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A Sequence of Two Servers with No Intermediate Queue

Author

Listed:
  • B. Avi-Itzhak

    (Cornell University, Ithaca, New York)

  • M. Yadin

    (Technion, Israel Institute of Technology, Haifa, Israel)

Abstract

Customers arriving randomly are served by a queueing system consisting of a sequence of two service stations with infinite queue allowable before the first station and no queue allowable between the stations. The moment generating functions of the steady-state queueing times as well as the generating functions of the steady-state numbers of customers in the various parts of the system are obtained under assumptions of Poisson process of arrivals and arbitrarily distributed service times at both stations. The cases of regular and exponential service times are investigated in some more detail, and the results obtained are extended to include the queueing system with a sequence of two stations with a finite intermediate queue allowable between them, infinite queue allowed before the first station, Poisson process of arrivals and regular service times at both stations.

Suggested Citation

  • B. Avi-Itzhak & M. Yadin, 1965. "A Sequence of Two Servers with No Intermediate Queue," Management Science, INFORMS, vol. 11(5), pages 553-564, March.
    • Handle: RePEc:inm:ormnsc:v:11:y:1965:i:5:p:553-564
    DOI: 10.1287/mnsc.11.5.553
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    Cited by:

    1. Palmer, Geraint I. & Harper, Paul R. & Knight, Vincent A., 2018. "Modelling deadlock in open restricted queueing networks," European Journal of Operational Research, Elsevier, vol. 266(2), pages 609-621.
    2. Papadopoulos, H. T. & Heavey, C., 1996. "Queueing theory in manufacturing systems analysis and design: A classification of models for production and transfer lines," European Journal of Operational Research, Elsevier, vol. 92(1), pages 1-27, July.
    3. Yarmand, Mohammad H. & Down, Douglas G., 2013. "Server allocation for zero buffer tandem queues," European Journal of Operational Research, Elsevier, vol. 230(3), pages 596-603.
    4. A. Gómez‐Corral, 2004. "Sojourn times in a two‐stage queueing network with blocking," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(8), pages 1068-1089, December.
    5. Genji Yamazaki & Hirotaka Sakasegawa, 1975. "Properties of duality in tandem queueing systems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 27(1), pages 201-212, December.
    6. Noa Zychlinski & Avishai Mandelbaum & Petar Momčilović, 2018. "Time-varying tandem queues with blocking: modeling, analysis, and operational insights via fluid models with reflection," Queueing Systems: Theory and Applications, Springer, vol. 89(1), pages 15-47, June.
    7. Hirotaka Sakasegawa & Genji Yamazaki, 1977. "Inequalities and an approximation formula for the mean delay time in tandem queueing systems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 29(1), pages 445-466, December.

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