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The non-ergodic Jackson network

Published online by Cambridge University Press:  14 July 2016

Jonathan B. Goodman  and
William A. Massey
Jonathan B. Goodman*
Affiliation:
Courant Institute of Mathematical Sciences
William A. Massey*
Affiliation:
AT&T Bell Laboratories
*
∗Postal address: Courant Institute of Mathematical Sciences, New York, NY 10012, USA.
∗∗Postal address: AT&T Bell Laboratories, 600 Mountain Avenue, Murray Hill, NJ 07974, USA.
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Abstract

We generalize Jackson's theorem to the non-ergodic case. Here, despite the fact that the entire Jackson network will not achieve steady state, it is still possible to determine the maximal subnetwork that does. We do so by formulating and algorithmically solving a new non-linear throughput equation. These results, together with the ergodic results and the ones for closed networks, completely characterize the large-time behavior of any Jackson network.

Keywords

NETWORKS OF QUEUESASYMPTOTIC BEHAVIOURSTOCHASTIC DOMINANCENEW THROUGHPUT EQUATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 21 , Issue 4 , December 1984 , pp. 860 - 869
Copyright
Copyright © Applied Probability Trust 1984 

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