IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v44y2010i10p1166-1185.html
   My bibliography  Save this article

Endogenous arrivals in batch queues with constant or variable capacity

Author

Listed:
  • Rapoport, Amnon
  • Stein, William E.
  • Mak, Vincent
  • Zwick, Rami
  • Seale, Darryl A.

Abstract

We study batch queueing systems with continuous time, finite commuter populations, single server, and endogenously determined arrival times. Symmetric equilibrium solutions in mixed strategies are constructed and subsequently tested in two experiments that examine two different batch queueing models, one with a fixed server capacity, and the other with a variable server capacity. With experience in playing the stage queueing game repeatedly, experimental results from groups of 20 subjects support equilibrium play on the aggregate level when the server capacity is fixed and commonly known. When it is known to be variable, randomly changing from round to round, subjects diverge from equilibrium play and increase their individual payoffs substantially by significantly shortening their waiting time.

Suggested Citation

  • Rapoport, Amnon & Stein, William E. & Mak, Vincent & Zwick, Rami & Seale, Darryl A., 2010. "Endogenous arrivals in batch queues with constant or variable capacity," Transportation Research Part B: Methodological, Elsevier, vol. 44(10), pages 1166-1185, December.
    • Handle: RePEc:eee:transb:v:44:y:2010:i:10:p:1166-1185
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191-2615(10)00013-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. de Palma, André & Lindsey, Robin, 2001. "Optimal timetables for public transportation," Transportation Research Part B: Methodological, Elsevier, vol. 35(8), pages 789-813, September.
    2. Anthony Ziegelmeyer & Frédéric Koessler & Kene Boun My & Laurent Denant-Boèmont, 2008. "Road Traffic Congestion and Public Information: An Experimental Investigation," Journal of Transport Economics and Policy, University of Bath, vol. 42(1), pages 43-82, January.
    3. Kraus, Marvin, 2003. "A new look at the two-mode problem," Journal of Urban Economics, Elsevier, vol. 54(3), pages 511-530, November.
    4. Rapoport, Amnon & Stein, William E. & Parco, James E. & Seale, Darryl A., 2004. "Equilibrium play in single-server queues with endogenously determined arrival times," Journal of Economic Behavior & Organization, Elsevier, vol. 55(1), pages 67-91, September.
    5. Terry E. Daniel & Eyran J. Gisches & Amnon Rapoport, 2009. "Departure Times in Y-Shaped Traffic Networks with Multiple Bottlenecks," American Economic Review, American Economic Association, vol. 99(5), pages 2149-2176, December.
    6. 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.
    7. 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.
    8. Darryl Seale & James Parco & William Stein & Amnon Rapoport, 2005. "Joining a Queue or Staying Out: Effects of Information Structure and Service Time on Arrival and Staying Out Decisions," Experimental Economics, Springer;Economic Science Association, vol. 8(2), pages 117-144, June.
    9. Daniel Kahneman & Jack L. Knetsch & Richard H. Thaler, 1991. "Anomalies: The Endowment Effect, Loss Aversion, and Status Quo Bias," Journal of Economic Perspectives, American Economic Association, vol. 5(1), pages 193-206, Winter.
    10. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    11. A. Glazer & R. Hassin, 1987. "Equilibrium Arrivals in Queues with Bulk Service at Scheduled Times," Transportation Science, INFORMS, vol. 21(4), pages 273-278, November.
    12. Stein, William E. & Rapoport, Amnon & Seale, Darryl A. & Zhang, Hongtao & Zwick, Rami, 2007. "Batch queues with choice of arrivals: Equilibrium analysis and experimental study," Games and Economic Behavior, Elsevier, vol. 59(2), pages 345-363, May.
    13. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
    14. Holt, Charles A, Jr & Sherman, Roger, 1982. "Waiting-Line Auctions," Journal of Political Economy, University of Chicago Press, vol. 90(2), pages 280-294, April.
    15. J. Medhi, 1975. "Waiting Time Distribution in a Poisson Queue with a General Bulk Service Rule," Management Science, INFORMS, vol. 21(7), pages 777-782, March.
    16. Kraus, Marvin & Yoshida, Yuichiro, 2002. "The Commuter's Time-of-Use Decision and Optimal Pricing and Service in Urban Mass Transit," Journal of Urban Economics, Elsevier, vol. 51(1), pages 170-195, January.
    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. Conte, Anna & Scarsini, Marco & Sürücü, Oktay, 2016. "The impact of time limitation: Insights from a queueing experiment," Judgment and Decision Making, Cambridge University Press, vol. 11(3), pages 260-274, May.
    2. Delgado-Alvarez, Carlos A. & van Ackere, Ann & Larsen, Erik R & Arango-Aramburo, Santiago, 2017. "Managing capacity at a service facility: An experimental approach," European Journal of Operational Research, Elsevier, vol. 259(1), pages 216-228.
    3. repec:cup:judgdm:v:11:y:2016:i:3:p:260-274 is not listed on IDEAS
    4. Moshe Haviv & Liron Ravner, 2021. "A survey of queueing systems with strategic timing of arrivals," Queueing Systems: Theory and Applications, Springer, vol. 99(1), pages 163-198, October.
    5. Rapoport, Amnon & Gisches, Eyran J. & Daniel, Terry & Lindsey, Robin, 2014. "Pre-trip information and route-choice decisions with stochastic travel conditions: Experiment," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 154-172.
    6. Anna Conte & Marco Scarsini & Oktay Sürücü, 2014. "An Experimental Investigation into Queueing Behavior," Jena Economics Research Papers 2014-030, Friedrich-Schiller-University Jena.
    7. Conte, Anna & Scarsini, Marco & Sürücü, Oktay, 2015. "Does time pressure impair performance? An experiment on queueing behavior," Center for Mathematical Economics Working Papers 538, Center for Mathematical Economics, Bielefeld University.
    8. Sun, Xiaoyan & Han, Xiao & Bao, Jian-Zhang & Jiang, Rui & Jia, Bin & Yan, Xiaoyong & Zhang, Boyu & Wang, Wen-Xu & Gao, Zi-You, 2017. "Decision dynamics of departure times: Experiments and modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 74-82.
    9. Cary Deck & Erik O Kimbrough & Steeve Mongrain, 2014. "Paying for Express Checkout: Competition and Price Discrimination in Multi-Server Queuing Systems," PLOS ONE, Public Library of Science, vol. 9(3), pages 1-13, March.
    10. Sun, Xiaoyan & Li, Wentao & Jiang, Rui & Zhu, Yubing & Chen, Dong, 2022. "Study on the influence of road capacity and information feedback on urban traffic system equilibrium state," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 593(C).

    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. Stein, William E. & Rapoport, Amnon & Seale, Darryl A. & Zhang, Hongtao & Zwick, Rami, 2007. "Batch queues with choice of arrivals: Equilibrium analysis and experimental study," Games and Economic Behavior, Elsevier, vol. 59(2), pages 345-363, May.
    2. Moshe Haviv & Liron Ravner, 2021. "A survey of queueing systems with strategic timing of arrivals," Queueing Systems: Theory and Applications, Springer, vol. 99(1), pages 163-198, October.
    3. Otsubo, Hironori & Rapoport, Amnon, 2008. "Vickrey's model of traffic congestion discretized," Transportation Research Part B: Methodological, Elsevier, vol. 42(10), pages 873-889, December.
    4. 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.
    5. Breinbjerg, Jesper, 2017. "Equilibrium arrival times to queues with general service times and non-linear utility functions," European Journal of Operational Research, Elsevier, vol. 261(2), pages 595-605.
    6. Breinbjerg, Jesper & Østerdal, Lars Peter, 2017. "Equilibrium Arrival Times to Queues: The Case of Last-Come First-Serve Preemptive-Resume," Discussion Papers on Economics 3/2017, University of Southern Denmark, Department of Economics.
    7. de Palma, André & Lindsey, Robin & Monchambert, Guillaume, 2017. "The economics of crowding in rail transit," Journal of Urban Economics, Elsevier, vol. 101(C), pages 106-122.
    8. Jesper Breinbjerg & Trine Tornøe Platz & Lars Peter Østerdal, 2024. "Equilibrium arrivals to a last-come first-served preemptive-resume queue," Annals of Operations Research, Springer, vol. 336(3), pages 1551-1572, May.
    9. Jesper Breinbjerg & Alexander Sebald & Lars Peter Østerdal, 2016. "Strategic behavior and social outcomes in a bottleneck queue: experimental evidence," Review of Economic Design, Springer;Society for Economic Design, vol. 20(3), pages 207-236, September.
    10. André de Palma & Robin Lindsey & Guillaume Monchambert, 2017. "The Economics of Crowding in Public Transport," Post-Print hal-01203310, HAL.
    11. Yang, Hai & Tang, Yili, 2018. "Managing rail transit peak-hour congestion with a fare-reward scheme," Transportation Research Part B: Methodological, Elsevier, vol. 110(C), pages 122-136.
    12. 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.
    13. Delgado-Alvarez, Carlos A. & van Ackere, Ann & Larsen, Erik R & Arango-Aramburo, Santiago, 2017. "Managing capacity at a service facility: An experimental approach," European Journal of Operational Research, Elsevier, vol. 259(1), pages 216-228.
    14. 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.
    15. Takayama, Yuki & Kuwahara, Masao, 2016. "Scheduling preferences, parking competition, and bottleneck congestion: A model of trip timing and parking location choices by heterogeneous commuters," MPRA Paper 68938, University Library of Munich, Germany.
    16. Fu, Haoran & Akamatsu, Takashi & Satsukawa, Koki & Wada, Kentaro, 2022. "Dynamic traffic assignment in a corridor network: Optimum versus equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 161(C), pages 218-246.
    17. Maria Arbatskaya & Kaushik Mukhopadhaya & Eric Rasmusen, 2001. "The Parking Lot Problem," CIRJE F-Series CIRJE-F-119, CIRJE, Faculty of Economics, University of Tokyo.
      • Maria Arbatskaya & Kaushik Mukhopadhaya & Eric Rasmusen, 2007. "The Parking Lot Problem," Working Papers 2007-04, Indiana University, Kelley School of Business, Department of Business Economics and Public Policy.
    18. Chaoda Xie & Xifu Wang & Daisuke Fukuda, 2020. "On the Pricing of Urban Rail Transit with Track Sharing Freight Service," Sustainability, MDPI, vol. 12(7), pages 1-29, April.
    19. Guo, Ren-Yong & Yang, Hai & Huang, Hai-Jun & Li, Xinwei, 2018. "Day-to-day departure time choice under bounded rationality in the bottleneck model," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 832-849.
    20. Basso, Leonardo J. & Feres, Fernando & Silva, Hugo E., 2019. "The efficiency of bus rapid transit (BRT) systems: A dynamic congestion approach," Transportation Research Part B: Methodological, Elsevier, vol. 127(C), pages 47-71.

    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:44:y:2010:i:10:p:1166-1185. 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.