An invariance principle for queues in heavy traffic
- 1 January 1977
- journal article
- research article
- Published by Taylor & Francis in Mathematische Operationsforschung und Statistik. Series Optimization
- Vol. 8 (4) , 591-631
- https://doi.org/10.1080/02331937708842454
Abstract
The paper deals with an invariance principle for queues in heavy traffic, The paper contains 5 sections. In the first one we give a description of queueing systems. Besides of well known results in section 1 there is a new one concerning the behaviour of the actual and virtual waiting time in heavy traffic situation. The applications to results of sections 2 (Functional limit theorems) and 3 (Invariance principle) are given in section 4.Keywords
This publication has 8 references indexed in Scilit:
- Dependent Central Limit Theorems and Invariance PrinciplesThe Annals of 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
- Martingale Central Limit TheoremsThe Annals of Mathematical Statistics, 1971
- The virtual waiting time of theGI/G/1 queue in heavy trafficAdvances in Applied Probability, 1971
- 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
- Some Problems in the Theory of DamsJournal of the Royal Statistical Society Series B: Statistical Methodology, 1957