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On the relation between the mean and variance of delay in dynamic queues with random capacity and demand

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  • Fosgerau, Mogens

Abstract

This paper investigates the distribution of delays during a repeatedly occurring demand peak in a congested facility with random capacity and demand, such as an airport or an urban road. Congestion is described in the form of a dynamic queue using the Vickrey bottleneck model and assuming Nash equilibrium in arrival times. The paper shows that the expected delay and the variance of delay vary differently over time during the peak and must hence be considered separately. The paper gives some characterization of how the expected delay and the variance of delay are related, which explain the looping phenomenon that has now been observed a number of times. Empirical illustration is provided.

Suggested Citation

  • Fosgerau, Mogens, 2008. "On the relation between the mean and variance of delay in dynamic queues with random capacity and demand," MPRA Paper 11994, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:11994
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    References listed on IDEAS

    as
    1. Fosgerau, Mogens & Engelson, Leonid, 2011. "The value of travel time variance," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 1-8, January.
    2. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1999. "Information and time-of-usage decisions in the bottleneck model with stochastic capacity and demand," European Economic Review, Elsevier, vol. 43(3), pages 525-548, March.
    3. Fosgerau, Mogens, 2008. "Congestion costs in bottleneck equilibrium with stochastic capacity and demand," MPRA Paper 10040, University Library of Munich, Germany.
    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. Fosgerau, Mogens & Karlström, Anders, 2010. "The value of reliability," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 38-49, January.
    6. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Li, Hao & Tu, Huizhao & Hensher, David A., 2016. "Integrating the mean–variance and scheduling approaches to allow for schedule delay and trip time variability under uncertainty," Transportation Research Part A: Policy and Practice, Elsevier, vol. 89(C), pages 151-163.
    2. Fosgerau, Mogens & Fukuda, Daisuke, 2010. "Valuing travel time variability: Characteristics of the travel time distribution on an urban road," MPRA Paper 24330, University Library of Munich, Germany.
    3. Paul Koster & Eric Pels & Erik Verhoef, 2016. "The User Costs of Air Travel Delay Variability," Transportation Science, INFORMS, vol. 50(1), pages 120-131, February.
    4. Fosgerau, Mogens & Lindsey, Robin, 2013. "Trip-timing decisions with traffic incidents," Regional Science and Urban Economics, Elsevier, vol. 43(5), pages 764-782.
    5. repec:eee:transb:v:99:y:2017:i:c:p:205-227 is not listed on IDEAS
    6. Mogens Fosgerau & Kurt Van Dender, 2013. "Road pricing with complications," Transportation, Springer, vol. 40(3), pages 479-503, May.
    7. Small, Kenneth A., 2015. "The bottleneck model: An assessment and interpretation," Economics of Transportation, Elsevier, vol. 4(1), pages 110-117.
    8. André de Palma & Mogens Fosgerau, 2011. "Dynamic Traffic Modeling," Chapters,in: A Handbook of Transport Economics, chapter 9 Edward Elgar Publishing.
    9. Koster, Paul & Kroes, Eric & Verhoef, Erik, 2011. "Travel time variability and airport accessibility," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1545-1559.
    10. repec:eee:ecotra:v:11-12:y:2017:i::p:1-14 is not listed on IDEAS
    11. Kim, Jiwon & Mahmassani, Hani S., 2015. "Compound Gamma representation for modeling travel time variability in a traffic network," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 40-63.
    12. Xiao, Yu & Coulombel, Nicolas & Palma, André de, 2017. "The valuation of travel time reliability: does congestion matter?," Transportation Research Part B: Methodological, Elsevier, vol. 97(C), pages 113-141.
    13. André De Palma & Mogens Fosgerau, 2010. "Dynamic and Static congestion models: A review," Working Papers hal-00539166, HAL.
    14. Nicholas B. Taylor & Benjamin G. Heydecker, 2015. "Estimating probability distributions of dynamic queues," Transportation Planning and Technology, Taylor & Francis Journals, vol. 38(1), pages 3-27, February.
    15. Kenneth Small, 2015. "The Bottleneck Model: An Assessment and Interpretation," Working Papers 141506, University of California-Irvine, Department of Economics.

    More about this item

    Keywords

    Bottleneck model; Random capacity; Congestion; Nash Equilibrium; Loop;

    JEL classification:

    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty
    • R41 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics - - - Transportation: Demand, Supply, and Congestion; Travel Time; Safety and Accidents; Transportation Noise

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