2ND-ORDER CONTINUUM TRAFFIC FLOW MODEL

A second-order traffic flow model is derived from microscopic equation s and is compared to existing models. In order to build in different d river characteristics on the microscopic level, we exploit the idea of an additional phase-space variable, called the desired velocity origi nally introduced by Paveri-Fontana [Trans. Res. 9, 225 (1975)]. By tak ing the moments of Paveri-Fontana's Boltzmann-like ansatz, a hierarchy of evolution equations is found. This hierarchy is closed by neglecti ng cumulants of third and higher order in the cumulant expansion of th e distribution function, thus leading to Euler-like traffic equations. As a consequence of the desired velocity, we find dynamical quantitie s, which are the mean desired velocity, the variance of the desired ve locity, and the covariance of actual and desired velocity. Through the se quantities an alternative explanation for the onset of traffic clus ters can be given, i.e., a spatial variation of the variance of the de sired velocity can cause the formation of a traffic jam. Furthermore, by taking into account the finite car length, Paveri-Fontana's equatio n is generalized to the high-density regime eventually producing corre ctions to the macroscopic equations. The relevance of the present dyna mic quantities is demonstrated by numerical simulations.