On the Mean Speed in the “Boltzmann-Like” Traffic Theory: A Numerical Method

A method has recently been developed by the authors for determining the mean speed of the speed distribution in the Boltzmann-like traffic theory developed by Prigogine, et al. This method has now been extended to more general functional forms assumed for the details of the interaction, relaxation, and adjustment processes. The mean speed for the more general case is again expressed in terms of the intersection of two mathematical functions identical to those previously obtained. On the basis of this method a numerical procedure for calculating the mean speed is given. For most reasonably well behaved desired speed distributions this method offers satisfactory rates of convergence and is applicable for both the “individual” and “collective” flow cases.