IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v92y2016ipbp234-252.html
   My bibliography  Save this article

Demand responsive transit systems with time-dependent demand: User equilibrium, system optimum, and management strategyAuthor-Name: Amirgholy, Mahyar

Author

Listed:
  • Gonzales, Eric J.

Abstract

The operating cost of a demand responsive transit (DRT) system strictly depends on the quality of service that it offers to its users. An operating agency seeks to minimize operating costs while maintaining the quality of service while users experience costs associated with scheduling, waiting, and traveling within the system. In this paper, an analytical model is employed to approximate the agency's operating cost for running a DRT system with dynamic demand and the total generalized cost that users experience as a result of the operating decisions. The approach makes use of Vickrey's (1969) congestion theory to model the dynamics of the DRT system in the equilibrium condition and approximate the generalized cost for users when the operating capacity is inadequate to serve the time-dependent demand over the peak period without excess delay. The efficiency of the DRT system can be improved by optimizing one of three parameters that define the agency's operating decision: (1) the operating capacity of the system, (2) the number of passengers that have requested a pick-up and are awaiting service, and (3) the distribution of requested times for service from the DRT system. A schedule management strategy and dynamic pricing strategies are presented that can be implemented to manage demand and reduce the total cost of the DRT system by keeping the number of waiting requests optimized over the peak period. In the end, proposed optimization strategies are compared using a numerical example.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:transb:v:92:y:2016:i:pb:p:234-252
    DOI: 10.1016/j.trb.2015.11.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191261515002374
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.trb.2015.11.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Björn Hårsman & John M. Quigley, 2010. "Political and public acceptability of congestion pricing: Ideology and self-interest," Journal of Policy Analysis and Management, John Wiley & Sons, Ltd., vol. 29(4), pages 854-874.
    2. Harsman, Bjorn & Quigley, John M., 2011. "Political and Public Acceptability of Congestion Pricing: Ideology and Self-Interest in Sweden," University of California Transportation Center, Working Papers qt9p99d890, University of California Transportation Center.
    3. Ida Kristoffersson & Leonid Engelson, 2009. "A Dynamic Transportation Model for the Stockholm Area: Implementation Issues Regarding Departure Time Choice and OD-pair Reduction," Networks and Spatial Economics, Springer, vol. 9(4), pages 551-573, December.
    4. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1993. "A Structural Model of Peak-Period Congestion: A Traffic Bottleneck with Elastic Demand," American Economic Review, American Economic Association, vol. 83(1), pages 161-179, March.
    5. Vold, Arild, 2006. "Phased implementation of transport pricing for Greater Oslo," Transport Policy, Elsevier, vol. 13(2), pages 140-148, March.
    6. Chen, Hongyu & Nie, Yu (Marco) & Yin, Yafeng, 2015. "Optimal multi-step toll design under general user heterogeneity," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 775-793.
    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. Lian, Jon Inge, 2008. "The Oslo and Bergen toll rings and road-building investment – Effect on traffic development and congestion," Journal of Transport Geography, Elsevier, vol. 16(3), pages 174-181.
    9. Shen, Wei & Zhang, H. Michael, 2009. "On the Morning Commute Problem in a Corridor Network with Multiple Bottlenecks: Its System-optimal Traffic Flow Patterns and the Realizing Tolling Scheme," Institute of Transportation Studies, Working Paper Series qt9bs815sq, Institute of Transportation Studies, UC Davis.
    10. de Palma, André & Lindsey, Robin, 2006. "Modelling and evaluation of road pricing in Paris," Transport Policy, Elsevier, vol. 13(2), pages 115-126, March.
    11. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    12. Yang, Hai & Meng, Qiang, 1998. "Departure time, route choice and congestion toll in a queuing network with elastic demand," Transportation Research Part B: Methodological, Elsevier, vol. 32(4), pages 247-260, May.
    13. Nikolas Geroliminis & David M. Levinson, 2009. "Cordon Pricing Consistent with the Physics of Overcrowding," Springer Books, in: William H. K. Lam & S. C. Wong & Hong K. Lo (ed.), Transportation and Traffic Theory 2009: Golden Jubilee, chapter 0, pages 219-240, Springer.
    14. Braid, Ralph M., 1989. "Uniform versus peak-load pricing of a bottleneck with elastic demand," Journal of Urban Economics, Elsevier, vol. 26(3), pages 320-327, November.
    15. Bhat, Chandra R. & Castelar, Saul, 2002. "A unified mixed logit framework for modeling revealed and stated preferences: formulation and application to congestion pricing analysis in the San Francisco Bay area," Transportation Research Part B: Methodological, Elsevier, vol. 36(7), pages 593-616, August.
    16. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1990. "Economics of a bottleneck," Journal of Urban Economics, Elsevier, vol. 27(1), pages 111-130, January.
    17. 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.
    18. Verhoef, Erik T. & Emmerink, Richard H. M. & Nijkamp, Peter & Rietveld, Piet, 1996. "Information provision, flat and fine congestion tolling and the efficiency of road usage," Regional Science and Urban Economics, Elsevier, vol. 26(5), pages 505-529, August.
    19. de Palma, André & Kilani, Moez & Lindsey, Robin, 2005. "Congestion pricing on a road network: A study using the dynamic equilibrium simulator METROPOLIS," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(7-9), pages 588-611.
    20. 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.
    21. Zhang, Xiaoning & Huang, Hai-Jun & Zhang, H.M., 2008. "Integrated daily commuting patterns and optimal road tolls and parking fees in a linear city," Transportation Research Part B: Methodological, Elsevier, vol. 42(1), pages 38-56, January.
    22. van den Berg, Vincent & Verhoef, Erik T., 2011. "Congestion tolling in the bottleneck model with heterogeneous values of time," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 60-78, January.
    23. Figliozzi, Miguel Andres, 2009. "Planning approximations to the average length of vehicle routing problems with time window constraints," Transportation Research Part B: Methodological, Elsevier, vol. 43(4), pages 438-447, May.
    24. Moshe Ben-Akiva & Andre de Palma & Pavlos Kanaroglou, 1986. "Dynamic Model of Peak Period Traffic Congestion with Elastic Arrival Rates," Transportation Science, INFORMS, vol. 20(3), pages 164-181, August.
    25. Yan, Hai & Lam, William H. K., 1996. "Optimal road tolls under conditions of queueing and congestion," Transportation Research Part A: Policy and Practice, Elsevier, vol. 30(5), pages 319-332, September.
    26. Yang, Hai & Liu, Wei & Wang, Xiaolei & Zhang, Xiaoning, 2013. "On the morning commute problem with bottleneck congestion and parking space constraints," Transportation Research Part B: Methodological, Elsevier, vol. 58(C), pages 106-118.
    27. Mahyar Amirgholy & Hojjat Rezaeestakhruie & Hossain Poorzahedy, 2015. "Multi-objective cordon price design to control long run adverse traffic effects in large urban areas," Netnomics, Springer, vol. 16(1), pages 1-52, August.
    28. Zheng, Nan & Waraich, Rashid A. & Axhausen, Kay W. & Geroliminis, Nikolas, 2012. "A dynamic cordon pricing scheme combining the Macroscopic Fundamental Diagram and an agent-based traffic model," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(8), pages 1291-1303.
    29. Nakamura, Katsuhiko & Kockelman, Kara Maria, 2002. "Congestion pricing and roadspace rationing: an application to the San Francisco Bay Bridge corridor," Transportation Research Part A: Policy and Practice, Elsevier, vol. 36(5), pages 403-417, June.
    30. Gonzales, Eric J. & Daganzo, Carlos F., 2012. "Morning commute with competing modes and distributed demand: User equilibrium, system optimum, and pricing," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1519-1534.
    31. Yang, Hai & Huang, Hai-Jun, 1998. "Principle of marginal-cost pricing: how does it work in a general road network?," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(1), pages 45-54, January.
    32. Eliasson, Jonas & Mattsson, Lars-Göran, 2006. "Equity effects of congestion pricing: Quantitative methodology and a case study for Stockholm," Transportation Research Part A: Policy and Practice, Elsevier, vol. 40(7), pages 602-620, August.
    33. Yang, Hai & Hai-Jun, Huang, 1997. "Analysis of the time-varying pricing of a bottleneck with elastic demand using optimal control theory," Transportation Research Part B: Methodological, Elsevier, vol. 31(6), pages 425-440, November.
    34. Mun, Se-il, 1994. "Traffic jams and the congestion toll," Transportation Research Part B: Methodological, Elsevier, vol. 28(5), pages 365-375, October.
    35. Henderson, J. V., 1974. "Road congestion : A reconsideration of pricing theory," Journal of Urban Economics, Elsevier, vol. 1(3), pages 346-365, July.
    36. Meland, Solveig & Tretvik, Terje & Welde, Morten, 2010. "The effects of removing the Trondheim toll cordon," Transport Policy, Elsevier, vol. 17(6), pages 475-485, November.
    37. Feng Xiao & Zhen Qian & H. Zhang, 2011. "The Morning Commute Problem with Coarse Toll and Nonidentical Commuters," Networks and Spatial Economics, Springer, vol. 11(2), pages 343-369, June.
    38. C. Robin Lindsey & Erik T. Verhoef, 2000. "Traffic Congestion and Congestion Pricing," Tinbergen Institute Discussion Papers 00-101/3, Tinbergen Institute.
    39. Shen, Wei & Zhang, H.M., 2009. "On the morning commute problem in a corridor network with multiple bottlenecks: Its system-optimal traffic flow patterns and the realizing tolling scheme," Transportation Research Part B: Methodological, Elsevier, vol. 43(3), pages 267-284, March.
    40. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Braekers, Kris & Kovacs, Attila A., 2016. "A multi-period dial-a-ride problem with driver consistency," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 355-377.
    2. Zhang, Jie & Wang, David Z.W. & Meng, Meng, 2018. "Which service is better on a linear travel corridor: Park & ride or on-demand public bus?," Transportation Research Part A: Policy and Practice, Elsevier, vol. 118(C), pages 803-818.
    3. Amirgholy, Mahyar & Gao, H. Oliver, 2017. "Modeling the dynamics of congestion in large urban networks using the macroscopic fundamental diagram: User equilibrium, system optimum, and pricing strategies," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 215-237.
    4. (Edward) Kim, Myungseob & Levy, Joshua & Schonfeld, Paul, 2019. "Optimal zone sizes and headways for flexible-route bus services," Transportation Research Part B: Methodological, Elsevier, vol. 130(C), pages 67-81.
    5. Masmoudi, Mohamed Amine & Hosny, Manar & Demir, Emrah & Genikomsakis, Konstantinos N. & Cheikhrouhou, Naoufel, 2018. "The dial-a-ride problem with electric vehicles and battery swapping stations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 118(C), pages 392-420.
    6. 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.
    7. Xu, Shu-Xian & Liu, Ronghui & Liu, Tian-Liang & Huang, Hai-Jun, 2018. "Pareto-improving policies for an idealized two-zone city served by two congestible modes," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 876-891.
    8. Amirgholy, Mahyar & Shahabi, Mehrdad & Gao, H. Oliver, 2017. "Optimal design of sustainable transit systems in congested urban networks: A macroscopic approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 103(C), pages 261-285.
    9. Jie Xiong & Biao Chen & Xiangnan Li & Zhengbing He & Yanyan Chen, 2020. "Demand Responsive Service-based Optimization on Flexible Routes and Departure Time of Community Shuttles," Sustainability, MDPI, vol. 12(3), pages 1-20, January.
    10. Mohajerpoor, Reza & Saberi, Meead & Vu, Hai L. & Garoni, Timothy M. & Ramezani, Mohsen, 2020. "H∞ robust perimeter flow control in urban networks with partial information feedback," Transportation Research Part B: Methodological, Elsevier, vol. 137(C), pages 47-73.
    11. 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.
    12. Bian, Zheyong & Liu, Xiang, 2019. "Mechanism design for first-mile ridesharing based on personalized requirements part I: Theoretical analysis in generalized scenarios," Transportation Research Part B: Methodological, Elsevier, vol. 120(C), pages 147-171.
    13. Nourinejad, Mehdi & Ramezani, Mohsen, 2020. "Ride-Sourcing modeling and pricing in non-equilibrium two-sided markets," Transportation Research Part B: Methodological, Elsevier, vol. 132(C), pages 340-357.
    14. Li, Chuan-Yao & Huang, Hai-Jun, 2017. "Morning commute in a single-entry traffic corridor with early and late arrivals," Transportation Research Part B: Methodological, Elsevier, vol. 97(C), pages 23-49.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li, Zhi-Chun & Huang, Hai-Jun & Yang, Hai, 2020. "Fifty years of the bottleneck model: A bibliometric review and future research directions," Transportation Research Part B: Methodological, Elsevier, vol. 139(C), pages 311-342.
    2. Kenneth Small, 2015. "The Bottleneck Model: An Assessment and Interpretation," Working Papers 141506, University of California-Irvine, Department of Economics.
    3. Small, Kenneth A., 2015. "The bottleneck model: An assessment and interpretation," Economics of Transportation, Elsevier, vol. 4(1), pages 110-117.
    4. Ma, Rui & Ban, Xuegang (Jeff) & Szeto, W.Y., 2017. "Emission modeling and pricing on single-destination dynamic traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 100(C), pages 255-283.
    5. Amirgholy, Mahyar & Shahabi, Mehrdad & Gao, H. Oliver, 2017. "Optimal design of sustainable transit systems in congested urban networks: A macroscopic approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 103(C), pages 261-285.
    6. Amirgholy, Mahyar & Gao, H. Oliver, 2017. "Modeling the dynamics of congestion in large urban networks using the macroscopic fundamental diagram: User equilibrium, system optimum, and pricing strategies," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 215-237.
    7. Mahyar Amirgholy & Hojjat Rezaeestakhruie & Hossain Poorzahedy, 2015. "Multi-objective cordon price design to control long run adverse traffic effects in large urban areas," Netnomics, Springer, vol. 16(1), pages 1-52, August.
    8. Bao, Yue & Verhoef, Erik T. & Koster, Paul, 2021. "Leaving the tub: The nature and dynamics of hypercongestion in a bathtub model with a restricted downstream exit," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 152(C).
    9. Ren-Yong Guo & Hai Yang & Hai-Jun Huang, 2018. "Are We Really Solving the Dynamic Traffic Equilibrium Problem with a Departure Time Choice?," Transportation Science, INFORMS, vol. 52(3), pages 603-620, June.
    10. Zhang, Xiaoning & Yang, Hai & Huang, Hai-Jun & Zhang, H. Michael, 2005. "Integrated scheduling of daily work activities and morning-evening commutes with bottleneck congestion," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(1), pages 41-60, January.
    11. de Palma, André & Kilani, Moez & Lindsey, Robin, 2005. "Congestion pricing on a road network: A study using the dynamic equilibrium simulator METROPOLIS," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(7-9), pages 588-611.
    12. Chen, Hongyu & Liu, Yang & Nie, Yu (Marco), 2015. "Solving the step-tolled bottleneck model with general user heterogeneity," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 210-229.
    13. Yang, Hai & Liu, Wei & Wang, Xiaolei & Zhang, Xiaoning, 2013. "On the morning commute problem with bottleneck congestion and parking space constraints," Transportation Research Part B: Methodological, Elsevier, vol. 58(C), pages 106-118.
    14. Li, Zhi-Chun & Lam, William H.K. & Wong, S.C., 2014. "Bottleneck model revisited: An activity-based perspective," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 262-287.
    15. Ling-Ling Xiao & Hai-Jun Huang & Ronghui Liu, 2015. "Congestion Behavior and Tolls in a Bottleneck Model with Stochastic Capacity," Transportation Science, INFORMS, vol. 49(1), pages 46-65, February.
    16. Chen, Hongyu & Nie, Yu (Marco) & Yin, Yafeng, 2015. "Optimal multi-step toll design under general user heterogeneity," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 775-793.
    17. van den Berg, Vincent A.C., 2014. "Coarse tolling with heterogeneous preferences," Transportation Research Part B: Methodological, Elsevier, vol. 64(C), pages 1-23.
    18. Verhoef, Erik T., 1999. "Time, speeds, flows and densities in static models of road traffic congestion and congestion pricing," Regional Science and Urban Economics, Elsevier, vol. 29(3), pages 341-369, May.
    19. Zheng, Nan & Geroliminis, Nikolas, 2020. "Area-based equitable pricing strategies for multimodal urban networks with heterogeneous users," Transportation Research Part A: Policy and Practice, Elsevier, vol. 136(C), pages 357-374.
    20. Xu, Da & Guo, Xiaolei & Zhang, Guoqing, 2019. "Constrained optimization for bottleneck coarse tolling," Transportation Research Part B: Methodological, Elsevier, vol. 128(C), pages 1-22.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:transb:v:92:y:2016:i:pb:p:234-252. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/548/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.