Enhancing Traffic State Estimation at Bottlenecks Through Improved Demand Modeling: A Greenshields-Grounded Approach

Accurate estimation of traffic state under oversaturated conditions is fundamental to a wide range of transportation applications. While intuitive, volume-to-capacity ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>q</mml:mi> <mml:mo stretchy="false">/</mml:mo> <mml:msub> <mml:mrow> <mml:mi>q</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>c</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ) ratio-based link performance functions (LPF) are challenged by the U-shaped pattern of real-world speed-flow plots, which contradict the monotonic assumptions of link performance models such as the Bureau of Public Roads (BPR) function, particularly when <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>q</mml:mi> <mml:mo stretchy="false">/</mml:mo> <mml:msub> <mml:mrow> <mml:mi>q</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>c</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ≥ 1. This study addresses this critical gap by proposing an enhanced demand estimation method grounded in the Greenshields model, incorporating a real-time inflow correction factor to more accurately capture traffic demand at bottlenecks. In parallel, a modified LPF is introduced, replacing the traditional volume-to-capacity ratio with a demand-to-capacity ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo stretchy="false">/</mml:mo> <mml:msub> <mml:mrow> <mml:mi>q</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>c</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ) ratio formulation. This enables a segmented travel time and speed estimation model capable of capturing nonlinear congestion dynamics under oversaturated conditions. The effectiveness of the proposed framework is evaluated using real-world traffic data collected from two highly congested urban corridors, namely West Third Ring Road in Beijing and I-405 in Los Angeles. Results show that the proposed method significantly outperforms both the symmetric method and the quasi-density model relating to demand and travel time estimation accuracy. In the I-405 case, for example, the mean absolute percentage error (MAPE) in travel time estimation drops from 8.54% to 3.86%, while the coefficient of determination (R 2 ) improves from 0.83 to 0.95. Comparative analysis further reveals that the Beijing corridor experiences higher demand, lower supply, and reduced discharge efficiency. These findings demonstrate the practical utility and robustness of the proposed method for real-world congestion diagnosis and urban mobility management.