On the many server queue with exponential service times
- 1 April 1973
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 5 (01) , 170-182
- https://doi.org/10.1017/s000186780003901x
Abstract
The general theory for the many server queue due to Pollaczek (1961) and generalized by the author (de Smit (1973)) is applied to the system with exponential service times. In this way many explicit results are obtained for the distributions of characteristic quantities, such as the actual waiting time, the virtual waiting time, the queue length, the number of busy servers, the busy period and the busy cycle. Most of these results are new, even for the special case of Poisson arrivals.Keywords
This publication has 4 references indexed in Scilit:
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- The queue gi/m/2 with service rate depending on the number of busy serversAnnals of the Institute of Statistical Mathematics, 1966
- On a queueing problem concering telephon trafficActa Mathematica Hungarica, 1957
- Stochastic Processes Occurring in the Theory of Queues and their Analysis by the Method of the Imbedded Markov ChainThe Annals of Mathematical Statistics, 1953