Multi-reservoir traffic dynamics: Outflow network MFD and state estimation with sparse traffic data

• Outflow ratio estimation using FCD with unknown penetration rate information. • Direct outflow-NMFD estimation using sparse floating car data. • Model-driven traffic state estimator for multi-reservoir systems. • Enhanced traffic state estimates with real-time integration of sparse FCD and LDD. • Precise estimation of traffic dynamics in both steady and transitional traffic states. This study introduces an innovative framework for traffic state estimation in multi-reservoir networks, tackling the challenges posed by sparse data in urban traffic networks. By integrating Floating Car Data (FCD) and Loop Detector Data (LDD), the framework estimates traffic dynamics, such as inflows, outflows, transfer flows, and accumulation, without requiring detailed trip information or path flow distribution methods. A step forward in this study is a method for the estimation of internal outflow and transfer flows, enabling the direct estimation of outflow Network Macroscopic Fundamental Diagrams (outflow-NMFDs) which overcomes the shortcomings of outflow-NMFD estimation through the full set of sensors or indirect estimation via the production-NMFD. As argued, the outflow-NMFD is deemed the more robust foundation for the accumulation-based modelling in multi-reservoir systems. Accordingly, the estimated outflow-NMFD is used to build the accumulation-based model, in which the model outputs are combined with sparse real-time measurements, improving the model’s alignment with actual traffic conditions. The framework’s adaptability allows it to function effectively under varying levels of probe vehicle penetration, making it suitable for real-world scenarios where data availability can be inconsistent or limited. Simulation results validate the model’s robustness in capturing both steady-state and dynamic traffic behaviours, maintaining high accuracy even during abrupt demand changes. Furthermore, the framework performs reliably under stochastic conditions, demonstrating its resilience to daily traffic fluctuations. By reducing dependence on widespread sensor deployment across the network or its boundaries, this cost-effective approach offers a practical solution for real-time traffic monitoring and management in multi-reservoir systems, even when the boundaries of the system are not fixed in the network.