tailieunhanh - Investigating Traffic Flow in The Nagel-Schreckenberg Model

I present the investigation involving two extensions of the cellular automaton based NagelSchreckenberg model, the Velocity-Dependent-Randomisation (VDR) model, and the two-lane model for symmetric and asymmetric lane changing rule sets. The study of the VDR model outlines a potential method in extending the lifetime of a metastable state and consequently postponing an inevitable traffic jam by orders of magnitude. The two lane model produces a so called "critical" and "sub-critical" flow which combined cause the collapse of flow at a critical density. | Investigating Traffic Flow in The Nagel-Schreckenberg Model Paul Wright School of Physics and Astronomy University of Southampton Highfield Southampton S017 1BJ Dated April 26 2013 I present the investigation involving two extensions of the cellular automaton based Nagel-Schreckenberg model the Velocity-Dependent-Randomisation VDR model and the two-lane model for symmetric and asymmetric lane changing rule sets. The study of the VDR model outlines a potential method in extending the lifetime of a metastable state and consequently postponing an inevitable traffic jam by orders of magnitude. The two lane model produces a so called critical and sub-critical flow which combined cause the collapse of flow at a critical density. 1. INTRODUCTION In the modern world the demand for mobility is increasing rapidly with the capacities of road networks becoming saturated or even exceeded. In densely populated countries such as the UK it can be financially or socially unfeasible to expand these road networks. It is therefore vital that the existing networks are used more efficiently. A cellular automaton CA is a so called mathematical machine which arises from basic mathematical principles. While cellular automata can be used to model a variety of applications one of the most extensive uses has been modelling single-lane traffic. The most prominent example of this kind of model was first introduced over 20 years ago by Kai Nagel and Michael Schreckenberg 1 . The Nagel-Schreckenberg NaSch model is a simple probabilistic CA based upon rule 184 for more information see Appendix A and was the first model of its kind to account for imperfect human behaviour which is key when modelling traffic networks. With the help of a suitable model and relevant extensions one can make realistic predictions about the development of real traffic situations and use these findings to optimise the efficiency of road networks. In this paper I study the flow for three different conditions. Sections two