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The dependence of sojourn times on service times in tandem queues

Published online by Cambridge University Press:  14 July 2016

Xi-Ren Cao
Xi-Ren Cao*
Affiliation:
Harvard University
*
∗Postal address: Division of Applied Sciences, Harvard University, Pierce Hall, Cambridge, MA 02138, USA.
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Abstract

In this paper we study a series of servers with exponentially distributed service times. We find that the sojourn time of a customer at any server depends on the customer's past history only through the customer's interarrival time to that server. A method of calculating the conditional probabilities of sojourn times is developed.

Keywords

MARKOV RENEWAL PROCESSREVERSIBILITY
Type
Short Communications
Information
Journal of Applied Probability , Volume 21 , Issue 3 , September 1984 , pp. 661 - 667
Copyright
Copyright © Applied Probability Trust 1984 

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Footnotes

Research supported by National Science Foundation Grant ECS 82–13680, and by U.S. Office of Naval Research Contract N00014-79-C-0776.

References

Disney, R. L. (1982) Sojourn times in queueing networks — an unsolved problem. Proc. 1982 IEEE Internat. Large Scale Systems Symp., Virginia Beach, 11–13 October.Google Scholar
Disney, R. L., Mcnickle, D. C. and Simon, B. (1980) The M/G/1 queue with instantaneous Bernoulli feedback. Naval Res. Logist. Quart. 27, 635–644.Google Scholar
Kelly, F. P. (1979) Reversibility and Stochastic Networks. Wiley, New York.Google Scholar
Lemoine, A. J. (1978) Networks of queues — a survey of equilibrium analysis. Management Sci. 24, 464–481.Google Scholar
Lemoine, A. J. (1979) On total sojourn times in networks of queues. Management Sci. 25, 1034–1035.CrossRefGoogle Scholar
Melamed, B. (1982) Sojourn times in queueing networks. Math. Operat. Res. 7, 223–244.Google Scholar
Mitrani, I. (1979) A critical note on a result by Lemoine. Management Sci. 25, 1026–1027.Google Scholar
Reich, E. (1963) Note on queues in tandem. Ann. Math. Statist. 34, 338–341.CrossRefGoogle Scholar
Simon, B. and Foley, R. D. (1979) Some results on sojourn time in acyclic Jackson networks. Management Sci. 25, 1027–1034.Google Scholar
Walrand, J. and Varaiya, P. (1980) Sojourn times and the overtaking condition in Jacksonian networks. Adv. Appl. Prob. 12, 1000–1018.Google Scholar