Approximating dynamic equilibrium conditions with macroscopic fundamental diagrams

Real-time coordinated traffic management strategies that benefit from parsimonious models with aggregated network dynamics, provide a new generation of smart hierarchical strategies to improve network capacity and performance. However, this raises the question of route choice behavior in case of heterogeneous urban networks, where different parts of the city are subject to different types of control. Traffic equilibrium phenomena have not been thoroughly investigated in these models. Approximate traffic equilibrium conditions can be integrated within the parsimonious traffic models to develop regional routing strategies, while detailed route choice strategies can be incorporated at a later stage in a hierarchical framework. In this study, we develop an aggregated and approximate dynamic traffic assignment (DTA) procedure to be incorporated in the macroscopic fundamental diagram (MFD) dynamics, and establish dynamic stochastic user equilibrium (DSUE) conditions. The methodology consists of two main components; stochastic network loading and a fixed-point solution method. Loading procedure is designed to handle stochastic components in the model such as trip length uncertainty, variation of speeds across the links, perception error of travelers. The results taken from this procedure are averaged through the well-known method of successive averages (MSA) to reach fixed-point solution for the system. Real-time route guidance strategies can be revisited towards a “system of systems” approach.