Hostname: page-component-5447f9dfdb-lxcff Total loading time: 0 Render date: 2025-07-30T03:34:48.096Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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.

Information

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

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