Abstract—Long lines and heavy congestion is always the bottleneck problem of highway toll plaza, the operation efficiency of tollbooths is crucial to the traffic throughout of expressway toll plaza. In this report, we explore M/G/1 model in stochastic service system theory for obtaining the important indicators (eg: delay time, traffic throughput, construction cost and accident prevention) for improving the operation efficiency of tollbooths. Combining with fluid mechanics theory, we get the relationship between some important indicators such as queue length, delay time (including service time and overall waiting time) of the tollbooths system and the single channel capacity, and also the proportion of the number of various windows type. At the same time, we give out the reasonable accident coefficient and safety distance between vehicles. We find that the security distance between vehicles will directly affect the queue length, and thus influence the traffic capacity of toll booths.

Index Terms—M/G/1 queue model, expressway toll plaza, fluid mechanics theory, optimal indicators.

Meilan Qiu, Dewang Li, and Dazhuo Zhou are with School of Mathematics and Statistics, Huizhou University, Huizhou, Guangdong 516007, China.

Cite:Meilan Qiu, Dewang Li, Dazhuo Zhou, "Determination Optimal Indicators of Expressway Toll Plaza with M/G/1 Queue Model," International Journal of Applied Physics and Mathematics vol. 10, no. 3, pp. 96-111, 2020.

Copyright © 2020 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).