The influence of tollbooths on highway traffic

We study the effects of tollbooths on the traffic flow. The highway traffic is simulated by the Nagel–Schreckenberg model. Various types of toll collection are examined, which can be characterized either by a waiting time or a reduced speed. A first-order phase transition is observed. The phase separation results a saturated flow, which is observed as a plateau region in the fundamental diagram. The effects of lane expansion near the tollbooth are examined. The full capacity of a highway can be restored. The emergence of vehicle queuing is studied. Besides the numerical results, we also obtain analytical expressions for various quantities. The numerical simulations can be well described by the analytical formulas. We also discuss the influence on the travel time and its variance. The tollbooth increases the travel time but decreases its variance. The differences between long- and short-distance travelers are also discussed.