Two-dimensional Traffic Flow Model Research Articles

Parametric study of microscopic two-dimensional traffic flow models: A literature review

Indian traffic is highly heterogeneous consisting of all-inclusive vehicle characteristics, occupying any lateral position over the entire road width which results in vehicles continuous interaction with the neighbouring vehicles (in both longitudinal and lateral directions), indicating two-dimensional (2D) traffic manoeuvre, opposite to the traditional one-dimensional (1D) interaction of vehicles in lane based traffic. Certain modifications were made in the existing 1D models to describe the overtaking and lane changing manoeuvre of the mixed traffic stream. However, the continuous lateral manoeuvre of the no-lane based mixed traffic cannot be described by these parameters. This paper initially provides a brief review of different 2D behavioural models, which describe the longitudinal and lateral movements simultaneously. Also, the various existing commercially available traffic micro-simulation frameworks developed for representing the real traffic are reviewed. Different microscopic traffic parameters used in the existing simulation models to mimic the real-world traffic are identified, which can be used to understand the 2D traffic stream.

EVACUATION PROCESS IN TWO-DIMENSIONAL TRAFFIC FLOW MODELS

Within the framework of Biham–Middleton–Levine traffic model with origin–destination trips, we study the evacuation processes of cars in cities. Cars move from the origin to the destination points. A driver which reaches its destination disappears with rate β. It is found that the evacuation processes are greatly influenced by the origin–destination distance probability distribution. We also find that the evacuation time of drivers diverges in the form of a power law τ ∝ β-ν, with ν = 1.

Second-order phase transition in two-dimensional cellular automaton model of traffic flow containing road sections

Two-dimensional cellular automaton model has been broadly researched for traffic flow, as it reveals the main characteristics of the traffic networks in cities. Based on the BML models, a first-order phase transition occurs between the low-density moving phase in which all cars move at maximal speed and the high-density jammed phase in which all cars are stopped. However, it is not a physical result of a realistic system. We propose a new traffic rule in a two-dimensional traffic flow model containing road sections, which reflects that a car cannot enter into a road crossing if the road section in front of the crossing is occupied by another car. The simulation results reveal a second-order phase transition that separates the free flow phase from the jammed phase. In this way the system will not be entirely jammed (“don’t block the box” as in New York City).

A two-dimensional CA model for traffic flow with car origin and destination

Dynamic phase transitions in a two-dimensional traffic flow model defined on a decorated square-lattice are studied numerically. The square-lattice point and the decorated site denote intersections and roads, respectively. In the present model, a car has a finite deterministic path between the origin and the destination, which is assigned to the car from the beginning. In this new model, we found a new phase between the free-flow phase and the frozen-jam phase that is absent from previous models. The new model is characterized by the persistence of a macroscopic cluster. Furthermore, the behavior in this macroscopic cluster phase is classified into three regions characterized by the shape of the cluster. The boundary of the three regions is phenomenologically estimated. When the trip length is short and the car density is high, both ends of the belt-like cluster connect to each other through the periodic boundary with some probability. This type of cluster is classified topologically as a string on a two-dimensional torus.

Numerical Simulations for Traffic Flow in Two-Dimensional Network with Obstacles

We investigate effect of obstacles on formation of a traffic jam for a traffic flow in a network of city roads, by numerical simulations. The network of city roads is implemented in a double-bond square lattice, instead of a usual single-bond square lattice; we assume that each bondhas five d ecoratedsites. A car or an obstacle is assumedto be locatedat one of those decorated sites or lattice sites. Two types (µ and ν types) of cars are assumed; cars of µ type (ν type) move mainly to the positive x (y) direction and change their direction to the positive y (x) direction with a probability. What we found is that a traffic jam is formed more easily for obstacles placedclose to traffic signals in the traffic flow d irection than for those in the other cases. Control of traffic flow is an important subject in our modern society. Traffic jams appear in highways, in networks of city roads or in computer networks and should be avoided if possible. The nature of a transition between a free-movingphase and a traffic-jam phase has to be clarified in order to control the traffic flow. Biham, Middleton and Levin (BML) proposed a two-dimensional traffic flow model on a network of city roads with one lane; 1) there is a crossingat each lattice site and cars are located only at crossings. There are two types of cars in the BML model, each of which moves only to the positive x (y) direction or the positive y direction. They found that there is a phase transition of the first-order type between the free-movingphase and the traffic-jam phase. The BML model has been modified by Cuesta et al. 2) so that cars can change their direction by a probability. In those models, cars move directly from a crossingto its nearest crossingif that movingis allowed. This direct movingfrom a crossingto its nearest crossinghas been lifted by puttingdecorated sites. 3), 4) In the present paper, we investigate effect of obstacles, such as illegally parking cars on roads, on the formation of a traffic jam, by using a network of city roads with two lanes, which is obtained by extendingthe model given by Horiguchi and Sakakibara. 4)

Jamming transition in a two-dimensional traffic flow model.

Phase transition and critical phenomenon are investigated in the two-dimensional traffic flow numerically and analytically. The one-dimensional lattice hydrodynamic model of traffic is extended to the two-dimensional traffic flow in which there are two types of cars (northbound and eastbound cars). It is shown that the phase transition among the freely moving phase, the coexisting phase, and the uniformly congested phase occurs below the critical point. Above the critical point, no phase transition occurs. The value a(c) of the critical point decreases as increasing fraction c of the eastbound cars for c<or=0.5. The linear stability theory is applied. The neutral stability lines are found. The time-dependent Ginzburg-Landau (TDGL) equation is derived by the use of nonlinear analysis. The phase separation lines, the spinodal lines, and the critical point are calculated from the TDGL equation.

Self-Organization and Phase Transition in Two-Dimensional Traffic-Flow Model

An analytical investigation is made on two-dimensional traffic-flow model with alternative movement and exclude-volume effect between right and up arrows. Several exact results are obtained, including the upper critical density above which there are only jamming configurations, and the lower critical density below which there are only moving configurations. The observed jamming transition takes place at another critical density , which is in the intermediate region between the lower and upper critical densities. This transition is suggested to be a second-order phase transition, the order parameter is found. The nature of self-organization, ergodicity breaking and synchronization are discussed. Comparison with the sandpile model is made.

Improved mean-field theory of two-dimensional traffic flow models

An improved mean-field theory is proposed for traffic-flow models in two dimensions, both in the absence and presence of faulty traffic lights. The present theory includes the effects of blockage of cars due to cars moving in the same direction, while previous theories included only the effects of cars moving in the perpendicular direction. In the absence of faulty lights, the theory gives a much better estimate of the critical car density, above which the traffic is in a jamming phase. In the presence of faulty lights, the theory captures all the essential features in published simulation data. It gives the correct behaviour of the velocity in the dilute limit of car density. The dependence of the critical car density on the fraction of faulty traffic lights is studied.

Random versus deterministic two-dimensional traffic flow models.

Deterministic and stochastic cellular automata models available to study two-dimensional traffic flow are compared in this paper. It is shown that a connection between them can be made only when the infinite time and infinite system limits are taken in the appropriate order. We also stress the crucial importance of the choice of boundary conditions in the deterministic model to obtain bulk properties.

Theoretical approach to two-dimensional traffic flow models.

In this paper we present a theoretical analysis of a recently proposed two-dimensional cellular automata model for traffic flow in cities with the ingredient of a turning capability. Numerical simulations of this model show that there is a transition between a freely moving phase with high velocity to a jammed state with low velocity. We study the dynamics of such a model, starting with the microscopic evolution equation, which will serve as a basis for further analysis. It is shown that a kinetic approach, based on the Boltzmann assumption, is able to provide a reasonably good description of the jamming transition. We further introduce a space-time continuous phenomenological model, leading to two partial differential equations whose preliminary results agree rather well with the numerical simulations.

Effect of Jam-Avoiding Turn on Jamming Transition in Two-Dimensional Traffic Flow Model

A stochastic cellular automaton (CA) model is presented to study traffic flow in cities. In order to avoid traffic jam, cars are allowed to turn with probability p turn when cars are blocked ahead by other cars. It is found that the jam-avoiding turn has an important effect on traffic jam. With increasing car density, jamming transitions occur from a maximal velocity phase, through a homogeneously moving phase, to a jamming phase, with a critical point. Above the critical point, the jamming transition does not appear. It is shown that allowing cars to turn results in a complex phase diagram.

Phase transitions in two-dimensional traffic-flow models.

We introduce two simple two-dimensional lattice models to study traffic flow in cities. We have found that a few basic elements give rise to the characteristic phase diagram of a first-order phase transition from a freely moving phase to a jammed state, with a critical point. The jammed phase presents new transitions corresponding to structural transformations of the jam. We discuss their relevance in the infinite-size limit.