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Sojourn Times and the Overtaking Condition in Jacksonian Networks
J. Walrand and P. Varaiya
Advances in Applied Probability
Vol. 12, No. 4 (Dec., 1980), pp. 1000-1018
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/1426753
Page Count: 19
You can always find the topics here!Topics: Customers, Poisson process, Markov processes, Stopping distances, Mathematics, Traffic, Random variables, Logical proofs
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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.
Advances in Applied Probability © 1980 Applied Probability Trust