Structural properties of solutions arising from a nonequilibrium traffic flow theory

This paper analyzes the structural properties of the shock and rarefaction wave solutions of a nonequilibrium theory of vehicular traffic flow. It shows that this nonequilibrium theory has two families of characteristics: one is slower and the other is faster than vehicular speed. Corresponding to the slower characteristic arise 1-shock and 1-rarefaction waves, whose behavior is similar to that of the shock and rarefaction waves in the LWR theory; corresponding to the faster characteristic there are 2-shocks (and 2-rarefaction waves) that behave as bores in rivers. The latter behavior does not accord with the generally held view that traffic is an anisotropic fluid. It is shown, however, those 2-shocks and 2-rarefactions in the studied nonequilibrium theory are transitory and their influence on traffic flow decays exponentially. It is further argued that as long as the 2-shocks and 2-rarefactions do not persist, they can be allowed in a nonequilibrium theory. Apart from the behavioral aspects, the paper also derives the formulae for solving the Riemann problem associated with the nonequilibrium theory. Most of the results carry over directly to other nonequilibrium theories of the same kind, including the PW theory.