A traffic cellular automata model based on road network grids and its spatial and temporal resolution’s influences on simulation

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Abstract

Microscopic Traffic Simulation Model based on Cellular Automata (CA) has become more and more popular since it was firstly introduced by Creamer and Ludwig in 1986. Cellular automata are simpler to implement on computers, provide a simple physical picture of the system and can be easily modified to deal with different aspects of traffic. However, in a traditional traffic CA model, the spatial resolution of CA and temporal resolution of simulation are low. Take TRANSIMS for example. The size of cellular automata is 7.5 m and the time step equals 1 s. In such a case, if a vehicle drives at a speed of 4 cells per s, the speed difference between 95 km/h (3.5  7.5 m/s) and 121 km/h (4.4999  7.5 m/s) will not be distinguished by simulation models. And the temporal resolution of 1 s makes the system hard to model different drivers’ reaction time, which plays a very important role in vehicular movement models. In this paper, a microscopic traffic cellular automata model based on road network grids is proposed to overcome the low spatial and temporal resolutions of traditional traffic CA models. In our model, spatial resolution can be changed by setting different grid size for lanes and intersections before or during simulation and temporal resolution can be defined according to simulation needs to model different drivers’ reaction time, whereas the vehicular movement models are still traditional CA models. By doing so, the low spatial and temporal resolution of CA model can be overcome and the advantages of using CA to simulate traffic are preserved. The paper also presents analyses of the influences on simulation of different 1D lane grid size, 2D intersection grid size and different combinations of temporal resolution and mean drivers’ reaction time. The analysis results prove the existence of spatial and temporal resolution thresholds in traffic CA models. They also reveal that the size of grids, the combinations of different temporal resolutions and mean drivers’ reaction time do pose influences on the speed of vehicles and lane/intersection occupancy, but do not affect the volume of traffic greatly.

Introduction

Cellular automata were originally introduced by von Neumann and Ulam (under the name of “cellular spaces”) as a possible idealization of biological systems [1], [2], with the particular purpose of modeling biological self-reproduction. Since then, they have been used in physics applications such as particle transport simulations and thermodynamics studies. In the field of traffic study, cellular automata were firstly introduced by Creamer and Ludwig in 1986 [3]. They used a cellular automaton model in the form of a boolean simulation of traffic flow. The boolean model represents individual vehicles by 1-bit variables that are placed in computer memory locations analogous to the locations of vehicles on the roadway. More recently, since the introduction of the Nagel–Schreckenberg model in 1992 [4], cellular automata have become a well-established method of traffic flow modeling. In traffic cellular automata model, the roadway is represented by a uniform cell lattice in which each cell belongs to a discrete set of states. The state of the cells is updated at discrete time steps with a set of update rules that combine a few vehicle motion models that are governed by a small set of parameters. This means that both time and space are discrete variables, and physical quantities take on a finite set of discrete values. Therefore, CA models are simpler to implement on computers, provide a simple physical picture of the system and can be easily modified to deal with different aspects of traffic [5], [6], [7]. For these reasons, traffic cellular automata models are getting more and more popular.

In microscopic traffic simulation models based on CA, the size of CA and the time step of the simulation, i.e., the spatial and temporal resolution of simulation are two key parameters while running simulations. However, till now, there are few relevant papers discussing such issues. For many microscopic traffic simulation system based on CA, the selection of size of CA and time step of simulation is somewhat a bit arbitrary. In TRANSIMS [8], the size of cellular automata is 7.5 m, while time step equals 1 s. In [7], the size of CA is set as 5 m, and time step equals 1 s as well. Apparently, both of the two spatial and temporal resolutions are low, for the velocity gap which the simulation system cannot distinguish from vehicles to vehicles is large. For instance, in TRANSIMS, if a vehicle drives at a speed of 4 cells per s, the speed difference between 95 km/h (3.5  7.5 m/s) and 121 km/h (4.4999  7.5 m/s) will not be distinguished by simulation models. All vehicles with the speed within such range will move at the same speed without any differences. For temporal resolution, if the time step is set uniformly as 1 s, simulation models are hardly able to depict accurately such differences among drivers as reaction time, intersection start-up delay and so forth. From most of the recent papers regarding traffic simulation models based on CA, we can find that many of these models are for highway traffic rather than for urban traffic. When using traditional CA models (traditional CA models denote those CA models whose spatial and temporal resolutions are invariable before or while running simulations) to simulate urban traffic, the spatial resolution and temporal resolution is not enough to make a good simulation result. Therefore, a more subtle simulation model based on CA is needed.

In this paper, a microscopic traffic cellular automata model based on road network grids is proposed to overcome the low spatial and temporal resolutions of traditional traffic CA models mentioned above. In this model, spatial resolution can be changed by setting different grid size for lanes and intersections before or during simulation and temporal resolution can be defined according to simulation needs to model different drivers’ reaction time, whereas vehicular movement models are still traditional CA models. By doing so, the low spatial and temporal resolution of CA model can be overcome and the advantages of using CA to simulate traffic are preserved.

The following section will discuss the road network data model designed for the revised CA model and the gridization process of one-dimensional traffic lanes and two-dimensional nodes.

Section snippets

Data structure of road network

The data model for road network in this paper is still a traditional “Node-Link-Segment-Lane” relationship which is shown in Fig. 1. However, considering different spatial resolution in road network, we add a new data element “grid” for both lanes (one-dimensional, 1D) and nodes (two-dimensional, 2D). The new relationship for the data model is illustrated in Fig. 2 [9]. And the gridization processes of nodes and traffic lanes are described in the remaining part of this section.

One-dimensional lanes gridization

The first step of

Influences of 1D lane grid size on simulation output

Simulation conditions: Road network is a one lane segment and a two lane segment. The length of the two segments is 1000 meters. The arriving rate distribution of vehicles is a Poisson distribution with a mathematic expectation of 300 vehicles per 15 min. The combinations of different types of vehicles are: 70% for small vehicles (length = 4.5 m), 22% for medium vehicles (length = 7.5 m) and 8% for large vehicles (length = 12 m). The initial speed for all vehicles is 30 km/h, and the maximum desired

Conclusions and final remarks

Large scale microscopic traffic simulation using CA is simpler to implement on computers, provides a simple physical picture of the system and can be easily modified to deal with different aspects of traffic. However, in traditional traffic CA models, the spatial resolution of CA and temporal resolution of simulation are low. In this paper, we proposed a new CA model based on road network grids, in which, the spatial resolution can be changed by setting different grid size for lanes and

Acknowledgements

The research is supported by the Beijing Nature Science Foundation (No. 8033015), NSFC (No. 70571076, 40471111) and MOST (No. 2006AA12Z215). The authors thank the anonymous reviewers for their valuable suggestions and contributions to this paper.

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