Incorporation of Endogenous Exit Capacities in Node Models with Various Movement Exit Speeds

Abstract

In macroscopic traffic assignment, the node model is fundamental for accurately capturing traffic dynamics at junctions and intersections, which are often the primary sources of travel delays in urban networks. The precision of the node model is important for predicting delays and managing flows, which directly impacts traffic condition simulations, congestion management, and network performance optimisation. However, existing node models typically assume exogenous exit capacities for links, movement, or lanes feeding the node. They do so by either assuming fixed capacities or adjusting externally based on traffic control. This assumption often overlooks variations in exit capacities caused by flow compositions and vehicle turning behaviours, leading to less reliable predictions and reduced applicability in real-world scenarios. This study proposes a novel approach that can achieve endogenous exit capacities within the node model. Rather than dynamically adjusting exit capacities, our approach moderates the flow rates endogenously with flow compositions. This adjustment is made by scaling inflows for each movement inversely proportional to their turn speeds in the pre-processing stage and rescaling outflows in the postprocessing stage without requiring modifications to the node model itself. Additionally, this study presents a solution algorithm consistent with our proposed method. Two numerical examples are provided to demonstrate the feasibility and capability of this approach. The results indicate that the node model that does not consider endogenous exit capacities may either overestimate or, in rare cases, underestimate the outflows.