The G/M/m queue with finite waiting room
- 1 March 1975
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 12 (04) , 779-792
- https://doi.org/10.1017/s0021900200048737
Abstract
The G/M/m queue with only s waiting places is studied. We start by studying the joint distribution of the number of customers present at time t and the time elapsing until the next arrival after t. This gives the asymptotic distribution of the number of customers at the moment of an arrival and at an arbitrary moment. Then waiting time and virtual waiting time distributions are easily obtained. For the G/M/1 queue also the transient solution is given. Finally the case s = ∞ is considered.Keywords
This publication has 2 references indexed in Scilit:
- On the many server queue with exponential service timesAdvances in Applied Probability, 1973
- On the Waiting Time in the Queuing System GI/G/1The Annals of Mathematical Statistics, 1970