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Cyclic Queue Models of Fleet Operations

Author

Listed:
  • Ernest Koenigsberg

    (University of California, Berkeley, California)

  • Richard C. Lam

    (University of California, Berkeley, California)

Abstract

Fleets of liquid natural gas vessels operating between one loading and one or two discharge ports are an example of vehicles that operate in closed cycles between a small number of terminals. We extend previous work to develop a cyclic queue model that represents such fleet operations. For any specific system we obtain the expected number of vessels in each stage, the expected number waiting in each stage, and, most important, the expected waiting time in port. Exponential service time distributions are assumed, but a series of parallel simulation computations examines the effects of other distributions. The results for exponential service are obtained in closed form, so that the simulation model can be tested and the confidence interval of the simulations estimated. Both analytic and simulation results are presented for the exponential service case under several sets of system parameters. Simulation results for the same sets are presented for normally distributed service and travel times. We restrict the detailed analysis to balanced systems but discuss extensions to more general systems.

Suggested Citation

  • Ernest Koenigsberg & Richard C. Lam, 1976. "Cyclic Queue Models of Fleet Operations," Operations Research, INFORMS, vol. 24(3), pages 516-529, June.
    • Handle: RePEc:inm:oropre:v:24:y:1976:i:3:p:516-529
    DOI: 10.1287/opre.24.3.516
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    Cited by:

    1. Vibhuti Dhingra & Debjit Roy & René B. M. Koster, 2017. "A cooperative quay crane-based stochastic model to estimate vessel handling time," Flexible Services and Manufacturing Journal, Springer, vol. 29(1), pages 97-124, March.
    2. Guoming Lai & Mulan X. Wang & Sunder Kekre & Alan Scheller-Wolf & Nicola Secomandi, 2011. "Valuation of Storage at a Liquefied Natural Gas Terminal," Operations Research, INFORMS, vol. 59(3), pages 602-616, June.
    3. Kochel, P., 2007. "Order optimisation in multi-location models with hub-and-spoke structure," International Journal of Production Economics, Elsevier, vol. 108(1-2), pages 368-387, July.
    4. Zhang, Xiaoju & Zeng, Qingcheng & Sheu, Jiuh-Biing, 2019. "Modeling the productivity and stability of a terminal operation system with quay crane double cycling," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 122(C), pages 181-197.
    5. Kochel, Peter & Kunze, Sophie & Nielander, Ulf, 2003. "Optimal control of a distributed service system with moving resources: Application to the fleet sizing and allocation problem," International Journal of Production Economics, Elsevier, vol. 81(1), pages 443-459, January.
    6. Milorad Vidovic & Kap Kim, 2006. "Estimating the cycle time of three-stage material handling systems," Annals of Operations Research, Springer, vol. 144(1), pages 181-200, April.
    7. Roy, D. & de Koster, M.B.M., 2014. "Modeling and Design of Container Terminal Operations," ERIM Report Series Research in Management ERS-2014-008-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    8. Klosterhalfen, S.T. & Kallrath, J. & Fischer, G., 2014. "Rail car fleet design: Optimization of structure and size," International Journal of Production Economics, Elsevier, vol. 157(C), pages 112-119.
    9. Debjit Roy & René De Koster & René Bekker, 2020. "Modeling and Design of Container Terminal Operations," Operations Research, INFORMS, vol. 68(3), pages 686-715, May.
    10. Branislav Dragovic & Nenad Dj. Zrnic, 2011. "A Queuing Model Study of Port Performance Evolution," Analele Universitatii "Eftimie Murgu" Resita Fascicola de Inginerie, "Eftimie Murgu" University of Resita, vol. 2(XVIII), pages 65-76, December.
    11. Felix Papier & Ulrich W. Thonemann, 2008. "Queuing Models for Sizing and Structuring Rental Fleets," Transportation Science, INFORMS, vol. 42(3), pages 302-317, August.
    12. Xiaoju Zhang & Huijuan Li & Meng Wu, 2022. "Optimization of Resource Allocation in Automated Container Terminals," Sustainability, MDPI, vol. 14(24), pages 1-16, December.
    13. Kang, Seungmo & Medina, Juan C. & Ouyang, Yanfeng, 2008. "Optimal operations of transportation fleet for unloading activities at container ports," Transportation Research Part B: Methodological, Elsevier, vol. 42(10), pages 970-984, December.
    14. Kallrath, J. & Klosterhalfen, S.T. & Walter, M. & Fischer, G. & Blackburn, R., 2017. "Payload-based fleet optimization for rail cars in the chemical industry," European Journal of Operational Research, Elsevier, vol. 259(1), pages 113-129.
    15. George, David K. & Xia, Cathy H., 2011. "Fleet-sizing and service availability for a vehicle rental system via closed queueing networks," European Journal of Operational Research, Elsevier, vol. 211(1), pages 198-207, May.
    16. Sönmez, Erkut & Kekre, Sunder & Scheller-Wolf, Alan & Secomandi, Nicola, 2013. "Strategic analysis of technology and capacity investments in the liquefied natural gas industry," European Journal of Operational Research, Elsevier, vol. 226(1), pages 100-114.

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