Ultradiscrete optimal velocity model: A cellular-automaton model for traffic flow and linear instability of high-flux traffic

Kanai, Masahiro; Isojima, Shin; Nishinari, Katsuhiro; Tokihiro, Tetsuji

doi:10.1103/physreve.79.056108

Cited by 24 publications

(17 citation statements)

References 37 publications

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“…In this work, we solve exactly the discrete delayed OV model firstly introduced in [12] and thereby integrate the previous results of [11] and [12]. In Section 2, we derive the discrete delayed OV model and give exact results.…”

Section: Introductionmentioning

confidence: 98%

Exact solution of a delay difference equation modeling traffic flow and their ultra-discrete limit

Matsuya¹,

Kanai²

2015

Preprint

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We consider a car-following model described by a delay difference equation and give its exact solutions that present propagation of a traffic jam. This model is a discrete-time version of the delayed optimal-velocity model; in the continuum limit, we recover the delay differential equation for this model and the exact solutions as well. We then work in the ultra-discrete limit, obtaining a delay cellular-automaton model, which successfully inherits the solutions. Also the dispersion relation for the present solutions suggests that a quick response of drivers does not always result in fast dissolution of a traffic jam.

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Section: Introductionmentioning

confidence: 98%

Exact solution of a delay difference equation modeling traffic flow and their ultra-discrete limit

Matsuya¹,

Kanai²

2015

Preprint

Self Cite

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“…In the year of 1992, Nagel and Schreckenberg [5] proposed the well-known NaSch model as a form of the promotion. Some other scholars and experts also achieved many research results concerning a variety of traffics or road conditions on that basis [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

An Extended Cellular Automaton Model for Train Traffic Flow on the Dedicated Passenger Lines

Zhao

Qian

Zhang

et al. 2014

Journal of Applied Mathematics

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As one of the key components for the railway transportation system, the Train Operation Diagram can be greatly influenced by many extrinsic and intrinsic factors. Therefore, the railway train flow has shown the strong nonlinear characteristics, which makes it quite difficult to take further relative studies. Fortunately, the cellular automaton model has its own advantages in solving nonlinear problems and traffic flow simulation. Considering the mixed features of multispeed running trains on the passenger dedicated lines, this paper presents a new train model under the moving block system with different types of trains running with the cellular automaton idea. By analyzing such key factors as the maintenance skylight, the proportion of the multispeed running trains, and the distance between adjacent stations and departure intervals, the corresponding running rules for the cellular automaton model are reestablished herewith. By means of this CA model, the program of train running system is designed to analyze the potential impact on railway carrying capacity by various factors; the model can also be implemented to simulate the actual train running process and to draw the train operation diagram by computers. Basically the theory can be applied to organize the train operation on the dedicated passenger lines.

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“…With the improvement of the simulation methods, the CA Model has been widely used for the study of the highway transportation. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] The CA Model has also been used to study the railway transportation, such as train control system, 20,21 railway signaling system, 22 tracking operation system, 23 railway carrying capacity, 24 as well as the railway traffic flow under the automatic block signaling 25,26 But all the above-mentioned studies on railway systems had used the fixed departing time intervals, not considering the signal control effect. In fact, the randomness of a train flow caused by the signal control has a huge impact on the train operation.…”

Section: Introductionmentioning

confidence: 99%

The Carrying Capacity Under Four-Aspect Color Light Automatic Block Signaling Based on Cellular Automata

et al. 2013

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With the application of the dynamic control system, Cellular Automata model has become a valued tool for the simulation of human behavior and traffic flow. As an integrated kind of railway signal-control pattern, the four-aspect color light automatic block signaling has accounted for 50% in the signal-control system in China. Thus, it is extremely important to calculate correctly its carrying capacity under the automatic block signaling. Based on this fact the paper proposes a new kind of "cellular automata model" for the four-aspect color light automatic block signaling under different speed states. It also presents rational rules for the express trains with higher speed overtaking trains with lower speed in a same or adjacent section and the departing rules in some intermediate stations. In it, the state of mixed-speed trains running in the section composed of many stations is simulated with CA model, and the train-running diagram is acquired accordingly. After analyzing the relevant simulation results, the needed data are achieved herewith for the variation of section carrying capacity, the average train delay, the train speed with the change of mixed proportion, as well as the distance between the adjacent stations.

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Ultradiscrete optimal velocity model: A cellular-automaton model for traffic flow and linear instability of high-flux traffic

Cited by 24 publications

References 37 publications

Exact solution of a delay difference equation modeling traffic flow and their ultra-discrete limit

Exact solution of a delay difference equation modeling traffic flow and their ultra-discrete limit

An Extended Cellular Automaton Model for Train Traffic Flow on the Dedicated Passenger Lines

The Carrying Capacity Under Four-Aspect Color Light Automatic Block Signaling Based on Cellular Automata

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