Transport system modelling based on analogies between road networks and electrical circuits

Alexander V Tolmachev,Dmitrii A Brusyanin,Evgeny V Sinitsyn

doi:10.15826/recon.2019.5.2.010

Abstract

This article describes a probabilistic mathematical model which can be used to analyse traffic flows in a road network. This model allows us to calculate the probability of distribution of vehicles in a regional road network or an urban street network. In the model, the movement of cars is treated as a Markov process. This makes it possible to formulate an equation determining the probability of finding cars at key points of the road network such as street intersections, parking lots or other places where cars concentrate. For a regional road network, we can use cities as such key points. This model enables us, for instance, to use the analogues of Kirchhoff First Law (Ohm's Law) for calculation of traffic flows. This calculation is based on the similarity of a real road network and resistance in an electrical circuit. The traffic flow is an analogue of the electric current, the resistance of the section between the control points is the time required to move from one key point to another, and the voltage is the difference in the number of cars at these points. In this case, well-known methods for calculating complex electrical circuits can be used to calculate traffic flows in a real road network. The proposed model was used to calculate the critical load for a road network and compare road networks in various regions of the Ural Federal District.

Highlights

The task of modelling road network dynamics is a widely discussed topic in modern research literature [1,2,3,4,5,6]
Such an analogy is justified by the fact that the movement of automobiles, which is to some extent similar to the movement of electrons in a conductor, can be measured by the number of corresponding units passing through a certain section per unit of time, while the movement itself is caused by the external electromotive force
The above-described probabilistic mathematical model, which determines the distribution of cars along intersections of a road network, makes it possible to substantiate the analogy between the traffic flow and the electric current in an equivalent electric circuit where the resistances are the times needed for a car to travel along a certain road section

Summary

Introduction

The task of modelling road network dynamics is a widely discussed topic in modern research literature [1,2,3,4,5,6]. Despite the availability of fairly complex software systems, such as VISUM, it is still quite difficult to build simple models that would allow us to analyse the distribution of traffic flows across the road network, without detailed information about the social, age and gender structure of the population Such macro-analysis is necessary, for example, in strategic planning for the development of urban transport, an integrated transport service system and in dealing with other problems. The calculation of traffic flows in real road networks, taking into account all the existing interconnections and conditions, is a rather complicated computational problem, but methods for solving such tasks are well developed [7] This analogy can be used to compare transport systems of different regions. With a more complex and rigorous approach, it is necessary to take into account the dependence of parameters on quantities, which will significantly complicate the task

Discussion

Conclusion