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Statistics of Extremes, Traffic Jams and Natural Disasters

Kühne, Reinhart (2007) Statistics of Extremes, Traffic Jams and Natural Disasters. In: Fluctuation and Noise Conference, Volume 6601, 66010L-1-66010L-12. Fluctuation and Noise 2007, 200705-20 - 2007-05-24, Florenz (Italien). ISBN 9780819467386. ISSN 0277-786X

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Abstract

Analyzing probability distributions from water level time series and calculating the first passage time distributions gives the probability of firstly exceeding a given threshold corresponding to a flood or general disaster event. The method will be applied to the water level recordings of the Danube river from which since 100 years very accurate notes exist. The method is transferred to time series of traffic volumes interpreting traffic breakdowns as extreme events. Three different traffic situations can be distinguished: (a) Stable traffic flow where any fluctuations decay over time (b) metastable traffic flow where fluctuations neither decay nor grow and (c) unstable traffic flow where a breakdown can be expected for sure if the observation time is long enough. The traffic dynamics is translated into a first passage time distribution. This describes the distribution of time periods observing for the first time the formation of a traffic jam of a certain length or number of vehicles. The distribution contains a time lag, a maximum corresponding to a time period of a Brownian motion drift reaching the critical jam length, and a tail describing exceptional long waiting times for jam formation. The cumulative first passage time distribution can be interpreted as breakdown probability distribution. It outlines when reaching a breakdown a given probability in an assumed observation time. It leads directly to the probabilistic definition of the capacity as a traffic volume leading to an unstable traffic pattern with a given probability within a given observation time. This definition can substitute the existing definitions and opens the possibility to quantitatively describing the influence of traffic control systems on the capacity.

Document Type:Conference or Workshop Item (Speech)
Title:Statistics of Extremes, Traffic Jams and Natural Disasters
Authors:
AuthorsInstitution or Email of Authors
Kühne, ReinhartUNSPECIFIED
Date:2007
Journal or Publication Title:Fluctuation and Noise Conference
Refereed publication:Yes
In ISI Web of Science:No
Volume:Volume 6601
Page Range:66010L-1-66010L-12
Editors:
EditorsEmail
Kertész, JánosUNSPECIFIED
Bornholdt, StefanUNSPECIFIED
Mantegna, Rosario N.UNSPECIFIED
Series Name:Proceedings of Spie
ISSN:0277-786X
ISBN:9780819467386
Status:Published
Keywords:Extremes, Traffic Jam, Natural Disasters, Statistics, disaster management, traffic flow, first passage time, breakdown probabillity
Event Title:Fluctuation and Noise 2007
Event Location:Florenz (Italien)
Event Type:international Conference
Event Dates:200705-20 - 2007-05-24
HGF - Research field:Aeronautics, Space and Transport (old)
HGF - Program:Transport
HGF - Program Themes:V SM - Sicherung der Mobilität (old)
DLR - Research area:Transport
DLR - Program:V SM - Sicherung der Mobilität
DLR - Research theme (Project):V -- no assignement
Location: Berlin-Adlershof
Institutes and Institutions:Verkehrsstudien
Deposited By: Sandra Zache
Deposited On:22 Aug 2007
Last Modified:15 Jan 2010 01:01

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