An invariant distribution for the G/G/1 queueing operator
- 1 March 1990
- journal article
- letter
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 22 (01) , 254-256
- https://doi.org/10.1017/s0001867800019467
Abstract
We consider the G/G/1 queue as an operator that maps inter-arrival times to inter-departure times of points, given the service times. For arbitrarily fixed statistics of service times, we are interested in the existence of distributions of inter-arrival times that induce identical distributions on the inter-departure times. In this note we prove, by construction, the existence of one of such distribution.Keywords
This publication has 1 reference indexed in Scilit:
- The stability of a queue with non-independent inter-arrival and service timesMathematical Proceedings of the Cambridge Philosophical Society, 1962