An Analysis of Vehicular Traffic Flow Using Langevin Equation
AbstractTraffic flow data are stochastic in nature, and an abundance of literature exists thereof. One way to express stochastic data is the Langevin equation. Langevin equation consists of two parts. The first part is known as the deterministic drift term, the other as the stochastic diffusion term. Langevin equation does not only help derive the deterministic and random terms of the selected portion of the city of Istanbul traffic empirically, but also sheds light on the underlying dynamics of the flow. Drift diagrams have shown that slow lane tends to get congested faster when vehicle speeds attain a value of 25 km/h, and it is 20 km/h for the fast lane. Three or four distinct regimes may be discriminated again from the drift diagrams; congested, intermediate, and free-flow regimes. At places, even the intermediate regime may be divided in two, often with readiness to congestion. This has revealed the fact that for the selected portion of the highway, there are two main states of flow, namely, congestion and free-flow, with an intermediate state where the noise-driven traffic flow forces the flow into either of the distinct regimes.
Kriso S, Peinke J, Friedrich R, Wagner P. Reconstruction of dynamical equations for traffic flow. Phys Lett A. 2002;299(2-3):287-291. doi:10.1016/S0375-9601(02)00288-8
Wang H, Li J, Chen QY, Ni D. Speed–density relationship: From deterministic to stochastic. The 88th Transportation Research Board (TRB) Annual Meeting. Washington, DC; 2009. Available from: http://people.umass.edu/ndh/Publications/C21.pdf
Schadschneider A. Traffic flow: A statistical physics point of view. Physica A. 2002;313(1-2):153-187. doi:10.1016/S0378-4371(02)01036-1
Boel R, Mihaylova L. A compositional stochastic model for real time freeway traffic simulation. Transportation Research Part B. 2006;40(4):319-334. doi: 10.1016/j.trb.2005.05.001
Kim T, Zhang HM. A stochastic wave propagation model. Transportation Research Part B. 2008;42(7-8):619-634. doi:10.1016/j.trb.2007.12.002
Li J, Chen QY, Wang H, Ni D. Analysis of LWR model with fundamental diagram subject to uncertainties. The 88th Transportation Research Board (TRB) Annual Meeting. Washington DC; 2009. Available from: http://people.umass.edu/ndh/Publications/C22.pdf
Alperovich T, Sopasakis A. Stochastic description of traffic flow. J Stat Phys. 2008;133(6):1083-1105. doi: 10.1007/s10955-008-9652-6
Liebe C, Mahnke R, Kühne R. From traffic breakdown to energy flow analysis. Transp Res Part C Emerg Technol. 2011; 19(2):172-181. doi:10.1016/j.trc.2010.05.005
Laval JA, Leclercq L. The Hamilton–Jacobi partial differential equation and the three representations of traffic flow. Transportation Research Part B. 2013;52:17-30. doi:10.1016/j.trb.2013.02.008
Jabari SE, Liu HX. A stochastic model of traffic flow: Theoretical foundations. Transportation Research Part B. 2012;46(1):156-174. doi:10.1016/j.trb.2011.09.006
Jabari SE, Liu HX. A stochastic model of traffic flow: Gaussian approximation and estimation. Transportation Research Part B. 2013;47:15-41. doi:10.1016/j.trb.2012.09.004
Friedrich R, Siegert S, Peinke J, Lück St, Siefert M, Lindemann M, Raethjen J, Deuschl G, Pfister G. Extracting model equations from experimental data. Phys Lett A. 2000;271(3):217-222. doi: 10.1016/S0375-9601(00)00334-0
Gradisek J, Friedrich R, Govekar E, Grabec I. Analysis of data from periodically forced stochastic processes. Phys Lett A. 2002;294(3-4): 234-238. doi:10.1016/S0375-9601(02)00060-9
Peebles PZ, Jr. Probability, random variables, and random signal principles. Singapore: McGraw-Hill; 1993.
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