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Sequential Arrays of Waiting Lines

Author

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  • Gordon C. Hunt

    (Massachusetts Institute of Technology, Cambridge, Massachusetts)

Abstract

The problem considered in this paper is that in which a sequence of service operations must be performed on the units to be serviced. Poisson arrivals and exponential service times are assumed. Four particular cases of service facilities in series are treated, involving infinite storage space between stages, no storage space between stages, finite storage space between stages, and the case of the unpaced belt-production line. A comparison is given for two stages, and the maximum possible utilization is obtained for all cases discussed.

Suggested Citation

  • Gordon C. Hunt, 1956. "Sequential Arrays of Waiting Lines," Operations Research, INFORMS, vol. 4(6), pages 674-683, December.
    • Handle: RePEc:inm:oropre:v:4:y:1956:i:6:p:674-683
    DOI: 10.1287/opre.4.6.674
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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Stephen G. Powell & Kenneth L. Schultz, 2004. "Throughput in Serial Lines with State-Dependent Behavior," Management Science, INFORMS, vol. 50(8), pages 1095-1105, August.
    6. 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.
    7. Papadopoulos, Hrissoleon T., 1996. "An analytic formula for the mean throughput of K-station production lines with no intermediate buffers," European Journal of Operational Research, Elsevier, vol. 91(3), pages 481-494, June.
    8. 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.
    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. Khalil, T.M. & Valisalo, P.E. & Copsey, A., 1973. "Hybrid computer solution of queueing systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 15(2), pages 49-53.
    11. 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.
    12. Lutz, Christian M. & Roscoe Davis, K. & Sun, Minghe, 1998. "Determining buffer location and size in production lines using tabu search," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 301-316, April.
    13. Kalir, Adar A. & Sarin, Subhash C., 2009. "A method for reducing inter-departure time variability in serial production lines," International Journal of Production Economics, Elsevier, vol. 120(2), pages 340-347, August.
    14. Baker, Kenneth R. & Powell, Stephen G., 1995. "A predictive model for the throughput of simple assembly systems," European Journal of Operational Research, Elsevier, vol. 81(2), pages 336-345, March.

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