Some general results for many server queues
- 1 April 1973
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 5 (01) , 153-169
- https://doi.org/10.1017/s0001867800039008
Abstract
Pollaczek's theory for the many server queue is generalized and extended. Pollaczek (1961) found the distribution of the actual waiting times in the model G/G/s as a solution of a set of integral equations. We give a somewhat more general set of integral equations from which the joint distribution of the actual waiting time and some other random variables may be found. With this joint distribution we can obtain distributions of a number of characteristic quantities, such as the virtual waiting time, the queue length, the number of busy servers, the busy period and the busy cycle. For a wide class of many server queues the formal expressions may lead to explicit results.Keywords
This publication has 3 references indexed in Scilit:
- On the many server queue with exponential service timesAdvances in Applied Probability, 1973
- On the expected number of crossings of a level in certain stochastic processesJournal of Applied Probability, 1970
- On the theory of queues with many serversTransactions of the American Mathematical Society, 1955