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Numerical Solutions of the Waiting Time Distribution and Idle Time Distribution of the Arithmetic GI/G/1 Queue

Author

Listed:
  • Winfried K. Grassmann

    (University of Saskatchewan, Saskatoon, Canada)

  • Joti L. Jain

    (University of Delhi, Delhi, India)

Abstract

In this paper, we present an efficient numerical method for calculating the waiting time and idle time distributions of the arithmetic GI/G/1 queue. Our method is based on the Wiener-Hopf factorization, which is briefly reviewed. Compared to the related methods suggested in the literature, our method seems to perform very well, and it is often faster by several orders of magnitude. A number of numerical examples conclude the paper.

Suggested Citation

  • Winfried K. Grassmann & Joti L. Jain, 1989. "Numerical Solutions of the Waiting Time Distribution and Idle Time Distribution of the Arithmetic GI/G/1 Queue," Operations Research, INFORMS, vol. 37(1), pages 141-150, February.
    • Handle: RePEc:inm:oropre:v:37:y:1989:i:1:p:141-150
    DOI: 10.1287/opre.37.1.141
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    Cited by:

    1. Martin Epp & Simon Wiedemann & Kai Furmans, 2017. "A discrete-time queueing network approach to performance evaluation of autonomous vehicle storage and retrieval systems," International Journal of Production Research, Taylor & Francis Journals, vol. 55(4), pages 960-978, February.
    2. Phelan, Carolyn E. & Marazzina, Daniele & Fusai, Gianluca & Germano, Guido, 2018. "Fluctuation identities with continuous monitoring and their application to the pricing of barrier options," European Journal of Operational Research, Elsevier, vol. 271(1), pages 210-223.
    3. Attahiru Alfa, 2002. "Discrete time queues and matrix-analytic methods," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 147-185, December.
    4. Carolyn E. Phelan & Daniele Marazzina & Gianluca Fusai & Guido Germano, 2017. "Fluctuation identities with continuous monitoring and their application to price barrier options," Papers 1712.00077, arXiv.org.
    5. Justus Schwarz & Judith Stoll née Matzka & Eda Özden, 2015. "A general model for batch building processes under the timeout and capacity rules," Annals of Operations Research, Springer, vol. 231(1), pages 5-31, August.
    6. Tang, Dong, 2011. "Managing finished-goods inventory under capacitated delayed differentiation," Omega, Elsevier, vol. 39(5), pages 481-492, October.
    7. Jain, Apurva, 2007. "Value of capacity pooling in supply chains with heterogeneous customers," European Journal of Operational Research, Elsevier, vol. 177(1), pages 239-260, February.
    8. Schleyer, Marc & Gue, Kevin, 2012. "Throughput time distribution analysis for a one-block warehouse," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(3), pages 652-666.

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