The suprema of the actual and virtual waiting times during a busy cycle of the Km/Kn/1 queueing system
- 1 August 1972
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 4 (2) , 339-356
- https://doi.org/10.2307/1426003
Abstract
For the single server queueing system, whose distributions of service and inter-arrival times have rational Laplace-Stieltjes transforms, limit theorems are derived for the supremum of the virtual waiting time during k successive busy cycles for k→∞. Similarly, for the supremum of the actual waiting times of all customers arriving in k successive busy cycles. Only the cases with the load of the system less than one and equal to one are considered. The limit distributions are extreme value distributions. The results are obtained by first deriving a number of asymptotic expressions for the quantities which govern the analytic description of the system Km/Kn/1. Using these asymptotic relations limit theorems for entrance times can also be obtained, a few examples are given.Keywords
This publication has 4 references indexed in Scilit:
- Extreme Values in the GI/G/1 QueueThe Annals of Mathematical Statistics, 1972
- Multiple channel queues in heavy traffic. IAdvances in Applied Probability, 1970
- Multiple channel queues in heavy traffic. IAdvances in Applied Probability, 1970
- Single server queues with restricted accessibilityJournal of Engineering Mathematics, 1969