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Heavy traffic results for single-server queues with dependent (EARMA) service and interarrival times

Published online by Cambridge University Press:  01 July 2016

Patricia A. Jacobs
Patricia A. Jacobs*
Affiliation:
Naval Postgraduate School, Monterey, California
*
∗Postal address: Department of Operations Research, Naval Postgraduate School, Monterey, CA 93940, U.S.A.
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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

HEAVY TRAFFIC RESULTSCORRELATED INTERARRIVAL AND SERVICE TIMESMULTIVARIATE EXPONENTIAL RANDOM VARIABLESWEAK CONVERGENCEARMA CORRELATED EXPONENTIAL SEQUENCES
Type
Research Article
Information
Advances in Applied Probability , Volume 12 , Issue 2 , June 1980 , pp. 517 - 529
Copyright
Copyright © Applied Probability Trust 1980 

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Footnotes

Support from NSF grants ENG-77-09020 and ENG-79-01438 and ONR contract NR-42-284 is gratefully acknowledged.

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