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Optimal Dispatching of an Infinite-Capacity Shuttle: Control at a Single Terminal

Author

Listed:
  • Edward Ignall

    (Columbia University, New York, New York)

  • Peter Kolesar

    (The City College (CUNY) and The New York City—Rand Institute, New York, New York)

Abstract

We study the optimal control of a shuttle system consisting of a single infinite-capacity carrier transporting passengers between two terminals. Passengers arrive according to independent Poisson processes, and at only one of the terminals can the dispatcher hold the carrier for more passengers. Our objective: to determine dispatching rules that minimize the long-run average of a linear passenger-waiting-time cost and a charge per trip made by the carrier. When complete information about the system state is available, and travel times are not random, we prove that it is best to dispatch the carrier if, and only if, the total number of passengers waiting at both terminals is greater than a cutoff value. To compute this cutoff value, we propose an iterative method and find that we can approximate it quite well by a simple function of system costs and parameters similar to the economic-lot-size formula. We propose a dispatching rule (which may not be optimal) for the case when only the number of passengers waiting at one terminal is known, and we compare its efficiency to that of the optimal rule that uses complete information. We outline extensions to other optimality criteria and to the case of stochastic travel times.

Suggested Citation

  • Edward Ignall & Peter Kolesar, 1974. "Optimal Dispatching of an Infinite-Capacity Shuttle: Control at a Single Terminal," Operations Research, INFORMS, vol. 22(5), pages 1008-1024, October.
    • Handle: RePEc:inm:oropre:v:22:y:1974:i:5:p:1008-1024
    DOI: 10.1287/opre.22.5.1008
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    Cited by:

    1. Daganzo, Carlos F. & Pilachowski, Josh, 2009. "Reducing bunching with bus-to-bus cooperation," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt0551g0zw, Institute of Transportation Studies, UC Berkeley.
    2. Chandra, Shailesh & Quadrifoglio, Luca, 2013. "A model for estimating the optimal cycle length of demand responsive feeder transit services," Transportation Research Part B: Methodological, Elsevier, vol. 51(C), pages 1-16.
    3. Czerny, Achim I. & Guo, Pengfei & Hassin, Refael, 2022. "Shall firms withhold exact waiting time information from their customers? A transport example," Transportation Research Part B: Methodological, Elsevier, vol. 166(C), pages 128-142.
    4. Hall, Randolph W. & Sabnani, Vikas C., 2002. "Control of vehicle dispatching on a cyclic route serving trucking terminals," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(3), pages 257-276, March.
    5. Andres, Matthias & Nair, Rahul, 2017. "A predictive-control framework to address bus bunching," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 123-148.
    6. Daganzo, Carlos F., 2009. "A headway-based approach to eliminate bus bunching: Systematic analysis and comparisons," Transportation Research Part B: Methodological, Elsevier, vol. 43(10), pages 913-921, December.
    7. Daganzo, Carlos F. & Pilachowski, Josh, 2011. "Reducing bunching with bus-to-bus cooperation," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 267-277, January.
    8. Howard J. Weiss & Stanley R. Pliska, 1976. "Optimal Control of Some Markov Processes with Applications to Batch Queueing and Continuous Review Inventory Systems," Discussion Papers 214, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    9. Dimitrios Logothetis & Antonis Economou, 2023. "The impact of information on transportation systems with strategic customers," Production and Operations Management, Production and Operations Management Society, vol. 32(7), pages 2189-2206, July.

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