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On sojourn time in Jackson networks of queues

Published online by Cambridge University Press:  14 July 2016

Austin J. Lemoine
Austin J. Lemoine*
Affiliation:
Ford Aerospace and Communications Corporation
*
∗Postal address: Ford Aerospace and Communications Corporation, Western Development Laboratories Division, 3939 Fabian Way, Palo Alto, CA 94303, USA.
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Abstract

This paper is about representations for equilibrium sojourn time distributions in Jackson networks of queues. For a network with N single-server nodes let hi be the Laplace transform of the residual system sojourn time for a customer ‘arriving' to node i, ‘arrival' meaning external input or internal transfer. The transforms {hi : i = 1, ···, N} are shown to satisfy a system of equations we call the network flow equations. These equations lead to a general recursive representation for the higher moments of the sojourn time variables {Ti : i = 1, ···, N}. This recursion is discussed and then, by way of illustration, applied to the single-server Markovian queue with feedback.

Keywords

EQUILIBRIUM DISTRIBUTIONSNETWORK FLOW EQUATIONSRECURSIVE REPRESENTATIONHIGHER MOMENTSMARTINGALE
Type
Research Papers
Information
Journal of Applied Probability , Volume 24 , Issue 2 , June 1987 , pp. 495 - 510
Copyright
Copyright © Applied Probability Trust 1987 

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Footnotes

The partial support of Army Research Office Contract DAAG29-82-K-0151 and Air Force Office of Scientific Research Contract F49620-86-C-0022 is gratefully acknowledged.

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