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Useful martingales for stochastic storage processes with Lévy input

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Offer Kella  and
Ward Whitt
Offer Kella
Affiliation:
Yale University
Ward Whitt*
Affiliation:
AT&T Bell Laboratories
*
∗∗Postal address: AT&T Bell Laboratories, Room 2C-178, 600 Mountain Avenue, Murray Hill, NJ 07974–0636, USA.
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Abstract

We apply the general theory of stochastic integration to identify a martingale associated with a Lévy process modified by the addition of a secondary process of bounded variation on every finite interval. This martingale can be applied to queues and related stochastic storage models driven by a Lévy process. For example, we have applied this martingale to derive the (non-product-form) steady-state distribution of a two-node tandem storage network with Lévy input and deterministic linear fluid flow out of the nodes.

Keywords

STOCHASTIC INTEGRATIONQUEUEING THEORYPOLLACZEK–KHINCHINE FORMULASTORAGE MODELS

MSC classification

Secondary: 60K25: Queueing theory 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 29 , Issue 2 , June 1992 , pp. 396 - 403
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

∗

Present address: Department of Statistics, The Hebrew University, Mount Scopus, Jerusalem 91905, Israel.

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