Tolling for Traffic Flow Networks: Positive Systems Modeling and Control

This paper addresses modeling and control of traffic flow networks aiming at reduced congestion. We first develop a state-space model of expressing city-level traffic flow controlled by tolling, which is in a class of positive systems depending on some designable parameters. Based on the positivity of the model, we next present a design method of optimal tolling in terms of nonlinear programming. The nonlinear programming is transformed into a linear one, which is numerically tractable, by applying the change of variable technique. Finally, the effectiveness of the presented tolling design is shown through a numerical experiment. Copyright (c) 2023 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)