Assessing the impact of non-compliant users response to System-Optimal Dynamic Traffic Assignment

In the present work, we address a pseudo-System Optimum Dynamic Traffic Assignment optimization problem on road networks relying on trajectory control over a portion of the flows and limited knowledge on user response. The fractions of controlled flow moving between each origin-destination couple are defined as "compliant", while the remaining portions, consisting of users free to make their own individual choices, are defined as "non-compliant". The objective is to globally improve the state of the network by controlling a varying subset of compliant traffic flows. A Godunov discretization of the Lighthill-Williams-Richards model coupled with a triangular fundamental diagram is employed as the flow dynamics model. At junctions, a multi-class solver is applied which requires a class-density-weighted aggregate distribution matrix and incoming links priorities. On one hand, the selfish response of non-compliant users to changing traffic conditions is computed at each time step by updating the class related turn ratios accordingly to a discrete-choice multinomial Logit model to represent users imperfect information. On the other hand, the control action is actuated by varying the flow rates over a precomputed set of routes while the coupled optimization problem takes into account an a priori fixed distribution of users at the nodes. We show how the effectiveness of the resulting finite horizon optimal control problem degrades by not considering the dynamic response of non-compliant users and how it varies according to the fraction of compliant ones.