An Analysis of Vehicular Traffic Flow Using Langevin Equation

  • Çağlar Koşun IZMIR INSTITUTE OF TECHNOLOGY
  • Hüseyin Murat Çelik ISTANBUL TECHNICAL UNIVERSITY
  • Serhan Özdemir IZMIR INSTITUTE OF TECHNOLOGY
Keywords: Langevin equation, traffic dynamics, Brownian motion, traffic regimes, traffic flow, stochastic forces, drift, diffusion,

Abstract

Traffic 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.

Author Biographies

Çağlar Koşun, IZMIR INSTITUTE OF TECHNOLOGY

Research Assistant Çağlar KOŞUN has Bachelor’s degree of City and Regional Planning in Dokuz Eylül University, Turkey. He has M.Sc. in City Planning at Izmir Institute of Technology, as of January 2010. He has attended the city planning PhD program shortly afterwards. Having passed the PhD qualification exam, he is now dealing with PhD dissertation on traffic flow in an entropy framework.  He is currently a research assistant at Izmir Institute of Technology. His main research interests are statistical analysis, econometrics, intelligent transportation systems, probabilistic reasoning, and artificial intelligence methods.

Hüseyin Murat Çelik, ISTANBUL TECHNICAL UNIVERSITY

Prof. Dr. Hüseyin Murat ÇELİK, working at Istanbul Technical University, has M.Sc. in Urban (Transportation) Planning at University of Kansas, School of Architecture and Urban Design, Graduate Program in Urban Planning, Lawrence-Kansas, USA and he did PhD at Ohio State University, Knowlton School of Architecture, Department of City and Regional Planning, Columbus-Ohio, USA.  He has Bachelor’s degree of City and Regional Planning at Mimar Sinan University, Turkey. Some of his main research interests are transportation planning, traffic engineering, logistics and logistics management, operations research (static and dynamic optimization), forecasting and simulation (statistical analysis, decision theory, and econometrics).

 

Serhan Özdemir, IZMIR INSTITUTE OF TECHNOLOGY

Prof. Dr. Serhan ÖZDEMİR was awarded a scholarship following his graduation from the Mechanical Eng. Dept of Dokuz Eylul University, Izmir, Turkey. Having received his masters degree in 1996 at Illinois Institute of Technology, he went on with his PhD studies at the University of Florida. The thesis has focused on the CVPSTs. On his return, he has founded the artificial intelligence & design lab at Izmir Institute of Technology. Even though the research at the lab ranges from intelligent control of artificial limbs to interpretation of EKG signals by fractals, the lab primarily focuses on the processing of time series for machine health and fault diagnostics.

References

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.

Published
2015-08-31
How to Cite
1.
Koşun Çağlar, Çelik HM, Özdemir S. An Analysis of Vehicular Traffic Flow Using Langevin Equation. PROMET [Internet]. 2015Aug.31 [cited 2020Oct.21];27(4):317-24. Available from: http://traffic.fpz.hr/index.php/PROMTT/article/view/1613
Section
Articles