A Minimax Variational Inequality Framework for Traffic Equilibrium Optimization in Intelligent Transportation Networks

Abstract

The fast development of intelligent transportation systems has complicated traffic congestion problems because of uncertainties associated with traffic demands, traffic networks, and interactions between multiple users on the roads. Current approaches in traffic equilibrium optimization have primarily focused on traffic demand and network conditions without taking into account possible worst-case scenarios. This paper solves this issue using a novel Minimax Variational Inequality (MVI) approach for traffic equilibrium optimization with uncertainty in intelligent transportation networks. It combines minimax optimization and variational inequality to develop an equilibrium optimization problem in traffic flows considering uncertainties. A robust uncertainty model is used to determine negative traffic scenarios, while a two-timescale projected extragradient scheme is constructed to reach stable traffic equilibria. The framework represents the transportation network model via constrained flow sets, monotonic cost operator, and worst-case optimization to enhance robustness against traffic dynamics. The experimental results performed on the benchmark transportation network prove that the approach allows for the successful determination of worst-case traffic condition, ensures the equilibrium stability, and decreases vulnerability to traffic dynamics changes. The analysis results in the growth of the overall cost of the system by 30.8% from nominal to worst-case traffic conditions. This framework provides an efficient mathematical background for making decisions in the intelligent transportation system.