Modern analyses of traffic flow frequently involve simulations of a
large number of individual vehicles whose motion is dictated by simple
rules. Large-scale cellular automata calculations can be done to study
emergent phenomena such as propagating jams, which are analogous to
kinematic waves in the hydrodynamic theory of Lighthill and Whitham.
To describe small-scale behavior, car-following and optimal velocity
models, where equations of motion are integrated, are appropriate.
Using a modified optimal velocity model that explicitly includes
driver reaction time, I will explore the dynamics of jamming and
synchronous flow. The latter is a new phase of traffic flow
identified by Kerner in instrumented-autobahn data. The effects of
adaptive cruise control on traffic flow will be discussed.
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