  A simple macroscopic model for the vehicular traffic flow with hysteresis is
proposed. The model includes drivers' hysteresis behavior into the classical
Lighthill-Whitham-Richard (LWR) model. One novelty of the model is how the
hysteresis is modeled based on hysteresis behavior reported in literature. By
comparing wave patterns producible by the classical LWR model versus this
model, the effect of hysteresis can be revealed. For this purpose, wave pattern
analysis is carried out by construction of viscous waves and Riemann solvers of
the model. Examples of solutions for initial data corresponding to some real
world setups or experimental observations are constructed. Many of them
qualitatively agree with experimental observations and intuition. These result
shows that the model not only keeps the successful part of the LWR model, but
also demonstrates many wave patterns observed real world traffic that LWR fails
to exhibit, such as stop-and-go waves and many other traffic patterns. A
mechanism for formation and decay of stop-and-go patterns and traffic jams is
revealed. Furthermore, acceleration shocks in congested zone are predicted,
which can serve as fronts of stop-and-go patterns.
