From Random Walker to Vehicular Traffic: Motion on a Circle

Hans Weber (), Reinhard Mahnke () and Jevgenijs Kaupužs ()
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Hans Weber: Luleå University of Technology, Department of Physics
Reinhard Mahnke: Rostock University, Institute of Physics
Jevgenijs Kaupužs: University of Liepaja, Institute of Mathematical Sciences and Information Technologies

A chapter in Traffic and Granular Flow '13, 2015, pp 347-359 from Springer

Abstract: Abstract Driving of cars on a highway is a complex process which can be described by deterministic and stochastic forces. It leads to equations of motion with asymmetric interaction and dissipation as well as to new energy flow law already presented at previous TRAFFIC AND GRANULAR FLOW meetings. Here we consider a model, where motion of an asymmetric random walker on a ring with periodic boundary conditions takes place. It is related to driven systems with active particles, energy input and depot. This simple model can be further developed towards more complicated ones, describing vehicular or pedestrian traffic. Three particular cases are considered, starting with discrete coordinate and time, then making time continuous and, finally, considering a drift–diffusion equation in a continuum limit.

Keywords: Asymmetric Random Walk; Drift-diffusion Equations; Discrete Coordinates; Optimal Velocity Model (OVM); Spiky Appearance (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-10629-8_40

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DOI: 10.1007/978-3-319-10629-8_40

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