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Sojourn times and the overtaking condition in Jacksonian networks

Published online by Cambridge University Press:  01 July 2016

J. Walrand  and
P. Varaiya
J. Walrand*
Affiliation:
University of California, Berkeley
P. Varaiya*
Affiliation:
University of California, Berkeley
*
∗Current address: School of Electrical Engineering, Cornell University, Ithaca, NY 14853.
∗∗Postal address: Electronics Research Laboratory, University of California, Berkeley, CA 94720, U.S.A.
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Abstract

Consider an open multiclass Jacksonian network in equilibrium and a path such that a customer travelling along it cannot be overtaken directly by a subsequent arrival or by the effects of subsequent arrivals. Then the sojourn times of this customer in the nodes constituting the path are all mutually independent and so the total sojourn time is easily calculated. Two examples are given to suggest that the non-overtaking condition may be necessary to ensure independence when there is a single customer class.

Keywords

SOJOURN TIMESJACKSONIAN NETWORKSPASSAGE TIMES
Type
Research Article
Information
Advances in Applied Probability , Volume 12 , Issue 4 , December 1980 , pp. 1000 - 1018
Copyright
Copyright © Applied Probability Trust 1980 

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Footnotes

Research sponsored in part by the National Science Foundation Grant, Grant ENG76-16816 and the Miller Institute.

References

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