The direct simulation Monte Carlo method applied to a Boltzmann-like vehicular traffic flow model

Waldeer, K.T.

doi:10.1016/s0010-4655(03)00368-0

Cited by 15 publications

(12 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Test calculations showed the stability of algorithms to errors in the initial data. We consider an acceleration oriented vehicular traffic flow (VTF) model, which was proposed in (Waldeer, 2003a). A special feature of this model is introduction of the acceleration variable into the set of phase coordinates, which describe the state of a vehicle, together with its velocity and spatial coordinate, traditionally used in kinetic models.…”

Section: Asymptotic Permutation Tests and Confidence Intervals For Pamentioning

confidence: 99%

“…In contrast to the gas dynamics, the interactions in the system result not in velocity, but in acceleration jumps. Such modification of the phase space allowed in (Waldeer, 2003a) to extend this kinetic model onto a wider class of the VTFs, as it also adequately describes the case of partly constrained flows, and denser VTFs.…”

Section: Asymptotic Permutation Tests and Confidence Intervals For Pamentioning

confidence: 99%

See 1 more Smart Citation

Simulating Correlated Ordinal and Discrete Variables with Assigned Marginal Distributions

Barbiero

Ferrari

2014

Springer Proceedings in Mathematics &Amp; Statistics

View full text Add to dashboard Cite

Section: Asymptotic Permutation Tests and Confidence Intervals For Pamentioning

confidence: 99%

Section: Asymptotic Permutation Tests and Confidence Intervals For Pamentioning

confidence: 99%

Simulating Correlated Ordinal and Discrete Variables with Assigned Marginal Distributions

Barbiero

Ferrari

2014

Springer Proceedings in Mathematics &Amp; Statistics

View full text Add to dashboard Cite

“…Any implementation of an advanced transportation system, therefore, needs a clear view of the present intricacies in traffic flows. Studies of vehicular traffic flows usually aim at understanding interactions among streams of vehicles (modelled occasionally as particles), and a substantial body of relevant work, ranging across multiple perspectives, has already come into existence [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. The practical motive behind these studies is to eliminate the problem of traffic congestion, and to devise effective methods of controlling traffic flow.…”

Section: Bimodality In Vehicular Traffic Flowsmentioning

confidence: 99%

Dynamics of Bimodality in Vehicular Traffic Flows

Mullick¹,

Ray²

2014

JAND

View full text Add to dashboard Cite

A model equation has been proposed to describe bimodal features in vehicular traffic flows. The dynamics of the bimodal distribution reveals the existence of a fixed point that is connected to itself by a homoclinic trajectory. The mathematical conditions associated with bimodality have been established. The critical factors necessary for both a breaking of symmetry and a transition from bimodal to unimodal behaviour, in the manner of a bifurcation, have been analysed.

show abstract

“…In this paper we use the kinetic model of VTF proposed in [13]. The distinctive feature of the model is the introduction of acceleration into the set of phase coordinates describing the state of a vehicle, together with its velocity and its spatial coordinate traditionally used in kinetic models.…”

Section: Kinetic Model Of Vtfmentioning

confidence: 99%

“…Within the model proposed in [13], the one-particle density f (a, v,t) of the vehicle distribution with acceleration a and velocity v satisfies the following integrodifferential equation of the Boltzmann type:…”

Section: Kinetic Model Of Vtfmentioning

confidence: 99%

Application of statistical methods for the study of kinetic model of traffic flow with separated accelerations

Burmistrov

Korotchenko

2011

Russian Journal of Numerical Analysis and Mathematical Modelling

View full text Add to dashboard Cite

The problem of numerical estimation of the functionals of the solutions to a Boltzmann type nonlinear equation in the kinetic model of a vehicle traffic flow with separated acceleration is considered. The authors construct a second-kind integral equation for the original probabilistic model of a vehicle traffic flow, which is related to a linear N-particle model of the vehicle system evolution. Weighted Monte Carlo methods are proposed for the estimation of the functionals of the solution to the obtained equation. The practical suitability of this approach to the solution of traffic problems is demonstrated by numerical experiments. It should be noted that, in contrast to the previous papers, the authors do not use an artificial time step not included in the original traffic flow model.This paper is focused on the study and simulation of a vehicular traffic flow (VTF). The urgency of this problem is related to the permanent growth of the vehicular traffic. This leads to the necessity to improve the traffic system taking into account the mechanisms of its development and the load distribution of its segments.Researchers from different scientific areas have been involved in the study of traffic systems, and now we have voluminous literature concerning the study and simulation of VTF. Two basic approaches have been formed historically in modelling of the vehicular traffic: the deterministic and probabilistic ones. Deterministic models are based on a functional dependence between particular parameters, for example, the velocity and the distance between the vehicles in the flow. Stochastic models of VTF are considered as a probabilistic process. In addition, all models can be divided into three classes: micro-, macro-, and mesoscale ones.Microscope models (e.g., leader-following model [1], cellular automata [10]) use motion equations similar to Newtonian ones written separately for each particle in the system of interacting particles. The driver's behaviour in the models of such type is described by deterministic parameters, or by random functions.Macroscope models (e.g. the Lighthill-Whitham model [7]) simulate the VTF by a flow of a one-dimensional compressible fluid. It is assumed in this case that the flow is preserved (this condition is expressed by the continuity equation) and there exists a one-to-one correspondence between the intensity (or mean velocity) and the density of the VTF.

show abstract

The direct simulation Monte Carlo method applied to a Boltzmann-like vehicular traffic flow model

Cited by 15 publications

References 13 publications

Simulating Correlated Ordinal and Discrete Variables with Assigned Marginal Distributions

Simulating Correlated Ordinal and Discrete Variables with Assigned Marginal Distributions

Dynamics of Bimodality in Vehicular Traffic Flows

Application of statistical methods for the study of kinetic model of traffic flow with separated accelerations

Contact Info

Product

Resources

About