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Abstract:Although particle hopping models were introduced into traffic science in the 1950s, their systematic use has only started recently. This paper shows connections between particle hopping models and traffic flow theory. It shows that the hydrodynamical limits of certain particle hopping models correspond to the Lighthill-Whitham theory for traffic flow, and that only slightly more complex particle hopping models produce already the correct traffic jam dynamics, consistent with recent fluid-dynamical models for traffic flow. This paper establishes that, on the macroscopic level, particle hopping models are at least as good as fluid-dynamical models. Yet, particle hopping models have at least two advantages over fluid-dynamical models: they allow microscopic simulations, and they include stochasticity.
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