Real-time estimation of critical values of the macroscopic fundamental diagram for maximum network throughput

Abstract

Perimeter flow control or gating has recently been found to be a practical and efficient control scheme in mitigating traffic congestion in urban road networks. This control scheme aims at stabilising the accumulation of vehicles (or a proxy of accumulation, e.g. average occupancy or density) of the macroscopic or network fundamental diagram near critical accumulation to achieve maximum network throughput. Nevertheless, the maximum throughput (capacity flow) in urban road networks may be observed over a range of accumulation-values. In this work, an extension of a previously proposed real-time feedback perimeter flow control strategy is proposed that allows the automatic monitoring of the critical accumulation to help maintain the accumulation near the optimal range of accumulation-values, while network’s throughput is maximised. To this end, the authors design a Kalman filter-based estimation algorithm that utilises real-time measurements of circulating flow and accumulation of vehicles to produce estimates of the currently prevailing critical accumulation. The developed strategy may be valuable whenever the network fundamental diagram is not well defined and the critical accumulation cannot accurately be specified or is subject change due to traffic-responsive signal control, traffic composition (e.g. cars versus buses), or nonrecurrent day-to-day traffic patterns. The authors use real experimental data from an urban area with 70 sensors and show that the area exhibits a fundamental diagram with low scatter. The authors demonstrate that the fundamental diagram is reproduced under different days but its shape and critical occupancy depend on the applied semi-real-time signal control and the distribution of congestion in the network. Preliminary results from the application of the estimation algorithm to the experimental data indicate good estimation accuracy and performance, and rapid tracking behaviour.