Modélisation stochastique macroscopique d'ordre supérieur du trafic sur les réseaux routiers : implications managériales

Auteurs

DOI :

https://doi.org/10.53102/2023.37.02.1156

Mots-clés :

Gestion de trafic , Modélisation stochastique du trafic , Modèles GSOM stochastique lagrangien

Résumé

Les systèmes de transport jouent un rôle primordial dans le développement de la croissance économique des pays. Cependant, l'apparition des véhicules autonomes et électriques et les restrictions mises en place pour limiter la diffusion et les impacts du Covid-19 dans les transports en commun ont eu un impact important sur l’augmentation des problèmes de transport notamment aux intersections. Le présent papier aide à résoudre ces problèmes. Cet article s'intéresse à la modélisation stochastique des flux du trafic sur les réseaux routiers, grâce à des modèles macroscopiques génériques de second ordre : la famille GSOM. Il a été montré que de tels modèles d'ordre supérieur peuvent être résolus dans un cadre lagrangien dont les coordonnées lagrangiennes se déplacent avec le trafic. La difficulté d'utiliser cette solution de résolution sur un réseau est de traiter les discontinuités eulériennes – fixes – telles que les jonctions. L'objectif de ce travail est double : d'une part, proposer des modèles d’intersection adaptés aux modèles stochastiques macroscopiques de flux de trafic de second ordre, et d'autre part, résoudre le modèle résultant dans le cadre d’un réseau routier. Quelques exemples numériques sont fournis pour montrer l'efficacité de l'approche proposée.

Biographies des auteurs

Asma KHELIFI, ESLI - GIP CEI, École Supérieure de Logistique Industrielle

Asma Khelifi is an associate professor at  ESLI - GIP CEI, École Supérieure de Logistique Industrielle. She is a Ph.D in Industrial Engineering at Université Gustave Eiffel, IFSTTAR/GRETTIA, France. Area of research: traffic flow modeling based on hybrid model, junction modeling, application of the advanced technique for the traffic control of road networks and the incident management, monitoring and traffic control of motorway corridor, and motorway ramp metering control.

Voir plus

Jean-Patrick LEBACQUE , Université Gustave Eiffel, IFSTTAR/GRETTIA

Jean-Patrick Lebacque is a professor at Université Gustave Eiffel IFSTTAR/GRETTIA France, ENPC France. He is a general engineer of Roads and Bridges France, CERMICS France. He is a researcher on applied mathematics, transportation engineering, computer science and scientific computing, and transport economics.

Voir plus

Habib HAJ-SALEM, Université Gustave Eiffel, IFSTTAR/GRETTIA

Habib Haj-Salem is a research director and responsible of the traffic modeling and control research area at Université Gustave Eiffel IFSTTAR/GRETTIA France, UEVP, IUP France University of Paris XII France, and ENTPE of Lyon France. He is a professor researcher on automatic control, numerical analysis and electronics, traffic flow modeling, hybrid modeling

Voir plus

Références

Aw and Rascle, M. (2000). Resurrection of second order models of traffic flow, in SIAM journal on applied mathematics. DOI: https://doi.org/10.1137/S0036139997332099 DOI: https://doi.org/10.1137/S0036139997332099

Bagnerini, P., Rascle, M.A. (2003). multiclass homogenized hyperbolic model of traffic flow. SIAM journal on mathematical analysis 35 (4), 949–973. DOI: https://doi.org/10.1137/S0036141002411490. DOI: https://doi.org/10.1137/S0036141002411490

Bara, N., (2021), Problèmes méthodologiques posés par les systèmes de valorisation dans les modèles économiques de management industriel. Revue Française de Gestion Industrielle. DOI : https://doi.org/10.53102/2021.35.01.905 DOI: https://doi.org/10.53102/2021.35.01.905 [RFGI]

Barcello, J. (2010). Fundamentals of Traffic Simulation. International Series in Operations Research and Management Science. Barcelona, Spain, pp. 68-69. DOI: https://doi.org/10.1051/matecconf/20181500300

Bar-Gera, H., and Ahn, S. (2010). Empirical macroscopic evaluation of freeway merge-ratios, in Transportation Research Part C: Emerging Technologies. DOI: https://doi.org/10.1016/j.trc.2009.09.002 DOI: https://doi.org/10.1016/j.trc.2009.09.002

Benzidia, S. (2012). Les places de marché électroniques: vers une e-supply chain coopérative. Revue Française de Gestion Industrielle, 31(1), 59-82. DOI : https://doi.org/10.53102/2012.31.01.647 DOI: https://doi.org/10.53102/2012.31.01.647

Benzidia, S. (2014). Les apports transactionnels et relationnels des enchères inversées B2B. Revue française de gestion industrielle, 33(1), 105-121. DOI : https://doi.org/10.53102/2014.33.01.720 DOI: https://doi.org/10.53102/2014.33.01.720 [RFGI]

Bexelius, S. (1968). An extended model for car-following, in Transportation Research Part B. DOI: https://doi.org/10.1016/0041-1647(68)90004-X

Boel, R., Mihaylova, L.A. (2006). Compositional stochastic model for real-time freeway traffic simulation. Transportation Research Part B 40 (4), pp 319-334. DOI: https://doi.org/10.1016/j.trb.2005.05.001 DOI: https://doi.org/10.1016/j.trb.2005.05.001

Cohen, S., et al. (2014). Assessing The Impact Of Speed Limit Changes On Urban Motorways: A Simulation Study In Lille, France, 17thXMeeting of the EURO Working Group on Transportation, EWGT2014, Sevilla, Spain. Transportation Research ProcediaX3 (2014) 915 – 924. DOI: https://doi.org/10.1016/j.trpro.2014.10.071

Colombo, R.M. (2002). Hyperbolic traffic flow model, in Mathematical and computer modelling. DOI: https://doi.org/10.1016/S0895-7177(02)80029-2 DOI: https://doi.org/10.1016/S0895-7177(02)80029-2

Dundon, N., Sopasakis A. (2007). Stochastic modelling and simulation of multi-lane traffic. Proceedings of the 17th ISTTT, ppX661-689. Link: https://lup.lub.lu.se/record/2201921

Fan, J., et al. (2013). Characterization of the sterol 14α-demethylases of Fusarium graminearum identifiesXaXnovelXgenus-specificXCYP51Xfunction. DOI: https://doi.org/10.1111/nph.12193 DOI: https://doi.org/10.1111/nph.12193

Friedrich, M. (2015). Multimodal Transport planning. Stuttgart University, Germany.

Garavello, M., and Piccoli, B. (2006). Traffic flow on networks, in American institute of mathematical sciences Spring field MO, USA. ISBN-10: 1-60133-000-6. ISBN-13: 978-1-60133-000-0.

Gazis, D.C., Herman, R., Rothery, W. (1961). Nonlinear follow-the-leader models of traffic flow, in Operation Research. DOI: https://doi.org/10.1287/opre.9.4.545 DOI: https://doi.org/10.1287/opre.9.4.545

Gertrude SAEM, 2018. IntelligentXtransport service. RetrievedXJanuaryX8, 2018, from http:// www.gertrude.fr/nos-missions/systeme-de-transport-intelligent/

Godunov, S.K. (1959). A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics, in Matematicheskii Sbornik.

Herty, M., Kirchner, C., Moutari, S., Rascle, M. (2008). Multicommodity flows on road networks. Communications in Mathematical Sciences 6 (1), 171–187. DOI. https://doi.org/10.4310/CMS.2008.v6.n1.a8 DOI: https://doi.org/10.4310/CMS.2008.v6.n1.a8

Hoogendoorn, S.P., van Lint H., Knoop V. (2007). Dynamic First Order Modeling of Phase-Transition Probabilities. In: Appert Rolland, C., Chevoir, F., Gondret, P., Lassarre, S., Lebacque, J., Schreckenberg, M. (eds.), Traffic and Granular Flow ’07. Springer, New York. DOI: https://doi.org/10.1007/s13676-014-0045-5 DOI: https://doi.org/10.1007/s13676-014-0045-5

Jabari, S.A., Liu H.X. (2012). A stochastic model of traffic flow: Theoretical foundations. Transportation Research Part B 46 pp 156-174. DOI: https://doi.org/10.1016/j.trb.2011.09.006 DOI: https://doi.org/10.1016/j.trb.2011.09.006

Jabari, S.A., Liu H.X. (2013). A stochastic model of traffic flow: Gaussian approximation and estimation. Transportation Research Part B: Methodological Volume 47, JanuaryX2013, pp 15-41. DOI: https://doi.org/10.1016/j.trb.2012.09.004 DOI: https://doi.org/10.1016/j.trb.2012.09.004

Jin, W., Zhang, H.M. (2004). Multicommodity kinematic wave simulation model for network traffic flow. Transportation Research Record: Journal of the Transportation Research Board 1883 (1), 26 59–67. DOI: https://doi.org/10.3141/1883-07 DOI: https://doi.org/10.3141/1883-07

Khelifi, A., et al. (2017). Lagrangian generic second order traffic flow models for node. Journal of Traffic and Transportation Engineering (English Edition), Volume 5, Issue 1, Pages 14-27. DOI: https://doi.org/10.1016/j.jtte.2017.08.001 DOI: https://doi.org/10.1016/j.jtte.2017.08.001

Khelifi, A., et al. (2015). Lagrangian discretization of Generic Second Order Models: Application to Traffic Control. Applied Mathematics & Information Sciences journal, 10, No. 4, Pages: 1243-1254, 2016. DOI: https://doi.org/10.18576/amis/100404 DOI: https://doi.org/10.18576/amis/100404

Kim, T., Zhang H.M. (2008). A stochastic wave propagation model. Transportation Research Part B: Methodological, 42, Issues 7–8, Pages 619-634, 2008. DOI : https://doi.org/10.1016/j.trb.2007.12.002 DOI: https://doi.org/10.1016/j.trb.2007.12.002

Klar, A., Greenberg, J., Rascle, M. (2003). Congestion on multilane highways. SIAM Journal on Applied MathematicsX63X (3), 818–833. DOI: https://doi.org/10.1137/S0036139901396309 DOI: https://doi.org/10.1137/S0036139901396309

Khoshyaran, M.M., and Lebacque, J.P. (2008). Lagrangian modelling of intersections for the gsom generic macroscopic traffic flow model, in Proceedings of the 10th International Conference on Application of Advanced Technologies in Transportation, Athens, Greece.

Khoshyaran, M.M., and Lebacque, J.P. (2009). A stochastic macroscopic traffic model devoid of diffusion, in Traffic and GranularFlow’07, Springer. DOI: https://doi.org/10.1007/978-3-540-77074-9_12

Kühne, R., Mahnke, R. (2005). Controlling Traffic Breakdowns, Transportation and Traffic Theory, Volume null, Issue null, Pages 229-244. DOI: https://doi.org/10.1016/B978-008044680-6/50014-3

Lebacque, J.P. (1984). Semimacroscopic simulation of urban traffic. Proc. of the Int. 84 Min-. neapolis Summer Conference. AMSE 4 (1984), pp. 273-291.

Lebacque, J.P., Haj-Salem, H., and Mammar, S. (2005). Second order traffic flow modeling: supply-demand analysis of the inhomogeneous Riemann problem and of boundary conditions, in Proceedings of the 10th Euro Working Group on Transportation. Journal ISSN : 0866-9546. Journal e-ISSN:2300-8830.

Lebacque, J.P., Haj-Salem, H., and Mammar, S. (2008). An intersection model based on the GSOM model, in Proceedings of the 17th World Congress, Seoul, Korea. DOI: https://doi.org/10.3182/20080706-5-KR-1001.01212. DOI: https://doi.org/10.3182/20080706-5-KR-1001.01212

Lebacque, J.P. Haj-Salem, H., and Mammar, S. (2007). Generic second order traffic flow modeling, in Proceeding of International Symposium on Transportation and Traffic Flow theory, London. DOI: https://doi.org/10.1016/j.ifacol.2018.07.011 DOI: https://doi.org/10.1016/j.ifacol.2018.07.011

Lebacque, J.P., and Khoshyaran, M.M. (2013). A variational formulation for higher order macroscopic traffic flow models of the GSOM family, in Proceeding of International Symposium on Transportation and Traffic Flow theory. DOI: https://doi.org/10.1016/j.trb.2013.07.005 DOI: https://doi.org/10.1016/j.trb.2013.07.005

Lebacque, J.P., Khoshyaran, M.M. (2005). First-order macroscopic traffic flow models: Intersection modeling, network modeling. In: Transportation and Traffic Theory. Flow, Dynamics and Human Interaction. 16th International Symposium on Transportation and Traffic Theory. Availability: http://worldcat.org/isbn/0080446809 DOI: https://doi.org/10.1016/B978-008044680-6/50021-0

Lebacque, J.P., and Khoshyaran, M.M. (2002). First order macroscopic traffic flow models for networks in the context of dynamic assignment, in Transportation Planning, Springer. DOI: https://doi.org/10.1007/0-306-48220-7_8 DOI: https://doi.org/10.1007/0-306-48220-7_8

Lebacque, J.P. (1996). The Godunov scheme and what it means for first order traffic flow models, in International symposium on transportation and traffic theory. Availability: http://worldcat.org/isbn/0080425860

Lebacque, J.P. (2003). Intersection modeling, application to macroscopic network traffic flow modelling and traffic management. Proceedings of the TGF’03 Traffic Granular Flow Conference, (Delft). ISBN: 978-3-540-28091-0.

Leclercq, L., Laval, J. A. and Chevallier, E. (2007). The lagrangian coordinates and what it means for first order traffic flow models, in Transportation and Traffic Theory. Availability: Order URL: http://worldcat.org/isbn/9780080453750

Leo, C.J., and Pretty, R.L. (1992). Numerical simulation of macroscopic continuum traffic models, in Transportation Research Part B. DOI: https://doi.org/10.1016/0191-2615(95)00007-Z DOI: https://doi.org/10.1016/0191-2615(92)90025-R

Lesuseur-Cazé M.; Bironneau L.; Lux G. ; Morvan T., (2022). Réflexions sur les usages de la blockchain pour la logistique et le Supply Chain Management : une approche prospective. Revue Française de Gestion Industrielle. DOI : https://doi.org/10.53102/2022.36. 01.917 DOI: https://doi.org/10.53102/2022.36.01.917 [RFGI]

Lighthill, M.J., and Whitham, G.B. (1955). On kinematic waves ii : A theory of traffic flow on long crowded roads, in. ProRoySoc. DOI: https://doi.org/10.1098/rspa.1955.0089 DOI: https://doi.org/10.1098/rspa.1955.0089

May, A.D. (1990). Traffic Flow Fundamentals, Prentice Hall Englewood Cliffs, New Jersey. ISBN:0139260722 9780139260728.

Ngoduy, D. (2006). Derivation of Continuum Traffic Model for Weaving Sections. On Freeways. Transportmetrica. Vol. 2, No. 3, pp. 199-222. DOI: https://doi.org/10.1080/18128600608685662 DOI: https://doi.org/10.1080/18128600608685662

Princeton. J., Cohen. S. (2011). Impact of a Dedicated Lane on the Capacity and the Level of Service of an Urban Motorway. 6thXInternational Symposium on Highway Capacity and Quality of Service Stockholm, Sweden. DOI: https://doi.org/10.1016/j.sbspro.2011.04.442 DOI: https://doi.org/10.1016/j.sbspro.2011.04.442

Richards, P.I. (1956). Shock waves on the highway, in Operations research. DOI: https://doi.org/10.1287/opre.4.1.42 DOI: https://doi.org/10.1287/opre.4.1.42

Sopasakis, A., Katsoulakis, M. (2006). Stochastic modelling and simulation of traffic flow: Asymmetric single exclusion process with Arrhenius look-ahead dynamics. SIAM Journal on AppliedXMathematicsX66 (3), ppX921-944. DOI: https://doi.org/10.1137/040617790 DOI: https://doi.org/10.1137/040617790

Sumalee, A., Zhong, R.X., Szeto, W.Y., and Pan, T.L. (2011). Stochastic cell transmission model (SCTM): A stochastic dynamic traffic model for traffic state surveillance and assignment. Transportation Research Part BX45 pp 507-533. DOI: https://doi.org/10.1177/0361198120937704 DOI: https://doi.org/10.1016/j.trb.2010.09.006

Tordeux, A., Roussignol, M., Lebacque, J.P., Lassarre, S. (2013). A stochastic jump process applied to traffic flow modelling. Transportmetrica A: Transport Science. DOI: https://doi.org/10.1080/23249935.2013.769648 DOI: https://doi.org/10.1080/23249935.2013.769648

Van Wageningen-Kessels, F., Yuan, Y., Hoogendoorn, S.XP., Lint, L. V., and Vuik, (2013). Discontinuities in the lagrangian formulation of the kinematic wave model, in Transportation Research Part C: Emerging Technologies. DOI: https://doi.org/10.1016/j.trc.2011.08.004 DOI: https://doi.org/10.1016/j.trc.2011.08.004

Wang, Y., Papageorgiou, M., Messmer, M. (2007). Real-Time Freeway Traffic State Estimation Based on Extended Kalman Filter: A Case Study. Transportation Science, Vol. 41, No. 2, pp. 167-181. https://www.jstor.org/stable/25769344 DOI: https://doi.org/10.1287/trsc.1070.0194

Weits, E. (1992). Stationary freeway traffic flow modelled by a linear stochastic partial differential equation. Transportation Research B, 26, 2, pp 115-126. https://www.jstor.org/stable/23070140 DOI: https://doi.org/10.1016/0191-2615(92)90002-E

Zhang, H.M. (2002). A non-equilibrium traffic model devoid of gas-like behaviour, in Transportation Research Part B. DOI: https://doi.org/10.1016/S0191-2615(00)00050-3 DOI: https://doi.org/10.1016/S0191-2615(00)00050-3

Zhang, P., Wong, S., Dai, S. (2009). A conserved higher-order anisotropic traffic flow model: description of equilibrium and non-equilibrium flows. Transportation Research Part B: MethodologicalX18 43 (5), 562–574.XDOI: https://doi.org/10.1016/j.trb.2008.10.001 DOI: https://doi.org/10.1016/j.trb.2008.10.001

Téléchargements

Publiée

21-09-2023

Soumis

19-09-2022

Comment citer

KHELIFI, A., LEBACQUE , J.-P. ., & HAJ-SALEM, H. . (2023). Modélisation stochastique macroscopique d’ordre supérieur du trafic sur les réseaux routiers : implications managériales. Revue Française De Gestion Industrielle, 37(2), 71–86. https://doi.org/10.53102/2023.37.02.1156

Rubrique

Article

Statistiques

Vues: 143
Téléchargements: 67

Articles similaires

Vous pouvez également Lancer une recherche avancée de similarité pour cet article.