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Finite Queues in Series with Exponential or Erlang Service Times—A Numerical Approach

Author

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  • Frederick S. Hillier

    (Stanford University, Stanford, California)

  • Ronald W. Boling

    (University of Tennessee, Knoxville, Tennessee)

Abstract

This paper considers a queuing system consisting of N service channels in series where each channel has an exponential or Erlang holding time and (except for the first channel) a finite queue, and where the input process is such that the first queue is never empty. The measures considered are the steady-state mean output rate and mean number of customers in the system (excluding the first queue). First, a procedure is described, for obtaining these measures, that is relatively efficient computationally. Second, an exceptionally efficient procedure is developed for approximating the mean output rate for the case of exponential holding times. It is demonstrated that this procedure provides an excellent approximation for most cases and that it is computationally feasible for large problems. Third, extensive new numerical results are obtained.

Suggested Citation

  • Frederick S. Hillier & Ronald W. Boling, 1967. "Finite Queues in Series with Exponential or Erlang Service Times—A Numerical Approach," Operations Research, INFORMS, vol. 15(2), pages 286-303, April.
    • Handle: RePEc:inm:oropre:v:15:y:1967:i:2:p:286-303
    DOI: 10.1287/opre.15.2.286
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    Cited by:

    1. Jean-Sébastien Tancrez & Philippe Chevalier & Pierre Semal, 2011. "Probability masses fitting in the analysis of manufacturing flow lines," Annals of Operations Research, Springer, vol. 182(1), pages 163-191, January.
    2. Konstantinos S. Boulas & Georgios D. Dounias & Chrissoleon T. Papadopoulos, 2023. "A hybrid evolutionary algorithm approach for estimating the throughput of short reliable approximately balanced production lines," Journal of Intelligent Manufacturing, Springer, vol. 34(2), pages 823-852, February.
    3. Federica Costa & Matthias Thürer & Alberto Portioli-Staudacher, 2023. "Heterogeneous worker multi-functionality and efficiency in dual resource constrained manufacturing lines: an assessment by simulation," Operations Management Research, Springer, vol. 16(3), pages 1476-1489, September.
    4. 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.
    5. Mohammadi Bidhandi, Hadi & Patrick, Jonathan & Noghani, Pedram & Varshoei, Peyman, 2019. "Capacity planning for a network of community health services," European Journal of Operational Research, Elsevier, vol. 275(1), pages 266-279.
    6. Michael Manitz, 2015. "Analysis of assembly/disassembly queueing networks with blocking after service and general service times," Annals of Operations Research, Springer, vol. 226(1), pages 417-441, March.
    7. Wu, Xiaodan & Li, Juan & Chu, Chao-Hsien, 2019. "Modeling multi-stage healthcare systems with service interactions under blocking for bed allocation," European Journal of Operational Research, Elsevier, vol. 278(3), pages 927-941.
    8. Noa Zychlinski & Avishai Mandelbaum & Petar Momčilović & Izack Cohen, 2020. "Bed Blocking in Hospitals Due to Scarce Capacity in Geriatric Institutions—Cost Minimization via Fluid Models," Manufacturing & Service Operations Management, INFORMS, vol. 22(2), pages 396-411, March.
    9. Saied Samiedaluie & Vedat Verter, 2019. "The impact of specialization of hospitals on patient access to care; a queuing analysis with an application to a neurological hospital," Health Care Management Science, Springer, vol. 22(4), pages 709-726, December.
    10. Beixin Xia & Binghai Zhou & Ci Chen & Lifeng Xi, 2016. "A generalized-exponential decomposition method for the analysis of inhomogeneous assembly/disassembly systems with unreliable machines and finite buffers," Journal of Intelligent Manufacturing, Springer, vol. 27(4), pages 765-779, August.
    11. Sachs, F.E. & Helber, S. & Kiesmüller, G.P., 2022. "Evaluation of Unreliable Flow Lines with Limited Buffer Capacities and Spare Part Provisioning," European Journal of Operational Research, Elsevier, vol. 302(2), pages 544-559.

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