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

  • Patricia A. Jacobs (a1)

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.

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Corresponding author

Postal address: Department of Operations Research, Naval Postgraduate School, Monterey, CA 93940, U.S.A.

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

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References

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1. Billingsley, P. (1968) Convergence of Probability Measures. Wiley, New York.
2. Boonsong, P. (1978) A Simulation Study of a Class of First-Come First-Served Queues with earma Correlation Structure. , Naval Postgraduate School, Monterey, California.
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Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
  • URL: /core/journals/advances-in-applied-probability
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