Abstract
The present work aims to compare the classic relations between density and speed in the context of continuous models of vehicular traffic, integrating a linear dependence of the spatial variable. Database from NGSIM was used in order to accomplish such task, specifically that belonging to I-80 highway. Furthermore, to make a balanced comparison, the parameters of the classical relations were also estimated without the linear modification of the spatial variable.
References
J.M. Alvarenga-Rodríguez, Reconstrucción del proyecto NGSIM, Youtube. https://youtu.be/hln3F8TRmKY
J. Buli, Y. Xing, A discontinuous Galerkin method for the aw-rascle traffic flow model on networks, Journal of
Computational Physics 406(2020), article 109183. Doi: 10.1016/j.jcp.2019.109183
J.L. Drake, J.L. Schofer, A statistical analysis of speed-density hypotheses, High Research Record 154(1966), 53–87.
D.R. Drew, Traffic flow theory and control, McGraw-Hill, New York NY, 1968.
P. Goatin, E. Rossi, A multiLane macroscopic traffic flow model for simple networks, SIAM Journal on Applied Mathematics 79(2019), no. 5, 1967–1989. Doi: 10.1137/19M1254386
H. Greenberg, An analysis of traffic flow, Op res, 7(1959), no. 1, 79–85. Doi: 10.1287/opre.7.1.79
B.D. Greenshields, J.R. Bibbins, W.S. Channing, H.H. Miller, A study of traffic capacity, High Research Board Proc.14(1935), no. 1, 448–477.
M.J. MacNicholas, A simple and pragmatic representation of traffic flow, in: Symp on the Fundamental Diagram: 75 Years (Greenshields 75 Symposium), Transportation Research Board, Woods Hole MA, United States, 2011. pp. 161–177.
L.A. Pipes, Car following models and the fundamental diagram of road traffic, Transp Res 1(1967), no. 1, 21–29. Doi: 10.1016/0041-1647(67)90092-5
Transportation.gov, Next Generation Simulation (NGSIM) Vehicle Trajectories and Supporting Data, U.S. Department of transportation, 2017. https://data.transportation.gov/Automobiles/Next-Generation-Simulation NGSIM-Vehicle-Trajector/8ect-6jqj
R.T. Underwood, Speed, Volume, and Density Relationships: Quality Theory of Traffic Flow. Yale University Bureau of Highway Traffic, University Park, PA, United States,1961, pp. 141–187.
P. Zhang, R. Liu, Hyperbolic conservation laws with space-dependent flux: I. Characteristics theory and Riemann problem, Jou. Comp. App. Maths.156(2003), no. 1, 1–21. Doi: 10.1016/S0377-0427(02)00880-4