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Periodic queues in heavy traffic

Published online by Cambridge University Press:  01 July 2016

G. I. Falin
G. I. Falin*
Affiliation:
Moscow State University
*
∗ Postal address: Department of Probability, Mechanics and Mathematics Faculty, Moscow State University, Moscow 119899, USSR.
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Abstract

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An analytic approach to the diffusion approximation in queueing due to Burman (1979) is applied to the M(t)/G/1/∞ queueing system with periodic Poisson arrivals. We show that under heavy traffic the virtual waiting time process can be approximated by a certain Wiener process with reflecting barrier at 0.

Keywords

POISSON ARRIVALSDIFFUSION APPROXIMATION

Information

Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 21 , Issue 2 , June 1989, pp. 485 - 487
Copyright
Copyright © Applied Probability Trust 1989 

References

[1] Burman, D. Y. (1979) An Analytic Approach to Diffusion Approximation in Queueing. Ph.D. thesis, Department of Applied Mathematics, Courant Instutute of Mathematics, New York University.Google Scholar
[2] Ethier, S. and Kurtz, T. (1986) Markov Processes: Characterization and Convergence. Wiley, New York.CrossRefGoogle Scholar