Reproduction of experimental spatio-temporal structures in traffic flows using mathematical model based on cellular automata theory

Antonina Chechina,Marina Trapeznikova,Natalia Churbanova

doi:10.21533/pen.v7i1.395

Abstract

The paper deals with mathematical modelling of traffic flows on urban road networks using cellular automata theory. Two versions of the model based on Nagel-Schreckenberg traffic flow model were created. They both are multilane, include complex driver behaviour algorithms and allow simulating traffic on various road elements and on road networks. One of the models is using “slow-to-start” concept that represents the fact that it takes drivers more time to accelerate when they just start moving in comparison with the situation when their speed is already above zero. The goal of the work was to reproduce experimental spatio-temporal patterns on traffic velocity diagrams with the created models and to research the difference between them and to determine the range of the applicability for each. Parallel algorithms of realisation for the models are created. Computations are carried out for each element of the road (T or X type intersection, on-ramp, road fragment with widening or bottleneck, straight road fragment, etc.) separately and in parallel, that allows performing calculations on various complex road networks. Different kinds of average characteristics (such as, for instance, the capacity of the crossroad) can be also obtained using the created program package. Computations show that the results obtained are in an agreement with experimental data and therefore can be used for practical traffic flow modelling in cities.

Highlights

The cellular automata theory (CA), first proposed and developed by John von Neumann in the mid-twentieth century, has found its application in many fields of science
Since 1992, when Kai Nagel and Michael Schreckenberg [1] proposed to apply the theory of cellular automata to transport modelling, scientists from around the world have created many variants of traffic flow models based on it
Due to the development of computer technology, it became possible to take into account more and more nuances in the behavior of traffic participants in the models created, and due to the development of the transport flow theory itself, new ideas about the patterns observed in the measurement data appeared

Summary

Introduction

The cellular automata theory (CA), first proposed and developed by John von Neumann in the mid-twentieth century, has found its application in many fields of science. Since 1992, when Kai Nagel and Michael Schreckenberg [1] proposed to apply the theory of cellular automata to transport modelling, scientists from around the world have created many variants of traffic flow models based on it. This approach seemed to be the most promising for a detailed description of local road situations at short distances, since the models are quite flexible due to the ability to implement any driver strategy without significant algorithmic costs. A large amount of data from sensors and surveillance cameras has been collected and stored, which means that the requirements for the mathematical models being created are increasing

Objectives

Conclusion