基于元胞自动机的交通流建模与应用(英文)

Research on Traffic Flow Modeling and Simulation Based on

Cellular Automaton

Abstract:Intelligent transportation system(ITS) improves the situation of transportation systems by managing advanced technologies such as

telecommunication, network, automatic control and traffic engineering to, thus establishing an intelligent, secure, convenient, efficient, comfortable and environmental protection transportation system. Traffic flow modeling is one of the most important parts of ITS. ITS can be categorized as microscopic modeling and macroscopic modeling.

Microscopic traffic models such as cellular automaton (CA) models and hybrid traffic models arisen in recent years have optential values in application.

Key word: CA

Traffic flow modelling Bicycle

I Introduction of Cellular Automaton

The conception of cellular automaton(CA) was firstly put forward by Von Nenmann in the 1950s, it was mainly applied in modelling the function of self-duplication of biosystem. It was paid widely attention to after the confliction of life was put forward by Conway in 1970. After that, CA was applied to various field. Because a simple model type like this could duplicate complex phenomena or dynamically demonstrate

phenomena of attraction, self organization and chaos conveniently.That’s the reason why CA was widely used in modeling diverse physical systems and natural phenomena, such as fluld flow, galaxy formation, snowslide, traffic flow calculation, concurrent computation , earthquake etc. Nowadays, the merits of making use of CA to modeling the physical process is that it can leave out the process using differential equations as transition, and performing nolinear physical phenomenon directly through making rules. In these practical applications, CA model uncovers

macroscopic behavior naturally happened through simple microscopic partial rules. It’s an ideal physical model for studying temporal-spatial discrete, and considered the most effective implement in terms of researching complex system.

CA model is made up of 4 parts basically: cell, lattice, neighbor and rule.Its ordinary features are summarized as follows:

Temporal discrete isometry, it means the deduction of system is

proceeding according to a uniformly-spaced discrete time distribution, the time step dt usually sets time unit 1.

Spatial discrete homogeneity, it reflects that variations of each cell obey the same rule, and the way of distribution of each cell is identical.

Status discrete finite, it means the status of CA can only be taken finite discrete values.

Calculation synchronously and concurrently. Considering the

forming and variation of CA as calculating or disposing of data or

information, it will show up that disposing process of CA is synchronous and concurrent, which means it is adapted to concurrent calculation especially.

Renew rules partially. The current status of each cell can only be affected by ones of its neighborhood. In terms of information transmission, the velocity of it in CA is finite.

Infinite dimension variables. In a dynamic system, the number of variables is often transformed into dimension. Status of each cell is

considered as a variable, so a CA model contains infinite cells is regarded as a type of infinite dimension dynamic system.

The features above are just some ordinary features of CA models. In practical application, builders of models often extent their CA models more or less, breaking through the limitations above to forming various extended CA models. That’s why the field of CA model application is widely. But every extention to CA should keep its ordinary feature , especially the feature of renew rules partially.

In the 1990s, with the demand of traffic flow simulation and the development of intelligent transportation, people attempted to apply the theory of cellular automaton in physics to the field of transportation, so cellular automaton models of traffic flow arised.

The merits of traffic flow CA models are: (1) models are

uncomplicated, it can be realized on a computer easily. When modeling, divide the road into several cells with a length of L, a cell corresponds to one car or several cars, or several cells correspond to one car. The status of each cell is empty or the velocity of cars that it contains, every car is motivated by a set of rules simultaneously. These rules consist of moving rules and traffic rules that moving vehicle should obey, random rules that contains driving behavior, interference of circumstance. (2)It is capable of recurring various complicated phenomena of transportation, indicating features of traffic flow. In the modeling process, through inspecting the transformation of status of cells, people can acquire the velocity,

displacement and headway of every car at any moment which describe microscopic features of traffic flow , with parameters of average velocity, density, flowrate that describe macroscopic features of traffic flow at the same time.

1.1 Single Lane CA model

N-S model is a simplified one-dimensional CA model, it was put forward by German bachelors Nagel and Schreckenberg in 1992. it is a minimal one-dimensional CA traffic flow model for describing freeway traffic flow. Each path of it is essential for modeling diverse features practical traffic flow. It provides basic rules for more complicated situation or urban traffic rules.

The model use a one-dimensional lattice to indicate a single lane, in

other words, divide the researching single lane into n parts (cells) with the length of L. each situation in the lattice corresponds to a cell, and each situation is either empty or containing a car. Defining the length of cell, L as headway when traffic jamming; the velocity of cars range from 0 to vmax, vmax=5 times the length of cell per second; time step can be supposed to the reaction time of drivers, sets 1s in common; there are 7 types of status in each situation, namely empty, the velocity of situation is 0,1,2,3,4 and 5. In the N-S model, the status of all cars are variable simultaneously according to 4 rules listed as follows:

Rules of Acceleration : if v(t)≤vmax, then v(t+l)=min(vmax,v(t)+l). Rules of Deceleration : if v(t)>gap, then v(t+1)=gap.

Rules of Ramdom : in the probability of P,

v(t+1)=max(v(t+1)-1,0).

Vehicle Movement: x(t+1)=x(t)+v(t+1).

The gap in the rules stands for the empty space between current car and former one. X stands for car’s situation. Because t=1s, vt=v. In this model, Rule of Acceleration reflects that driver accelerates the car to max velocity gradually; Rule of Deceleration reflects driver decelerates the car in order to avoid colliding with former car; Rule of Random indicates the uncertainty of driver’s action. In N-S model, the probability of random deceleration is a critical parameter, when P=0, N-S model is a deterministic traffic CA.