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2. Halphen Distribution System, Toolbox for Modeling Travel Time Variability

Author

Nour-Eddin El Faouzi, Romain Billot, Aurélien Duret, and Raphaël Delhome

Subjects
050210 logistics & transportation, Decision support system, Mesoscopic physics, Engineering, Scale (ratio), business.industry, Mechanical Engineering, 05 social sciences, Real-time computing, Diagram, Traffic simulation, 010501 environmental sciences, computer.software_genre, 01 natural sciences, Toolbox, Data set, 0502 economics and business, 11. Sustainability, Range (statistics), Data mining, business, computer, 0105 earth and related environmental sciences, Civil and Structural Engineering
Abstract

This paper introduces the Halphen system as a toolbox for modeling travel time variability. The three distributions of the Halphen family and the moment–ratio diagram (MRD), a graphical tool for selecting the best distribution given a specific data set, are presented. The mapping between the positions of travel time samples on the MRD and traffic conditions based on mesoscopic traffic simulation was explored. A comprehensive supply–demand scenario enabled a comparison between day-to-day and hour-by-hour travel time variability in terms of selection of the optimal distribution. The results highlight the capability of the Halphen system to model a wide range of traffic conditions. This flexible tool has the potential to be integrated into a practice-ready decision support system for modeling travel time variability at the network scale.

Published
2015

3. Travel time statistical modeling with the Halphen distribution family

Author

Romain Billot, Nour-Eddin El Faouzi, Raphaël Delhome, OSLANDIA (Entreprise), Lab-STICC_TB_CID_DECIDE, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance ( Lab-STICC ), École Nationale d'Ingénieurs de Brest ( ENIB ) -Université de Bretagne Sud ( UBS ) -Université de Brest ( UBO ) -Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques ( IBNM ), Université de Brest ( UBO ) -Université européenne de Bretagne ( UEB ) -ENSTA Bretagne-Institut Mines-Télécom [Paris]-Centre National de la Recherche Scientifique ( CNRS ) -École Nationale d'Ingénieurs de Brest ( ENIB ) -Université de Bretagne Sud ( UBS ) -Université de Brest ( UBO ) -Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques ( IBNM ), Université de Brest ( UBO ) -Université européenne de Bretagne ( UEB ) -ENSTA Bretagne-Institut Mines-Télécom [Paris]-Centre National de la Recherche Scientifique ( CNRS ), Département Logique des Usages, Sciences sociales et Sciences de l'Information ( LUSSI ), IMT Atlantique Bretagne-Pays de la Loire ( IMT Atlantique ), École Nationale d'Ingénieurs de Brest ( ENIB ) -Université de Bretagne Sud ( UBS ) -Université de Brest ( UBO ) -ENSTA Bretagne-Institut Mines-Télécom [Paris]-Centre National de la Recherche Scientifique ( CNRS ) -Université Bretagne Loire ( UBL ) -IMT Atlantique Bretagne-Pays de la Loire ( IMT Atlantique ), Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux ( IFSTTAR ), Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS), Département Logique des Usages, Sciences sociales et Sciences de l'Information (IMT Atlantique - LUSSI), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT), Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR), Institut Mines-Télécom [Paris] (IMT)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), and Institut Mines-Télécom [Paris] (IMT)-École Nationale d'Ingénieurs de Brest (ENIB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS)-Université Bretagne Loire (UBL)

Subjects
Computer science, Diagram (category theory), Aerospace Engineering, 010501 environmental sciences, computer.software_genre, 01 natural sciences, Set (abstract data type), [INFO.INFO-CY]Computer Science [cs]/Computers and Society [cs.CY], [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], 0502 economics and business, Econometrics, [ MATH.MATH-ST ] Mathematics [math]/Statistics [math.ST], Representation (mathematics), Reliability (statistics), 0105 earth and related environmental sciences, 050210 logistics & transportation, [STAT.AP]Statistics [stat]/Applications [stat.AP], Mathematical model, Applied Mathematics, 05 social sciences, [ STAT.AP ] Statistics [stat]/Applications [stat.AP], Statistical model, Computer Science Applications, Data set, [ INFO.INFO-CY ] Computer Science [cs]/Computers and Society [cs.CY], Control and Systems Engineering, Automotive Engineering, Probability distribution, Data mining, computer, Software, Information Systems
Abstract

International audience; This paper introduces the Halphen distribution family for modeling travel time distributions and their reliability on single road links. This probability family originally used in hydrology has a set of relevant characteristics. It is composed of three probability distribution functions for which the mathematical properties are described here. The paper uses a graphical representation, the δ-Moment Ratio Diagram (δ-MRD). This tool allows characterizing travel time reliability as well as selecting best distribution candidates within the fitting processes, by considering empirical data sets. A systematic methodology is developed to take advantage of both aspects. From maximum log-likelihood estimation it is shown that Halphen distributions are amongst the best state-of-the-art solutions for the travel time modeling purpose. This global framework is validated using two empirical data sets: an urban data set gathered in Portland, Oregon (USA) and a periurban data set from Lyon (France). The model calibration is eased through the use of the δ-MRD; this property opens new research directions about the mapping between traffic states and statistical modeling. It comes out from all these considerations that the Halphen family is suitable to describe accurately the travel time dynamics on single links. Therefore it could be part of a decision support system for practitioners interested in travel time variability.

Published
2017

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