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Identifiability in GI/G/k queues

Published online by Cambridge University Press:  14 July 2016

Sheldon M. Ross
Sheldon M. Ross*
Affiliation:
University of California, Berkeley
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Extract

Consider a queueing system in which customers arrive in accordance with a renewal process having an interarrival distribution F, and in which the service times of customers are independent and have distribution G. Moreover, suppose that there are k (k ≦ ∞) servers and that an arriving customer is immediately served if he finds one of the servers free, and if not then he joins the queue.

Type
Short Communications
Information
Journal of Applied Probability , Volume 7 , Issue 3 , December 1970 , pp. 776 - 780
Copyright
Copyright © Applied Probability Trust 1970 

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References

[1] Brown, M. (1969) An M/G/∞ estimation problem. Ann. Math. Statist. To appear.Google Scholar
[2] Cox, D. R. (1965) Some problems of statistical analysis connected with congestion. Proceedings of the Symposium on Congestion Theory. University of North Carolina Press, Chapel Hill.Google Scholar
[3] Kendall, D. G. and Lewis, T. (1965) On the structural information contained in the output of GI/G/8. Z. Wahrscheinlichkeitsth. 4, 144–148.Google Scholar
[4] Kiefer, J. and Wolfowitz, J. (1955) On the theory of queues with many servers. Trans. Amer. Math. Soc. 78, 1–18.Google Scholar
[5] Kiefer, J. and Wolfowitz, J. (1956) On the characteristics of the general queueing process, with applications to random walk. Ann. Math. Statist. 27, 147–161.Google Scholar