Exponential approximation of waiting time and queue size for queues in heavy traffic
- 1 March 1990
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 22 (1) , 230-240
- https://doi.org/10.2307/1427606
Abstract
An exponential approximation for the stationary waiting time distribution and the stationary queue size distribution for single-server queues in heavy traffic is given for a wide class of queues. This class contains for example not only queues for which the generic sequence, i.e. the sequence of service times and interarrival times, is stationary but also such queues for which the generic sequence is asymptotically stationary in some sense. The conditions ensuring the exponential approximation of the characteristics considered in heavy traffic are expressed in terms of the invariance principle for the stationary representation of the generic sequence and its first two moments.Keywords
This publication has 9 references indexed in Scilit:
- Stationary representation of queues. IAdvances in Applied Probability, 1986
- Stationary representation of queues. IIAdvances in Applied Probability, 1986
- Heavy traffic theory for queues with several servers. IIJournal of Applied Probability, 1979
- On queues in discrete regenerative environments, with application to the second of two queues in seriesAdvances in Applied Probability, 1979
- Heavy traffic theory for queues with several servers. IJournal of Applied Probability, 1974
- Heavy Traffic Limit Theorems for Queues: A SurveyPublished by Springer Nature ,1974
- Weak convergence of probability measures and random functions in the function space D[0,∞)Journal of Applied Probability, 1973
- The stability of a queue with non-independent inter-arrival and service timesMathematical Proceedings of the Cambridge Philosophical Society, 1962
- The single server queue in heavy trafficMathematical Proceedings of the Cambridge Philosophical Society, 1961