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On Optimal Arrangement of Stations in a Tandem Queueing System with Blocking

Author

Listed:
  • Genji Yamazaki

    (Department of Engineering Management, Tokyo Metropolitan Institute of Technology, Hino City, Tokyo 191, Japan)

  • Hirotaka Sakasegawa

    (Institute of Socio-Economic Planning, University of Tsukuba, Tsukuba City, Ibaraki 305, Japan)

  • J. George Shanthikumar

    (Walter A. Haas School of Business, University of California, Berkeley, Berkeley, California 94720)

Abstract

We consider tandem queueing networks with no waiting spaces and address the issue of ordering the stations so that the throughput (i.e., the departure rate) is maximized. Based on some theoretical and extensive empirical results, we propose two rules for ordering the stations. The first rule recommends arranging the two worst stations (according to our ordering) to the first and last stages. Numerical results show that this rule almost always agrees with the optimal ordering of stations. In cases where this rule does not agree with the optimal ordering, numerical results show that this rule leads to station arrangements that are near optimal. In addition, numerical results also indicate that the first rule is the most important one to achieve a near optimal throughput. The second rule arranges the remaining stations according to the so-called "bowl phenomenon." Numerical results illustrate that an optimal arrangement of stations need not exhibit the "bowl phenomenon," but the differences in the throughput between the optimal and the one obtained by the second rule are always very small (less than 0.5%).

Suggested Citation

  • Genji Yamazaki & Hirotaka Sakasegawa & J. George Shanthikumar, 1992. "On Optimal Arrangement of Stations in a Tandem Queueing System with Blocking," Management Science, INFORMS, vol. 38(1), pages 137-153, January.
    • Handle: RePEc:inm:ormnsc:v:38:y:1992:i:1:p:137-153
    DOI: 10.1287/mnsc.38.1.137
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    Citations

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    Cited by:

    1. Sigrún Andradóttir & Hayriye Ayhan & Douglas G. Down, 2001. "Server Assignment Policies for Maximizing the Steady-State Throughput of Finite Queueing Systems," Management Science, INFORMS, vol. 47(10), pages 1421-1439, October.
    2. Simin Huang & Rajan Batta & Rakesh Nagi, 2005. "Distribution network design: Selection and sizing of congested connections," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(8), pages 701-712, December.
    3. Kirkavak, Nureddin & Dincer, Cemal, 1999. "The general behavior of pull production systems: The allocation problems," European Journal of Operational Research, Elsevier, vol. 119(2), pages 479-494, December.
    4. Hillier, Frederick S. & So, Kut C., 1996. "On the robustness of the bowl phenomenon," European Journal of Operational Research, Elsevier, vol. 89(3), pages 496-515, March.
    5. Benjamin Avi-Itzhak & Hanoch Levy, 2001. "Buffer Requirements and Server Ordering in a Tandem Queue with Correlated Service Times," Mathematics of Operations Research, INFORMS, vol. 26(2), pages 358-374, May.
    6. Subba Rao, S. & Gunasekaran, A. & Goyal, S. K. & Martikainen, T., 1998. "Waiting line model applications in manufacturing," International Journal of Production Economics, Elsevier, vol. 54(1), pages 1-28, January.
    7. Liu, Liming & Yuan, Xue-Ming & Liu, John J., 2004. "Operational capacity allocation for unreliable module-based assembly systems," European Journal of Operational Research, Elsevier, vol. 155(1), pages 134-153, May.
    8. Ramesh Arumugam & Maria Mayorga & Kevin Taaffe, 2009. "Inventory based allocation policies for flexible servers in serial systems," Annals of Operations Research, Springer, vol. 172(1), pages 1-23, November.
    9. Li, Xue & Yamazaki, Genji & Iimura, Kiyoaki, 2000. "Order relations among the optimal values under three evaluation criteria and their applications," European Journal of Operational Research, Elsevier, vol. 122(1), pages 69-78, April.
    10. Nilay Tanık Argon & Sigrún Andradóttir, 2017. "Pooling in tandem queueing networks with non-collaborative servers," Queueing Systems: Theory and Applications, Springer, vol. 87(3), pages 345-377, December.

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