Design and Evaluation of the Tollbooth Plaza based on Mathematical Model

Zhendong Peng, Hongyu Chen, Xiaofeng Wu

School of Glasgow, University of Electronic Science and Technology, Chengdu, 611731, China

Abstract: Nowadays, how to design a scientific tollbooth plaza on high way has been an issue of hot discus-sion. To find the solution about building the tollbooth plaza as reasonable as possible, we construct two models from two aspects to consider it, those are: Cost Model and Time Model. Cost model refers to the total cost of building a tollbooth plaza. It is connected to the area of the tollbooth plaza and the proportions of conventional tollbooths, exact-change tollbooths and electronic toll collection booths. In addition, the safety problems should also be considered during the process of building the tollbooth plaza. As a result, the Gradual Change Rate is put forward, describing the area of the gradual change section. Gradual change section refers to the area L lanes on highway change into B lanes on passageway, and vice versa. Besides, a widening passageway is built specially for freight vehicles on the right side of the plaza to reduce accidents. Time model refers to the expectation of total time spent on tollbooth plaza for one vehicle. It can be divided into three parts: The expectation of time spent before the barrier toll in the toll plaza, the expectation of time spent on service and the expectation of time spent after the barrier toll in the toll plaza. To determine this physical quantity, we use to Queuing Theory and Free Flow Model. Queuing theory show the time spent before the barrier toll and on service and Free flow model show the time spent in the gradual change sections. Similarly, the total time spent on tollbooth plaza is also influenced by the proportions of different kinds of tollbooths. Lastly, we discuss the effect of my solution in light and heavy traffic as well as the autonomous vehicles conditions and give the detailed solution to explain it with the Evaluation model that we construct.

Keywords: Cost model; Time model; Queuing theory; Free flow model; Free flow model; Genetic algorithm