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Two dimensional anisotropic macroscopic second-order traffic flow model

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Języki publikacji
EN
Abstrakty
EN
In the past, the density-gradient term of second-order macroscopic models was replaced with a speed-gradient term to rectify the rearward movement of traffic waves. Hither, a classical speed-gradient macroscopic model is extended to account for the lateral flow dynamics on a multi-lane road. The anisotropic model is modified to capture some inherent vehicular multi-lane traffic features; lateral viscosity and velocity differentials. These variables are quantized within the scope of a two-dimensional spatial domain as opposed to the existing one-dimensional model. A detailed exemplification of acceleration and deceleration waves, stop-and-go waves, and cluster effects are presented to explain the path of information flow. All these non-linear flow properties are evident throughout the simulation.
Rocznik
Strony
59--71
Opis fizyczny
Bibliogr. 26 poz., rys.
Twórcy
  • Department of Mathematics, Presbyterian University College, Ghana
  • African Institute for Mathematical Sciences, Ghana
Bibliografia
  • [1] Lighthill, M.J., & Whitham, G.B. (1955). On kinematic waves II: A theory of traffic flow on long crowded roads. Proceedings of the Royal Society of London. Series A Mathematical and Physical Sciences, 229(1178), 317-345.
  • [2] Richards, P.I. (1956). Shock waves on the highway. Operations Research, 4(1), 42-51.
  • [3] Payne, H.J. (1971). Models of freeway traffic and control. In: G.A. Bekey (ed.), Mathematical Models of Public Systems (Simulation Council, La Jolla, CA), 1, 51-61.
  • [4] Daganzo, C.F., Lin, W.H., & Del Castillo, J. (1997). A simple physical principle for the simulation of freeways with special lanes and priority vehicles. Transportation Research Part B: Methodological, 31(2), 103-125.
  • [5] Lebacque, J.P. (2002). A two phase extension of the LWR model based on the boundedness of traffic acceleration. In: M. Taylor (ed.), Transportation and traffic theory in the 21st century. Proceedings of the 15th International Symposium on Transportation and Traffic Theory, p. 697-718.
  • [6] Whitham, G.B. (1974). Linear and Nonlinear Waves. New York: John Wiley and Sons.
  • [7] Daganzo, C.F. (1995). Requiem for second-order approximations of traffic flow. Transportation Research B, 29(4), 277-286.
  • [8] Zhang, H.M. (1998). A theory of nonequilibrium traffic flow. Transportation Research B, 32(7), 485-498.
  • [9] Zhang, H.M. (2002). A non-equilibrium traffic model devoid of gas-like behavior. Transportation Research Part B, 36, 275-290.
  • [10] Aw, A., & Rascle, M. (2000). Resurrection of “second order” models of traffic flow. SIAM Journal on Applied Mathematics, 60(3), 916-938.
  • [11] Jiang, R., Wu, Q.S., & Zhu, Z.J. (2002). A new continuum model for traffic flow and numerical tests. Transportation Research Part B, 36, 405-419.
  • [12] Khan, Z.H., Gulliver, T.A., Nasir, H., Rehman, A., & Shahzada, K. (2019). A macroscopic traffic model based on physiological response. Journal of Engineering Mathematics, 115(1), 21-41.
  • [13] Khan, Z.H., Imran, W., Azeem, S., Khattak, K.S., Gulliver, T.A., & Aslam M.S. (2019). A macroscopic traffic model based on driver reaction and traffic stimuli. Applied Sciences, 9, 2848.
  • [14] Yu, L., Li, T., & Shi, Z. (2010). The effect of diffusion in a new viscous continuum traffic model. Physics Letters A, 374, 2346-2355.
  • [15] Herty, M., Moutari, S., & Visconti, G. (2018). Macroscopic modeling of multi-lane motorways using a two-dimensional second-order model of traffic flow. Society for Industrial and Applied Mathematics, 78(4), 2252-2278.
  • [16] K¨uhne, R. (1984). Macroscopic freeway model for dense traffic-stop-start waves and incident detection. In: J. Vollmuler & R. Hamerslag (ed). Proceedings of the 9th International Symposium on Transportation and Traffic Theory (ISTTT9), 21-42.
  • [17] Kerner, B.S., & Konh¨auser, P. (1994). Structure and parameters of clusters in traffic flow. Physical Review E, 50, 54-83.
  • [18] Berg, P., Mason, A., & Woods, A. (2000). Continuum approach to car-following models. Physical Review E, 61, 1056-1066.
  • [19] Janna, W.S. (2010). Introduction to Fluid Mechanics. CRC Press, Taylor & Francis Group.
  • [20] Versteeg, H.K., & Malalasekera, W. (2007). An Introduction to Computational Fluid Dynamics; The Finite Volume Method. Pearson, Prentice Hall.
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  • [22] Rosas-Jaimes, O.A., Luckie-Aguirre, O., & Rivera, J.C.L. (2013). Sensitivity parameter of a microscopic traffic model. Congreso Nacional de Control Autom´atico, Ensenada, Baja California, Mexico.
  • [23] Del Castillo, J.M., & Benitez, F.G. (1995). On functional form of the speed-density relationship - i: general theory, ii: empirical investigation. Transportation Research B, 29, 373-406.
  • [24] Courant, R., Friedrichs, K., & Lewy, H. (1967). On the partial difference equations of mathematical physics. IBM Journal, 11, 215-234.
  • [25] British Columbia Ministry of Transportation (2003). Review and analysis of posted speed limits and speed limit setting practices in British Columbia.
  • [26] Herrmann, M., & Kerner, B.S. (1998). Local cluster effect in different traffic flow models. Physica A, 255, 163-188.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-3f614c9a-0d41-47fd-9348-a85b6f2de6ff
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