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Stability and structural properties of stochastic storage networks

Part of: Special processes Stochastic processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Offer Kella  and
Ward Whitt
Offer Kella*
Affiliation:
The Hebrew University of Jerusalem
Ward Whitt*
Affiliation:
AT&T Laboratories
*
∗Postal address: Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem 91905, Israel. email:kella@olive.mscc.huji.ac.il
∗∗Postal address: AT&T Laboratories, Room 2C-178, 600 Mountain Avenue, Murray Hill, NJ 07974–0636, USA. email:wow@research.att.com
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Abstract

We establish stability, monotonicity, concavity and subadditivity properties for open stochastic storage networks in which the driving process has stationary increments. A principal example is a stochastic fluid network in which the external inputs are random but all internal flows are deterministic. For the general model, the multi-dimensional content process is tight under the natural stability condition. The multi-dimensional content process is also stochastically increasing when the process starts at the origin, implying convergence to a proper limit under the natural stability condition. In addition, the content process is monotone in its initial conditions. Hence, when any content process with non-zero initial conditions hits the origin, it couples with the content process starting at the origin. However, in general, a tight content process need not hit the origin.

Keywords

STABILITYFLUID NETWORKSSTATIONARY INCREMENTSLEVY PROCESSREFLECTED PROCESSSTOCHASTICALLY INCREASINGTIGHTNESSSTOCHASTIC ORDERBOUNDS

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60G10: Stationary processes 90B22: Queues and service
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 4 , December 1996 , pp. 1169 - 1180
Copyright
Copyright © Applied Probability Trust 1996 

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Footnotes

This work was partially supported by Grant No. 92–00035 from the United States Israel Binational Science Foundation.

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