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An Analytical Model for the Many-to-One Demand Responsive Transit Systems

Author

Listed:
  • Di Huang

    (Jiangsu Key Laboratory of Urban ITS, Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic Technologies, School of Transportation, Southeast University, Nanjing 211189, China)

  • Weiping Tong

    (Jiangsu Key Laboratory of Urban ITS, Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic Technologies, School of Transportation, Southeast University, Nanjing 211189, China)

  • Lumeng Wang

    (Jiangsu Key Laboratory of Urban ITS, Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic Technologies, School of Transportation, Southeast University, Nanjing 211189, China)

  • Xun Yang

    (Jiangsu Key Laboratory of Urban ITS, Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic Technologies, School of Transportation, Southeast University, Nanjing 211189, China)

Abstract

The demand-responsive transit (DRT) service is an emerging and flexible transit mode to enhance the mobility of the urban transit system by providing personalized services. Passengers can make advanced appointments through smartphone applications. In this paper, an analytical model is proposed for the many-to-one DRT system. The agency and user costs are approximated by closed-form expressions. The agency cost, which is also the operation cost, is approximated by the continuum approximation technique. A nearest-neighbor routing strategy is applied, whereby the vehicle always collects the nearest passenger waiting in the system. The Vickrey queueing theory is adopted as the basis for approximating each component of the user cost, which is composed of the out-of-vehicle and in-vehicle waiting times and schedule deviations, which also depend on the service quality of the DRT system. The results of the numerical experiment show that (1) the agency and user costs are influenced significantly by the demand density, and (2) the DRT operator cannot further decrease the operating cost by solely deploying larger vehicles.

Suggested Citation

  • Di Huang & Weiping Tong & Lumeng Wang & Xun Yang, 2019. "An Analytical Model for the Many-to-One Demand Responsive Transit Systems," Sustainability, MDPI, vol. 12(1), pages 1-17, December.
    • Handle: RePEc:gam:jsusta:v:12:y:2019:i:1:p:298-:d:303401
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    References listed on IDEAS

    as
    1. 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.
    2. Gonzales, Eric J., 2016. "Demand responsive transit systems with time-dependent demand: User equilibrium, system optimum, and management strategyAuthor-Name: Amirgholy, Mahyar," Transportation Research Part B: Methodological, Elsevier, vol. 92(PB), pages 234-252.
    3. Rahimi, Mahour & Amirgholy, Mahyar & Gonzales, Eric J., 2018. "System modeling of demand responsive transportation services: Evaluating cost efficiency of service and coordinated taxi usage," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 112(C), pages 66-83.
    4. Ansari, Sina & Başdere, Mehmet & Li, Xiaopeng & Ouyang, Yanfeng & Smilowitz, Karen, 2018. "Advancements in continuous approximation models for logistics and transportation systems: 1996–2016," Transportation Research Part B: Methodological, Elsevier, vol. 107(C), pages 229-252.
    5. Zhiling Han & Yanyan Chen & Hui Li & Kuanshuang Zhang & Jiyang Sun, 2019. "Customized Bus Network Design Based on Individual Reservation Demands," Sustainability, MDPI, vol. 11(19), pages 1-25, October.
    6. Tian, Qiong & Huang, Hai-Jun & Yang, Hai, 2007. "Equilibrium properties of the morning peak-period commuting in a many-to-one mass transit system," Transportation Research Part B: Methodological, Elsevier, vol. 41(6), pages 616-631, July.
    7. Robin Lindsey, 2004. "Existence, Uniqueness, and Trip Cost Function Properties of User Equilibrium in the Bottleneck Model with Multiple User Classes," Transportation Science, INFORMS, vol. 38(3), pages 293-314, August.
    8. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    9. Rodney Vaughan, 1984. "Approximate Formulas for Average Distances Associated with Zones," Transportation Science, INFORMS, vol. 18(3), pages 231-244, August.
    10. Anna Franceschetti & Ola Jabali & Gilbert Laporte, 2017. "Rejoinder on: Continuous approximation models in freight distribution management," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 443-444, October.
    11. Daganzo, Carlos F., 1984. "The length of tours in zones of different shapes," Transportation Research Part B: Methodological, Elsevier, vol. 18(2), pages 135-145, April.
    12. Anna Franceschetti & Ola Jabali & Gilbert Laporte, 2017. "Continuous approximation models in freight distribution management," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 413-433, October.
    13. Carlos F. Daganzo, 2005. "Logistics Systems Analysis," Springer Books, Springer, edition 0, number 978-3-540-27516-9, September.
    14. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1990. "Economics of a bottleneck," Journal of Urban Economics, Elsevier, vol. 27(1), pages 111-130, January.
    15. Carlos F. Daganzo, 1985. "The Uniqueness of a Time-dependent Equilibrium Distribution of Arrivals at a Single Bottleneck," Transportation Science, INFORMS, vol. 19(1), pages 29-37, February.
    16. Diana, Marco & Dessouky, Maged M. & Xia, Nan, 2006. "A model for the fleet sizing of demand responsive transportation services with time windows," Transportation Research Part B: Methodological, Elsevier, vol. 40(8), pages 651-666, September.
    17. Luca Quadrifoglio & Randolph W. Hall & Maged M. Dessouky, 2006. "Performance and Design of Mobility Allowance Shuttle Transit Services: Bounds on the Maximum Longitudinal Velocity," Transportation Science, INFORMS, vol. 40(3), pages 351-363, August.
    18. Chebbi, Olfa & Chaouachi, Jouhaina, 2016. "Reducing the wasted transportation capacity of Personal Rapid Transit systems: An integrated model and multi-objective optimization approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 89(C), pages 236-258.
    19. James F. Campbell, 1993. "One-to-Many Distribution with Transshipments: An Analytic Model," Transportation Science, INFORMS, vol. 27(4), pages 330-340, November.
    20. An, Shi & Cui, Na & Li, Xiaopeng & Ouyang, Yanfeng, 2013. "Location planning for transit-based evacuation under the risk of service disruptions," Transportation Research Part B: Methodological, Elsevier, vol. 54(C), pages 1-16.
    21. Small, Kenneth A, 1982. "The Scheduling of Consumer Activities: Work Trips," American Economic Review, American Economic Association, vol. 72(3), pages 467-479, June.
    22. Aldaihani, Majid M. & Quadrifoglio, Luca & Dessouky, Maged M. & Hall, Randolph, 2004. "Network design for a grid hybrid transit service," Transportation Research Part A: Policy and Practice, Elsevier, vol. 38(7), pages 511-530, August.
    23. Carlos F. Daganzo, 1984. "The Distance Traveled to Visit N Points with a Maximum of C Stops per Vehicle: An Analytic Model and an Application," Transportation Science, INFORMS, vol. 18(4), pages 331-350, November.
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