  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, $\dot T_i =
\alpha (m_T - T_i) + D T_i\xi$. 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.
