Cellular Automata model for heterogeneous traffic

Journal of Advanced Transportation, Fall, 2009 by Ch. Mallikarjuna, K. Ramachandra Rao

Introduction

There exists a need for traffic flow modelling in developing countries on account of the growth in personalized traffic. Since the past decade, and for many developing cities, traffic management schemes are gaining importance. The core of any traffic management scheme is a better understanding of the traffic behaviour. There exist several traffic models to study homogeneous traffic behaviour. However, since the traffic is heterogeneous in nature and vehicle characteristics vary widely, it is not known whether any conventional microscopic (car following) or macroscopic models are applicable to study traffic in developing countries.

In spite of this, microscopic simulation models were developed to study the heterogeneous traffic and it was found that these models had limited applicability for traffic analysis and further, they required enormous computational effort. Moreover, interactions between different elements such as the road conditions, type of vehicle, and the driver were also explicitly considered in these simulations, though this could limit the applicability of these models for different traffic conditions. In most of the simulation models, either space or time or both are considered as continuous variables, and since these models involve numerous elements (various vehicle types, different road conditions etc.), they require immense computational time. The objective of this study is to achieve a better computational efficiency in modelling complex traffic systems for different scenarios.

The model developed in the present study is based on the Nagel and Schreckenberg's (NS) approach (1992). In the NS model, interactions between different elements (vehicles, road and driver) were considered implicitly and even though this basic model could not reproduce all the observed traffic characteristics, it was however able to reproduce the trends observed in real traffic. The model has undergone many changes since then and its applicability is now extended to model network traffic flows (Simon and Nagel, 1998). Keeping the basic structure of CA intact, an attempt has been made to utilize its efficiency in modelling complex systems, for heterogeneous traffic. The basic structure of the model is modified to incorporate typical heterogeneous traffic features such as no-lane discipline and finite lateral movements besides physical and mechanical characteristics of different vehicles observed in the heterogeneous traffic. A new methodology suitable for collecting the data of some basic macroscopic characteristics that are relevant to characterize heterogeneous traffic behaviour is also proposed in this study. Furthermore the effects of different vehicle compositions are also studied using various relationships that exist among the macroscopic traffic variables.

A detailed literature review is presented in the next section which is followed by discussion on the basic structure of the CA model and its evolution with time. Later, some modifications are proposed and a new model is developed. The significance of different parameters and the results of the model are discussed in the next section and finally, the validation of the model and its limitations are discussed.

Literature Review

Heterogeneous Traffic Models

Many attempts were made in 80's (Chari and Badarinath, 1983; Ramanayya, 1988) to develop a modelling approach for heterogeneous traffic. Palaniswamy et al (1985) developed a discrete-event-based simulation model based on Swedish Road Traffic Simulation model (SWERTS) with modifications to include heterogeneous traffic.

Likewise, Kumar (1994) developed a simulation model for highway traffic which was continuous in space but discrete in time. In this model he used a combination of the time and event scanning to incorporate all important events that occurred during simulation. This simulation model was microscopic in nature and all the interactions between the elements (vehicles, drivers, road elements etc.) were modelled explicitly. Later, Singh (1999) developed a simulation model for heterogeneous urban traffic which was discrete in both time as well as space. In this model, the road space was divided into a grid of lm x lm size such that the vehicle could occupy a multiple number of cells depending on their physical dimension. The model considered motorized and non-motorized traffic with no-lane discipline such that the vehicle was free to position itself on road at any position laterally. This model was later validated for a mid-block section, however its applicability is limited since it could not be extended to a network level flow modelling on account of its complex nature. Similarly, Oketch (2000) introduced a new modelling approach that was suitable for a heterogeneous traffic stream taking non-standard vehicles. Further, this model adopted a detailed lateral movement modelling approach in which both longitudinal and lateral movements of vehicles were considered. Using this model, Oketch (2003) later suggested theoretical performance characteristics for heterogeneous traffic and observed that the traffic stream behaviour in heterogeneous flow might not be consistent with the fundamental relationships on which the macroscopic analysis is based on. Also, Arasan and Koshy (2005) proposed a methodology to model a highly heterogeneous traffic stream wherein the entire road was considered as a single unit and the vehicles were assigned some coordinates. The vehicles were updated sequentially with respect to an origin and the procedure of updating was similar to that suggested in the earlier models, and due to which the models implicitly incorporated full driver anticipation.