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When Does Forced Idle Time Improve Performance in Polling Models?

Author

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  • Robert B. Cooper

    (Department of Computer Science and Engineering, Florida Atlantic University, Boca Raton, Florida 33431-0991)

  • Shun-Chen Niu

    (School of Management, The University of Texas at Dallas, Richardson, Texas 75083-0688)

  • Mandyam M. Srinivasan

    (Management Science Program, College of Business Administration, The University of Tennessee, Knoxville, Tennessee 37996-0562)

Abstract

Sarkar and Zangwill (1991) showed by numerical examples that reduction in setup times can, surprisingly, actually increase work in process in some cyclic production systems (that is, reduction in switchover times can increase waiting times in some polling models). We present, for polling models with exhaustive and gated service disciplines, some explicit formulas that provide additional insight and characterization of this anomaly. More specifically, we show that, for both of these models, there exist simple formulas that define for each queue a critical value z* of the mean total setup time z per cycle such that, if z z*, then the expected waiting time at that queue will be minimized if the server is forced to idle for a constant length of time z* - z every cycle; also, for the symmetric polling model, we give a simple explicit formula for the expected waiting time and the critical value z* that minimizes it.

Suggested Citation

  • Robert B. Cooper & Shun-Chen Niu & Mandyam M. Srinivasan, 1998. "When Does Forced Idle Time Improve Performance in Polling Models?," Management Science, INFORMS, vol. 44(8), pages 1079-1086, August.
    • Handle: RePEc:inm:ormnsc:v:44:y:1998:i:8:p:1079-1086
    DOI: 10.1287/mnsc.44.8.1079
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    References listed on IDEAS

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    1. Robert B. Cooper & Shun-Chen Niu & Mandyam M. Srinivasan, 1996. "A Decomposition Theorem for Polling Models: The Switchover Times are Effectively Additive," Operations Research, INFORMS, vol. 44(4), pages 629-633, August.
    2. Mandyam M. Srinivasan & Diwakar Gupta, 1996. "When Should a Roving Server Be Patient?," Management Science, INFORMS, vol. 42(3), pages 437-451, March.
    3. D. Sarkar & W. I. Zangwill, 1989. "Expected Waiting Time for Nonsymmetric Cyclic Queueing Systems---Exact Results and Applications," Management Science, INFORMS, vol. 35(12), pages 1463-1474, December.
    4. S. W. Fuhrmann & Robert B. Cooper, 1985. "Stochastic Decompositions in the M / G /1 Queue with Generalized Vacations," Operations Research, INFORMS, vol. 33(5), pages 1117-1129, October.
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    6. Awi Federgruen & Ziv Katalan, 1996. "The Stochastic Economic Lot Scheduling Problem: Cyclical Base-Stock Policies with Idle Times," Management Science, INFORMS, vol. 42(6), pages 783-796, June.
    7. Willard I. Zangwill, 1992. "The Limits of Japanese Production Theory," Interfaces, INFORMS, vol. 22(5), pages 14-25, October.
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    Cited by:

    1. Gupta, Diwakar & Gunalay, Yavuz & Srinivasan, Mandyam M., 2001. "The relationship between preventive maintenance and manufacturing system performance," European Journal of Operational Research, Elsevier, vol. 132(1), pages 146-162, July.
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    5. Samaddar, Subhashish & Hill, Craig A., 2007. "Controlling adverse effect on work in process inventory while reducing machine setup time," European Journal of Operational Research, Elsevier, vol. 180(1), pages 249-261, July.

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