Controlling highway toll stations using deep learning, queuing theory, and differential evolution

Traffic congestion is, nowadays, one of the most important highway problems. Highway tolls with booth operators are one of the causes of traffic congestion on highways, especially in rush hour periods, or during seasonal holiday travels. The value of driver waiting time (needed to stop and pay the toll) and the cost of the toll booth operators can reach up to about one-third of the revenue. In this paper we propose a novel methodology for continuous-time optimal control of highway tolls by predicting the optimal number of active modules (booths) in toll stations. The proposed methodology is based on a combination of recurrent neural networks, queuing theory, and metaheuristics. We utilized several recurrent neural network architectures for predicting the average intensity of vehicle arrivals. Moreover, the prediction error of the first recurrent neural network was modelled by another one in order to provide confidence estimates, additional regularization, and robustness. The predicted intensity of vehicle arrival rates was used as an input of the queuing model, whereas differential evolution was applied to minimize the total cost (waiting and service costs) by determining the optimal number of active modules on a highway toll in continuous time. The developed methodology was experimentally tested on real data from highway E70 in the Republic of Serbia. The obtained results showed significantly better performance compared to the currently used toll station opening pattern. The solutions obtained by solving a system of differential equations of the queuing model were also validated by a simulation procedure.