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On the independence of sojourn times in tandem queues

Published online by Cambridge University Press:  01 July 2016

Thomas M. Chen
Thomas M. Chen*
Affiliation:
University of California, Berkeley
*
∗Postal address: Department of EECS, University of California, Berkeley, CA 94720, USA.
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Abstract

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Reich (1957) proved that the sojourn times in two tandem queues are independent when the first queue is M/M /1 and the second has exponential service times. When service times in the first queue are not exponential, it has been generally expected that the sojourn times are not independent. A proof for the case of deterministic service times in the first queue is offered here.

Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 21 , Issue 2 , June 1989 , pp. 488 - 489
Copyright
Copyright © Applied Probability Trust 1989 

References

Gross, D. and Harris, C. (1974) Fundamentals of Queueing Theory. Wiley, New York.Google Scholar
Reich, E. (1957) Waiting times when queues are in tandem. Ann. Math. Statist. 28, 768–773.CrossRefGoogle Scholar