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A note on networks of infinite-server queues

Published online by Cambridge University Press:  14 July 2016

J. Michael Harrison  and
Austin J. Lemoine
J. Michael Harrison*
Affiliation:
Stanford University
Austin J. Lemoine*
Affiliation:
Systems Control, Inc.
*
∗Postal address: Graduate School of Business, Stanford University, Stanford, CA 94305, U.S.A.
∗∗Postal address: Systems Control, Inc., 1801 Page Mill Road, Palo Alto, CA 94304, U.S.A.
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Abstract

The subject of this paper is networks of queues with an infinite number of servers at each node in the system. Our purpose is to point out that independent motions of customers in the system, which are characteristic of infinite-server networks, lead in a simple way to time-dependent distributions of state, and thence to steady-state distributions; moreover, these steady-state distributions often exhibit an invariance with regard to distributions of service in the network. We consider closed systems in which a fixed and finite number of customers circulate through the network and no external arrivals or departures are permitted, and open systems in which customers originate from an external source according to a Poisson process, possibly non-homogeneous, and each customer eventually leaves the system.

Keywords

NETWORKS OF QUEUESINFINITE-SERVER STATIONSCLOSED SYSTEMOPEN SYSTEMMIGRATION PROCESSESCOLONIESREGENERATIVE ROUTINGPOISSON PROCESSORDER-STATISTIC PROPERTYINVARIANCE PROPERTY OF STEADY-STATE DISTRIBUTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 18 , Issue 2 , June 1981 , pp. 561 - 567
Copyright
Copyright © Applied Probability Trust 

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Footnotes

This work was sponsored in part by the National Science Foundation under Grant No. ENG-7824568.

References

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