The transient behaviour of the queueing system Gi/M/1
- 1 May 1963
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society
- Vol. 3 (2), 249-256
- https://doi.org/10.1017/s1446788700027993
Abstract
SUMMARY: 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 .Keywords
This publication has 3 references indexed in Scilit:
- On the busy period in the queueing system GI/G/1Journal of the Australian Mathematical Society, 1961
- On the Transient Behaviour of a Simple QueueJournal of the Royal Statistical Society Series B: Statistical Methodology, 1960
- Transient Behavior of Single-Server Queuing Processes with Recurrent Input and Exponentially Distributed Service TimesOperations Research, 1960