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Register a new userA new cellular automata model for city traffic
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Added by
Andreas Schadschneider
Publication date
1999
fields
Physics
and research's language is
English
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We present a new cellular automata model of vehicular traffic in cities by combining ideas borrowed from the Biham-Middleton-Levine (BML) model of city traffic and the Nagel-Schreckenberg (NaSch) model of highway traffic. The model exhibits a dynamical phase transition to a completely jammed phase at a critical density which depends on the time periods of the synchronized signals.
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City traffic is a dynamic system of enormous complexity. Modeling and predicting city traffic flow remains to be a challenge task and the main difficulties are how to specify the supply and demands and how to parameterize the model. In this paper we attempt to solve these problems with the help of large amount of floating car data. We propose a coarse-grained cellular automata model that simulates vehicles moving on uniform grids whose size are much larger compared with the microscopic cellular automata model. The car-car interaction in the microscopic model is replaced by the coupling between vehicles and coarse-grained state variables in our model. To parameterize the model, flux-occupancy relations are fitted from the historical data at every grids, which serve as the coarse-grained fundamental diagrams coupling the occupancy and speed. To evaluate the model, we feed it with the historical travel demands and trajectories obtained from the floating car data and use the model to predict road speed one hour into the future. Numerical results show that our model can capture the traffic flow pattern of the entire city and make reasonable predictions. The current work can be considered a prototype for a model-based forecasting system for city traffic.
We present results on the modeling of on- and off-ramps in cellular automata for traffic flow, especially the Nagel-Schreckenberg model. We study two different types of on-ramps that cause qualitatively the same effects. In a certain density regime one observes plateau formation in the fundamental diagram. The plateau value depends on the input-rate of cars at the on-ramp. The on-ramp acts as a local perturbation that separates the system into two regimes: A regime of free flow and another one where only jammed states exist. This phase separation is the reason for the plateau formation and implies a behaviour analogous to that of stationary defects. This analogy allows to perform very fast simulations of complex traffic networks with a large number of on- and off-ramps because one can parametrise on-ramps in an exceedingly easy way.
To provide a more accurate description of the driving behaviors in vehicle queues, a namely Markov-Gap cellular automata model is proposed in this paper. It views the variation of the gap between two consequent vehicles as a Markov process whose stationary distribution corresponds to the observed distribution of practical gaps. The multiformity of this Markov process provides the model enough flexibility to describe various driving behaviors. Two examples are given to show how to specialize it for different scenarios: usually mentioned flows on freeways and start-up flows at signalized intersections. The agreement between the empirical observations and the simulation results suggests the soundness of this new approach.
A two-lane extension of a recently proposed cellular automaton model for traffic flow is discussed. The analysis focuses on the reproduction of the lane usage inversion and the density dependence of the number of lane changes. It is shown that the single-lane dynamics can be extended to the two-lane case without changing the basic properties of the model which are known to be in good agreement with empirical single-vehicle data. Therefore it is possible to reproduce various empirically observed two-lane phenomena, like the synchronization of the lanes, without fine-tuning of the model parameters.
Based on a detailed microscopic test scenario motivated by recent empirical studies of single-vehicle data, several cellular automaton models for traffic flow are compared. We find three levels of agreement with the empirical data: 1) models that do not reproduce even qualitatively the most important empirical observations, 2) models that are on a macroscopic level in reasonable agreement with the empirics, and 3) models that reproduce the empirical data on a microscopic level as well. Our results are not only relevant for applications, but also shed new light on the relevant interactions in traffic flow.
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