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Characterization for the queueing system M/G/∞

Published online by Cambridge University Press:  24 October 2008

D. N. Shanbhag
D. N. Shanbhag
Affiliation:
Sheffield University
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Extract

Consider a queueing system M/G/s with the arrival intensity λ, the service time distribution function B(t) (B(0) < 1) having a finite mean and the waiting room size N ≤ ∞. If s < ∞ and N = ∞, we shall also assume that its relative traffic intensity is less than 1. Since the arrival process of this system is Poisson, it is immediate that in this case the distribution of the number of arrivals during an interval is infinitely divisible.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 74 , Issue 1 , July 1973 , pp. 141 - 143
Copyright
Copyright © Cambridge Philosophical Society 1973

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References

REFERENCES

(1)Burke, P. J.The output of a queueing system. Operations Res. 4 (1956), 699–704.CrossRefGoogle Scholar
(2)Daley, D. J.A bivariate Poisson queueing process that is not infinitely divisible. Proc. Cambridge Philos. Soc. 72 (1972), 449–450.CrossRefGoogle Scholar
(3)Feller, W.An introduction to probability theory and its applications, vol. I (Wiley and Sons, 1957).Google Scholar
(4)Mirasol, N. M.The output of an M/G/∞ queueing system is Poisson. Operations Res. 11 (1963), 282–284.CrossRefGoogle Scholar
(5)Shanbhag, D. N. and Tambouratzis, D. G.Erlang's formula of some results on the departure process of a loss system, to appear in J. Appl. Probability (1973).CrossRefGoogle Scholar