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The transient behaviour of the queueing system Gi/M/1

Published online by Cambridge University Press:  09 April 2009

P. J. Brockwell
P. J. Brockwell
Affiliation:
University of Melbourne.
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Summary

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We consider a single server queue for which the interarrival times are identically and independently distributed with distribution function A(x) and whose service times are distributed independently of each other and of the interarrival times with distribution function B(x) = 1 − e−x, x ≧ 0. We suppose that the system starts from emptiness and use the results of P. D. Finch [2] to derive an explicit expression for qnj, the probability that the (n + 1)th arrival finds more than j customers in the system. The special cases M/M/1 and D/M/1 are considerend and it is shown in the general case that qnj is a partial sum of the usual Lagrange series for the limiting probability .

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 3 , Issue 2 , May 1963 , pp. 249 - 256
Copyright
Copyright © Australian Mathematical Society 1963

References

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