On the relation between the mean and variance of delay in dynamic queues with random capacity and demand
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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- Fosgerau, Mogens, 2008. "Congestion costs in bottleneck equilibrium with stochastic capacity and demand," MPRA Paper 10040, University Library of Munich, Germany.
- Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1999.
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- Richard Arnott & Andre de Palma & Robin Lindsey, 1996. "Information and Time-of-Usage Decisions in the Bottleneck Model with Stochastic Capacity and Demand," Boston College Working Papers in Economics 355., Boston College Department of Economics.
- 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.
- Fosgerau, Mogens & Engelson, Leonid, 2011.
"The value of travel time variance,"
Transportation Research Part B: Methodological,
Elsevier, vol. 45(1), pages 1-8, January.
- Fosgerau, Mogens & Karlström, Anders, 2007.
"The value of reliability,"
5733, University Library of Munich, Germany.
- Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-60, May.
- 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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