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Jackson networks with unlimited supply of work

Part of: Special processes Operations research and management science Computer system organization

Published online by Cambridge University Press:  14 July 2016

Gideon Weiss
Gideon Weiss*
Affiliation:
The University of Haifa
*
∗Postal address: Department of Statistics, The University of Haifa, Mount Carmel, 31905, Israel. Email address: [email protected]
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Abstract

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We consider a Jackson network in which some of the nodes have an infinite supply of work: when all the customers queued at such a node have departed, the node will process a customer from this supply. Such nodes will be processing jobs all the time, so they will be fully utilized and experience a traffic intensity of 1. We calculate flow rates for such networks, obtain conditions for stability, and investigate the stationary distributions. Standard nodes in this network continue to have product-form distributions, while nodes with an infinite supply of work have geometric marginal distributions and Poisson inflows and outflows, but their joint distribution is not of product form.

Keywords

QueueJackson networkinfinite virtual buffer

MSC classification

Primary: 60K25: Queueing theory 90B22: Queues and service 68M20: Performance evaluation; queueing; scheduling 90B15: Network models, stochastic
Type
Short Communications
Information
Journal of Applied Probability , Volume 42 , Issue 3 , September 2005 , pp. 879 - 882
Copyright
© Applied Probability Trust 2005 

Footnotes

Supported in part by Israel Science Foundation grant number 249/02.

References

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