Heavy traffic results for single-server queues with dependent (EARMA) service and interarrival times
- 1 June 1980
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 12 (2) , 517-529
- https://doi.org/10.2307/1426610
Abstract
Models are given for sequences of correlated exponential interarrival and service times for a single-server queue. These multivariate exponential models are formed as probabilistic linear combinations of sequences of independent exponential random variables and are easy to generate on a computer. Limiting results for customer waiting time under heavy traffic conditions are obtained for these queues. Heavy traffic results are useful for analyzing the effect of correlated interarrival and service times in queues on such quantities as queue length and customer waiting time. They can also be used to check simulation results.Keywords
This publication has 6 references indexed in Scilit:
- A cyclic queueing network with dependent exponential service timesJournal of Applied Probability, 1978
- A mixed autoregressive-moving average exponential sequence and point process (EARMA 1,1)Advances in Applied Probability, 1977
- Weak convergence of probability measures and random functions in the function space D[0,∞)Journal of Applied Probability, 1973
- Markov Processes. Structure and Asymptotic BehaviorPublished by Springer Nature ,1971
- The stability of a queue with non-independent inter-arrival and service timesMathematical Proceedings of the Cambridge Philosophical Society, 1962
- On Queues in Heavy TrafficJournal of the Royal Statistical Society Series B: Statistical Methodology, 1962