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Dynamic Modeling and Control of Congestion-Prone Systems

Author

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  • Carson E. Agnew

    (Mathematica, Inc., Princeton, New Jersey)

Abstract

This paper constructs a dynamic model of a general congestion-prone system using a nonlinear differential equation to represent the relation between throughput and the system load. Although the model is not stochastic, it can give a good approximation of the dynamics of oversaturated or undersaturated system operation. The model is used to study the stability and transient behavior of a congestion-prone system and to analyze policies for the control of congestion in a simple optimal control model.

Suggested Citation

  • Carson E. Agnew, 1976. "Dynamic Modeling and Control of Congestion-Prone Systems," Operations Research, INFORMS, vol. 24(3), pages 400-419, June.
    • Handle: RePEc:inm:oropre:v:24:y:1976:i:3:p:400-419
    DOI: 10.1287/opre.24.3.400
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    Citations

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    Cited by:

    1. Fosgerau, Mogens, 2015. "Congestion in the bathtub," Economics of Transportation, Elsevier, vol. 4(4), pages 241-255.
    2. Arnott, Richard, 2013. "A bathtub model of downtown traffic congestion," Journal of Urban Economics, Elsevier, vol. 76(C), pages 110-121.
    3. van Ackere, Ann & Haxholdt, Christian & Larsen, Erik R., 2013. "Dynamic capacity adjustments with reactive customers," Omega, Elsevier, vol. 41(4), pages 689-705.
    4. Kefeli, Ali & Uzsoy, Reha & Fathi, Yahya & Kay, Michael, 2011. "Using a mathematical programming model to examine the marginal price of capacitated resources," International Journal of Production Economics, Elsevier, vol. 131(1), pages 383-391, May.
    5. Hu, Lu & Zhao, Bin & Zhu, Juanxiu & Jiang, Yangsheng, 2019. "Two time-varying and state-dependent fluid queuing models for traffic circulation systems," European Journal of Operational Research, Elsevier, vol. 275(3), pages 997-1019.
    6. Jakob Asmundsson & Ronald L. Rardin & Can Hulusi Turkseven & Reha Uzsoy, 2009. "Production planning with resources subject to congestion," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(2), pages 142-157, March.
    7. Richard J. Arnott & Anatolii Kokoza & Mehdi Naji, 2015. "A Model of Rush-Hour Traffic in an Isotropic Downtown Area," CESifo Working Paper Series 5465, CESifo.
    8. Jin, Wen-Long, 2020. "Generalized bathtub model of network trip flows," Transportation Research Part B: Methodological, Elsevier, vol. 136(C), pages 138-157.
    9. Rong Yuan & Stephen C. Graves, 2016. "Setting optimal production lot sizes and planned lead times in a job shop," International Journal of Production Research, Taylor & Francis Journals, vol. 54(20), pages 6105-6120, October.
    10. Richard Arnott & Anatolii Kokoza & Mehdi Naji, 2016. "A Model of Rush-Hour Traffic Dynamics in an Isotropic Downtown Area," Working Papers 201612, University of California at Riverside, Department of Economics.
    11. Arnott, Richard & Kokoza, Anatolii & Naji, Mehdi, 2016. "Equilibrium traffic dynamics in a bathtub model: A special case," Economics of Transportation, Elsevier, vol. 7, pages 38-52.
    12. Julia Pahl & Stefan Voß & David Woodruff, 2007. "Production planning with load dependent lead times: an update of research," Annals of Operations Research, Springer, vol. 153(1), pages 297-345, September.

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