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Approximate Formula of Delay-Time Variance in Renewal-Input General-Service-Time Single-Server Queueing System

In: Operations Research Proceedings 2011

Author

Listed:
  • Yoshitaka Takahashi

    (Waseda University)

  • Yoshiaki Shikata

    (Shobi University)

  • Andreas Frey

    (University of Applied Sciences Osnabrueck)

Abstract

Approximate formulas of the variance of the waiting-time (also called as delay-time variance) in a renewal-input general-service-time single-server (GI/GI/1) system play an important role in practical applications of the queueing theory. However, there exists almost no literature on the approximate formulas of the delay-time variance in the GI/GI/1 system. The goal of this paper is to present an approximate formula for the delay-time variance. Our approach is based on the combination of a higher-moment relationship between the unfinished work and the waiting time, and the diffusion process approximation for the unfinished work. To derive the former relationship, we apply Miyazawa’s rate conservation law for the stationary point process. Our approximate formula is shown to converge to the exact result for the Poisson-input system as traffic intensity goes to the unity. The accuracy of our approximation is validated by simulation results.

Suggested Citation

  • Yoshitaka Takahashi & Yoshiaki Shikata & Andreas Frey, 2012. "Approximate Formula of Delay-Time Variance in Renewal-Input General-Service-Time Single-Server Queueing System," Operations Research Proceedings, in: Diethard Klatte & Hans-Jakob Lüthi & Karl Schmedders (ed.), Operations Research Proceedings 2011, edition 127, pages 503-508, Springer.
    • Handle: RePEc:spr:oprchp:978-3-642-29210-1_80
    DOI: 10.1007/978-3-642-29210-1_80
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