Nash Equilibrium and Stackelberg Approach for Traffic Flow Optimization in Road Transportation Networks—A Case Study of Warsaw

Abstract

The article discusses the issue of modelling traffic flows and the transport network. Faced with an increase in the number of vehicles in road networks, the problem of congestion and the need to optimise traffic and adapt the transport infrastructure to changing demand are growing, especially in large cities. With this in mind, the authors of this publication developed a model of the road network in the north-eastern part of the Warsaw agglomeration based on the proposed algorithm. Two methods were used to optimise the distribution of traffic flows: the Nash equilibrium and the Stackelberg approach. The Nash equilibrium assumes the aim of achieving equal average times on all roads for each origin–destination (O-D) pair. This describes the state pursued by a decentralised system guided by the individual benefits of the traffic users. On the contrary, the Stackelberg approach aims to achieve optimal travel times for the entire system. The study was carried out for three scenarios that differed in the assumed traffic demand on the road network. The basic scenario assumed the average hourly traffic demand during the morning peak hour based on traffic measurements. On the other hand, the two alternative scenarios were developed as a 10% variation in traffic volumes from the baseline scenario. On the basis of the results, it was concluded that an increase in traffic volumes for all O-D pairs could result in a decrease in traffic volumes on some links of the road network. This means that the transport network is a complex system and any change in parameters can cause significant and difficult to predict changes. Therefore, the proposed approach is useful in terms of traffic forecasting for road networks under conditions of changing traffic flow volumes. Additionally, the total travel time for the entire system differed for each scenario by a percentage difference of 0.67–1.07% between the optimal solution according to the Nash equilibrium and the Stackelberg approach.