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Technical Note—A Transient Solution to the Multistage Poisson Queueing System with Infinite Servers

Author

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  • R. R. P. Jackson

    (Department of Health and Social Security, London, England)

  • P. Aspden

    (Department of Health and Social Security, London, England)

Abstract

This paper gives an alternative method of deriving the time dependent solution of a multistage nonqueueing process, with random arrivals into the first stage of the system, sufficient servers at each stage and exponential service time distributions. In the standard notation, the system is a finite number of M / M /∞ queues in series (tandem). This method has the advantage over previous methods of being able to solve the case when any of the stage average service times are equal. The solution was obtained during a project concerned with developing a mathematical model of Acute Myeloid Leukemia patient progress.

Suggested Citation

  • R. R. P. Jackson & P. Aspden, 1980. "Technical Note—A Transient Solution to the Multistage Poisson Queueing System with Infinite Servers," Operations Research, INFORMS, vol. 28(3-part-i), pages 618-622, June.
    • Handle: RePEc:inm:oropre:v:28:y:1980:i:3-part-i:p:618-622
    DOI: 10.1287/opre.28.3.618
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    Cited by:

    1. Ying Shi & Xin Li & Ping Fan, 2016. "Optimization of an M/M/∞ Queueing System with Free Experience Service," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(06), pages 1-17, December.
    2. Qihui Bu, 2024. "Transient Analysis for a Queuing System with Impatient Customers and Its Applications to the Pricing Strategy of a Video Website," Mathematics, MDPI, vol. 12(13), pages 1-14, June.

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