Fosgerau, Mogens (2008): On the relation between the mean and variance of delay in dynamic queues with random capacity and demand.
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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.
Item Type:  MPRA Paper 

Original Title:  On the relation between the mean and variance of delay in dynamic queues with random capacity and demand 
Language:  English 
Keywords:  Bottleneck model; Random capacity; Congestion; Nash Equilibrium; Loop 
Subjects:  D  Microeconomics > D8  Information, Knowledge, and Uncertainty R  Urban, Rural, Regional, Real Estate, and Transportation Economics > R4  Transportation Economics > R41  Transportation: Demand, Supply, and Congestion ; Travel Time ; Safety and Accidents ; Transportation Noise 
Item ID:  11994 
Depositing User:  Mogens Fosgerau 
Date Deposited:  08. Dec 2008 09:22 
Last Modified:  16. Feb 2013 11:33 
References:  Arnott, R. A., de Palma, A. and Lindsey, R. (1993) A structural model of peakperiod congestion: A traffic bottleneck with elastic demand, American Economic Review 83(1), 161179. Arnott, R. A., de Palma, A. and Lindsey, R. (1999) Information and timeofusage decisions in the bottleneck model with stochastic capacity and demand, European Economic Review 43, 525548. Department for Transport (2006) Frameworks for Modelling the Variability of Journey Times on the Highway Network. Fosgerau, M. (2008) Congestion costs in bottleneck equilibrium with stochastic capacity and demand. Working Paper. Fosgerau, M. and Hjorth, K. (2008) The value of travel time variability for a scheduled service. Proceedings of the European Transport Conference. Fosgerau, M. and Jensen, H. (2008) A note on the existence of Nash equilibrium in the stochastic bottleneck model. Working Paper. Fosgerau, M. and Karlstrom, A. (2007) The value of reliability. Working Paper. Vickrey, W. S. (1969) Congestion theory and transport investment. American Economic Review 59, 251261. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/11994 
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 On the relation between the mean and variance of delay in dynamic queues with random capacity and demand. (deposited 08. Dec 2008 09:22) [Currently Displayed]