Analyses of the stability and wave properties of a new continuum traffic theory

This paper investigates certain qualitative properties of a new continuum traffic flow theory developed by Zhang. It shows that the linearized version of the new theory is inherently stable, as is the LWR theory, that the theory has a hierarchy of first and second order waves through which small disturbances are propagated, and that it does not admit smooth traveling wave solutions. The paper also compares the instability criteria of traffic flow for a number of related theories. It is found that various instability criteria can be reduced to a single criterion derived from first order waves traveling faster than slow second order waves in the higher order theories, and that viscosity is not necessary for the existence of two critical concentrations in traffic flow.