A perimeter control method for a congested urban road network with dynamic and variable ranges

Abstract

• A continuous division method is developed for the dynamic boundary of single congested region. • A congested area range estimation method is applied to determine the boundary change trend. • A three-dimensional MFD surface model is proposed considering the scope of the sub-region. • A sliding mode control method is integrated for the perimeter flow of dynamic changing congested sub-region. • The proposed control method can improve the efficiency of road network compared to PI and PIDB. The urban traffic system is a complex dynamic system, and its state changes with the real-time traffic demand; correspondingly, the range of congested areas also continuously transforms spatiotemporally. Affected by the traffic congestion range, the dynamics of a road network and the macroscopic control model that describes the road network also change. The existing sub-region division methods divide sub-regions based on cluster algorithms, and their results cannot be directly used to establish a dynamic congested area model with varying ranges or to implement perimeter control because they fail to consider the continuity of congested area transfer. To achieve control of the dynamic entrance boundary of a continuously changing congested range, this paper carries out three related analyses. First, depending on the section data of the kernel congested area, a continuous division method for generating sub-regions is proposed on the basis of similarity theory to determine the dynamic boundary of the congested area. Then, after the boundary intersections of bottlenecks are categorized as output, input, or passing types, a congested area range estimation model is established using the density wave transfer speed to estimate the boundary range change trend caused by the influence of traffic congestion diffusion or dissipation. A three-dimensional macroscopic fundamental diagram (MFD) surface model with an independent section length, traffic flow density, and road network trip completion rate of the congested area is then established according to the changes in the congested area. On the basis of the three-dimensional MFD surface model, a sliding mode control with dynamic boundary (SMCDB) method is proposed to determine the entrance of the congested area. With a regional road network in Hefei taken as an example, numerical experiments are carried out, and the simulation results are compared with those of PI control with and without boundary changes, showing that the SMCDB method can track congested boundaries and adjust boundary flows according to the traffic state, protect the centre network from over-saturation, effectively improve the trip completion flow, and decrease the network travel delay.