KINETIC THEORY OF TRAFFIC FLOW

UNTERSUCHUNGEN ZUR KINETISCHEN THEORIE DES VERKEHRSFLUSSES

A MATHEMATICAL THEORY WAS DEVELOPED WHICH CAN DESCRIBE TRAFFIC FLOW ON TWO LANED ROADS FROM FREE-FLOWING TO RESTRICTED TRAFFIC. A CLUSTER DESCRIPTION WAS SELECTED TO DEAL WITH THE TRANSITION AREA OF PARTLY RESTRICTED TRAFFIC. KINETIC FUNDAMENTAL EQUATIONS SIMILAR TO THE BOLTZMANN EQUATIONS FOR GAS MIXTURES WERE DEVELOPED WHICH COMPLETELY DESCRIBE THE SPEED DISTRIBUTIONS OF THE INDIVIDUAL CLUSTERS ON LANES. FOR THIS PURPOSE THE INDIVIDUAL RELAXATION, CONDENSATION AND DISSOCIATION TERMS OF THE RIGHT-HAND SIDES OF THE KINETIC EQUATIONS HAD TO BE DERIVED AGAIN, AS THE CORRESPONDING TERMS FROM KINETIC GAS THEORY CANNOT BE TRANSFERRED. THE SYSTEM OF EQUATIONS WAS TESTED ON SIMPLE CASES OF RELAXATION AND LOW CONCENTRATION. FOR HIGHER CONCENTRATION THE SYSTEM OF EQUATIONS IS SOLVED FOR THE HOMOGENEOUS CASE BY INTEGRAL ITERATION. KNOWLEDGE OF THE DISTRIBUTION FUNCTION FACILITATES DETERMINATION OF ALL MACROSCOPIC MAGNITUDES, E.G. VEHICLE FLOW, DISPERSION, LANE OCCUPANCY AND ENTROPY. TO COMPARE THE NUMERIC CALCULATIONS USE WAS MADE OF THE RESULTS OF A SPECIALLY DEVELOPED SIMULATION MODEL IN WHICH THE SAME BEHAVIOURAL RULES WERE CONSIDERED AS IN THE KINETIC MODEL.