Abstract
Cars are considered as points on an infinite road with no intersections. They can overtake each other without any delay and they travel at constant speed. Contrary to earlier models the journeys are of finite lengths. The speeds and journey length are independent identically distributed random variables also independent of the initial positions in the time-road-plane of the vehicles. The model is analyzed with respect to observations at a time point or at a point of the road and further overtakings and single accidents are considered.