  A generalized optimal velocity model is analyzed, where the optimal velocity
function depends not only on the headway of each car but also the headway of
the immediately preceding one. The stability condition of the model is derived
by considering a small perturbation around the homogeneous flow solution. The
effect of the generalized optimal velocity function is also confirmed with
numerical simulation, by examining the hysteresis loop in the headway-velocity
phase space, and the relation between flow and density of cars. In the model
with a specific parameter choice, it is found that an intermediate state
appears for the movement of cars, where the car keeps a certain velocity though
the headway is short or long. This phenomenon is different from the ordinary
stop-and-go state.

Pattern Formation and Solitons