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Stochastic storage networks: stationarity and the feedforward case

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  14 July 2016

Offer Kella
Offer Kella*
Affiliation:
The Hebrew University of Jerusalem
*
∗Postal address: Department of Statistics, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem 91905, Israel. Email: mskella@olive.mscc.huji.ac.il
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Abstract

We show that for a certain storage network the backward content process is increasing, and when the net input process has stationary increments then, under natural stability conditions, the content process has a stationary version under which the cumulative lost capacities have stationary increments. Moreover, for the feedforward case, we show that under some minimal conditions, two content processes with net input processes which differ only by initial conditions can be coupled in finite time and that the difference of two content processes vanishes in the limit if the difference of the net input processes monotonically approaches a constant. As a consequence, it is shown that for the natural stability conditions, when the net input process has stationary increments, the distribution of the content process converges in total variation to a proper limit, independent of initial conditions.

Keywords

STABILITYFLUID NETWORKSSTORAGE NETWORKSREFLECTED PROCESSES

MSC classification

Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.) 90B05: Inventory, storage, reservoirs 90B15: Network models, stochastic
Type
Research Article
Information
Journal of Applied Probability , Volume 34 , Issue 2 , June 1997 , pp. 498 - 507
Copyright
Copyright © Applied Probability Trust 1997 

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Footnotes

Supported in part by grant 92-00035 from the United States Israel Binational Science Foundation.

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