Modelling traffic flow fluctuations

Peter Wagner

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arXiv · cond-mat/0411066

Modelling traffic flow fluctuations

Peter Wagner

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Abstract

By analyzing empirical time headway distributions of traffic flow, a hypothesis about the underlying stochastic process can be drawn. The results found lead to the assumption that the headways $T_i$ of individual vehicles follow a linear stochastic process with multiplicative noise, $\dot T_i = α(m_T - T_i) + D T_iξ$. The resulting stationary distribution has a power-law tail, especially for densities where cars are interacting strongly. Analyzing additionally the headways for accelerating and decelerating cars, the slow-to-start effect proposed as a mechanism for traffic jam stability can be demonstrated explicitly. Finally, the standard deviation of the speed differences between following cars can be used to get a clear characterization of (at least) three different regimes of traffic flow that can be identified in the data. Using the empirical results to enhance a microscopic traffic flow model, it can be demonstrated that such a model describes the fluctuations of traffic flow quite satisfactorily.

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Peter Wagner. 2004-11-02. Modelling traffic flow fluctuations. https://arxiv.org/abs/cond-mat/0411066

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