A Vehicular Traffic Flow Model Based on a Stochastic Acceleration Process

Waldeer, K.T.

doi:10.1081/tt-120030341

Cited by 10 publications

(15 citation statements)

References 35 publications

(62 reference statements)

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“…In order to verify the algorithm formulated at the end of Section 2, we took three test problems that have known analytic solutions in the case of stochastic equilibrium; these solutions were presented in [13,14]. The first two examples consider a spatially homogeneous, almost free stationary VTF, where all the vehicles have velocities close to some mean velocity V ≫ 0.…”

Section: Numerical Resultsmentioning

confidence: 99%

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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

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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.

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Section: Numerical Resultsmentioning

confidence: 99%

“…The following semiheuristic fact is well known: for N → ∞ under the assumption of the 'vehicle chaos' (see, e.g., [11,12,14]), i.e., the factorization of the twoparticle density, the solution to equation (2.1) turns into the solution to equation (1.1) [5].…”

Section: Construction Of the Basic Integral Equationmentioning

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

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“…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

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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.

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“…However, this early traffic jam analysis model did not consider physical parameters of cars and environment such as acceleration and gravity force, tire conditions or a driver's reaction time. More complex car following models have been developed and evaluated in the meantime, a clearly arranged overview is given e. g. in [7], [8], [9], [10].…”

Section: Modeling Traffic Flowmentioning

confidence: 99%

“…Dry asphalt with summer tires, good road conditions (7) Typical value on dry asphalt (8) Kinetic friction is about 70 to 80% of static friction (9) According to the Computer Support Group (CSG), http://www.csgnetwork.com/stopdistcalc.html (10) 3 Braking: Static friction (µ) 0.05 (5) 1.0 (6) 0.75 (7) Kinetic friction (µ) (8) (9) 0.5 1.0 0.5 + rnd(0.5)…”

Section: A Model Characteristicsmentioning

confidence: 99%

Effect of Proactive Braking on Traffic Flow and Road Throughput

Riener

Ferscha

2009

2009 13th IEEE/ACM International Symposium on Distributed Simulation and Real Time Applications

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Abstract-With the emergence of pervasive computing technologies into vehicles, driving has moved from an active task of steering towards an interaction or adaptation task with respect to the driver-vehicle feedback loop. Up to now vehicular interfaces have mostly been evaluated from a single-driver singlecar viewpoint, however, driving is a more complex task involving -beside the local interaction -the interrelationship between all the cars in a certain community of interest.The question investigated in this research work is how a vehicle's local parameters in a bulk of cars (e. g. vehicle speed, braking parameters) affect the global behavior of this system (traffic congestion, driving speed variation, throughput). To explore this, two traffic models have been developed and simulated using the NetLogo simulation environment.Simulation results have shown that the intercar distance has a direct impact on both the throughput and the mean trip time. The proactive driving approach using vibro-tactile driver notification followed in the second, advanced model achieved much better results regarding these parameters compared to the simple manual-driven case. Finally, the outcomes legitimate the implementation of a prototype, and the installation of such a technology into a large number of cars in order to provide evidence for the improved traffic flow and decreased probability of traffic accidents in real driving scenarios.Index Terms-Traffic congestion, Stop-and-go traffic, Trip time, Intercar distance, Throughput, ACC, Vibro-tactile notification, Complex adaptive systems. I. PERVASIVE COMPUTING REVOLUTIONIZES TRAFFICSince the diffusion of pervasive computing technologies into cars both vehicle handling (steering, braking, accelerating, etc.) and driving comfort (route guiding, communication, driving assistance, entertainment, etc.) have changed massively [1] and have led, particularly for the formerly traditional controls, to a strong interrelationship between the driver and the technical systems in a car.Up to now, most of these advances concern the interaction between a single driver and a single car. With latest achievements in wireless communication technologies, a new class of vehicle-to-"x" applications arises, allowing the spontaneous formation of collections of cars (cooperative crowds) to offer car-to-car (safety functions, proactive traffic jam avoidance, accident prevention, negotiation of driving parameters, etc.), car-to-roadside and car-to-infrastructure applications. A. Complex Adaptive Systems (CASs)Bulks of cars on a road segment of interest can be assumed to be complex adaptive systems, as it can be observed that every driver-car pair acts on its own interests (following its local navigation goal using different strategies such as reaching the destination as fast as possible, as cheap as possible with respect to road toll, as short as possible regarding the distance, etc.) and affected by the personal style of driving, leading to a (apparently) random behavior of the collection of these pairs. Howeve...

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A Vehicular Traffic Flow Model Based on a Stochastic Acceleration Process

Cited by 10 publications

References 35 publications

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

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

Dynamics of Bimodality in Vehicular Traffic Flows

Effect of Proactive Braking on Traffic Flow and Road Throughput

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