of growth‒collapse processes; thus, all of the processes mentioned above also satisfy similar factorization identities. In the Lévy case, our identities simplify to both the well-known Wiener‒Hopf factorization, and another interesting factorization of reflected Lévy processes starting at an arbitrary initial state. We also show how the ideas can be used to derive transforms for some well-known state-dependent/inhomogeneous birth‒death processes and diffusion processes.

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Brian H. Fralix. Johan S. H. van Leeuwaarden. Onno J. Boxma. "Factorization identities for reflected processes, with applications." J. Appl. Probab. 50 (3) 632 - 653, September 2013. https://doi.org/10.1239/jap/1378401227

Information

Published: September 2013
First available in Project Euclid: 5 September 2013

zbMATH: 1284.60161
MathSciNet: MR3102506
Digital Object Identifier: 10.1239/jap/1378401227

Subjects:
Primary: 60G50, 60G51, 60G55, 60K25

Rights: Copyright © 2013 Applied Probability Trust

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Vol.50 • No. 3 • September 2013
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