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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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 34 (2010)
Issue (Month): 4 (April)
Pages: 598-603

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Handle: RePEc:eee:dyncon:v:34:y:2010:i:4:p:598-603

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Keywords: Bottleneck model Random capacity Congestion Nash equilibrium Loop;

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References

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  1. R. Arnott & A. de Palma & R. Lindsey, 1997. "Information and time-of-usage decisions in the bottleneck model with stochastic capacity and demand," THEMA Working Papers 97-13, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  2. Fosgerau, Mogens, 2008. "Congestion costs in bottleneck equilibrium with stochastic capacity and demand," MPRA Paper 10040, University Library of Munich, Germany.
  3. Fosgerau, Mogens & Karlström, Anders, 2010. "The value of reliability," Transportation Research Part B: Methodological, Elsevier, vol. 44(1), pages 38-49, January.
  4. Fosgerau, Mogens & Engelson, Leonid, 2011. "The value of travel time variance," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 1-8, January.
  5. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-60, May.
  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 161-79, March.
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Citations

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Cited by:
  1. Mogens Fosgerau & Kurt Van Dender, 2013. "Road pricing with complications," Transportation, Springer, vol. 40(3), pages 479-503, May.
  2. Fosgerau, Mogens & Lindsey, Robin, 2013. "Trip-timing decisions with traffic incidents," MPRA Paper 48708, University Library of Munich, Germany.
  3. André De Palma & Mogens Fosgerau, 2010. "Dynamic and Static congestion models: A review," Working Papers hal-00539166, HAL.
  4. 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.
  5. Stefanie Peer & Erik Verhoef & Jasper Knockaert & Paul Koster & Yin-Yen Tseng, 2011. "Long-Run vs. Short-Run Perspectives on Consumer Scheduling: Evidence from a Revealed-Preference Experiment among Peak-Hour Road Commuters," Tinbergen Institute Discussion Papers 11-181/3, Tinbergen Institute, revised 16 May 2012.
  6. 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.

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