document: 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
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