Microscopic traffic flow model


Microscopic traffic flow model

Microscopic traffic flow models are a class of scientific models of vehicular traffic dynamics.

In contrast to macroscopic models, microscopic traffic flow models simulate single vehicle-driver units, thus the dynamic variables of the models represent microscopic properties like the position and velocity of a single vehicle.

Contents

Car-following models

Also known as time-continuous models, all car-following models have in common that they are defined by ordinary differential equations describing the complete dynamics of the vehicles' positions xα and velocities vα. It is assumed that the input stimuli of the drivers are restricted to the own velocity vα, the net distance (bumper-to-bumper distance) sα: = xα − 1xαlα − 1 to the leading vehicle α − 1 (lα − 1 denotes the vehicle length), and the velocity vα − 1 of the leading vehicle. The equation of motion of each vehicle is characterized by an acceleration function that depends on those input stimuli:

\ddot{x}_\alpha(t) = \dot{v}_\alpha(t) = F(v_\alpha(t), s_\alpha(t), v_{\alpha-1}(t))

In general, the driving behavior of a single driver-vehicle unit α might not merely depend on the immediate leader α − 1 but on the na vehicles in front. The equation of motion in this more generalized form reads:

\dot{v}_\alpha(t) = f(x_\alpha(t), v_\alpha(t), x_{\alpha-1}(t), v_{\alpha-1}(t), \ldots, x_{\alpha-n_a}(t), v_{\alpha-n_a}(t))

Examples of car-following models

Cellular automaton models

Cellular automaton (CA) models are using integer variables to describe the dynamical properties of the system. The road is divided into sections of a certain length Δx and the time is discretized to steps of Δt. Each road section can either be occupied by a vehicle or empty and the dynamics are given by update rules of the form:

v_\alpha^{t+1} = f(s_\alpha^t, v_\alpha^t, v_{\alpha-1}^t, \ldots)
x_\alpha^{t+1} = x_\alpha^t + v_\alpha^{t+1}

(the simulation time t is measured in units of Δt and the vehicle positions xα in units of Δx).

The time scale is typically given by the reaction time of a human driver, Δt = 1s. With Δt fixed, the length of the road sections determines the granularity of the model. At a complete standstill, the average road length occupied by one vehicle is approximately 7.5 meters. Setting Δx to this value leads to a model where one vehicle always occupies exactly one section of the road and a velocity of 5 corresponds to x / Δt = 135km/h, which is then set to be the maximum velocity a driver wants to drive at. However, in such a model, the smallest possible acceleration would be Δx / (Δt)2 = 7.5m / s2 which is unrealistic. Therefore, many modern CA models use a finer spatial discretization, for example Δx = 1.5m, leading to a smallest possible acceleration of 1.5m / s2.

Although cellular automaton models lack the accuracy of the time-continuous car-following models, they still have the ability to reproduce a wide range of traffic phaenomena. Due to the simplicity of the models, they are numerically very efficient and can be used to simulate large road networks in realtime or even faster.

Examples of CA models


Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Traffic flow — The mathematical or engineering study of traffic flow, and in particular vehicular traffic flow, is done with the aim of achieving a better understanding of these phenomena and to assist in the reduction of traffic congestion problems.The first… …   Wikipedia

  • Intelligent Driver Model — In traffic flow modeling, the Intelligent Driver Model (IDM) is a time continuous car following model for the simulation of freeway and urban traffic.Model definitionAs a car following model, the IDM describes the dynamics of the positions and… …   Wikipedia

  • VISSIM — Infobox Software name = VISSIM developer = PTV Planung Transport Verkehr AG latest release version = VISSIM 5.10 00 (2008) operating system = Microsoft Windows license = Software license agreement genre = Multi modal traffic flow simulation… …   Wikipedia

  • VISSIM — Entwickler PTV Planung Transport Verkehr AG Aktuelle Version VISSIM 5.30 (09/2010) Betriebssystem Microsoft Windows Kategorie Multi modale Verkehrssimulation …   Deutsch Wikipedia

  • VISSIM — Desarrollador PTV Planung Transport Verkehr AG http://www.vissim.de/ Información general Última versión estable VISSIM 5.30 (9/2010) …   Wikipedia Español

  • List of mathematics articles (M) — NOTOC M M estimator M group M matrix M separation M set M. C. Escher s legacy M. Riesz extension theorem M/M/1 model Maass wave form Mac Lane s planarity criterion Macaulay brackets Macbeath surface MacCormack method Macdonald polynomial Machin… …   Wikipedia

  • IDM — may refer to:* Intelligent dance music, a genre of electronic music * Infant of a diabetic mother * Internal Dramatic Monologue (Drama Terminology)In science and technology: * Intelligent Driver Model, a microscopic traffic flow model *… …   Wikipedia

  • Nagel-Schreckenberg-Modell — Das Nagel Schreckenberg Modell (kurz NaSch Modell) ist ein theoretisches Modell zur Simulation des Straßenverkehrs. Es wurde Anfang der 1990er Jahre von den Festkörperphysikern Kai Nagel und Michael Schreckenberg formuliert. Mit Hilfe elementarer …   Deutsch Wikipedia

  • Robert Herman — (August 29, 1914 February 13, 1997) was a United States scientist, best known for his work with Ralph Alpher in 1948 50, on estimating the temperature of cosmic microwave background radiation from the Big Bang explosion.Born in the Bronx, New… …   Wikipedia

  • Dirk Helbing — is a physicist, and professor of sociology, in particular for modelling and simulation. Contents 1 Biography …   Wikipedia