A rolling-horizon quadratic-programming approach to the signal control problem in large-scale congested urban road networks

Aboudolas, Konstantinos; Papageorgiou, M.; Kouvelas, Anastasios; Kosmatopoulos, Elias B. · 2009 · OpenAlex-citations

DOI: 10.1016/j.trc.2009.06.003

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Summary

This paper addresses the challenge of real-time, network-wide traffic signal control in large-scale urban road networks, particularly under congested conditions where traditional strategies often fail. The authors investigate a rolling-horizon quadratic-programming control (QPC) methodology designed to minimize and balance link queues, thereby reducing the risk of queue spillback and gridlock. The motivation stems from the limitations of existing systems: while strategies like SCOOT and SCATS perform well in undersaturated traffic, their efficiency deteriorates under congestion. Conversely, model-based strategies using dynamic programming or mixed-integer programming suffer from exponential computational complexity, making them infeasible for real-time application across large networks. The proposed QPC approach utilizes a store-and-forward modeling paradigm to circumvent discrete variables, enabling efficient optimization with polynomial complexity. The study employs a simulation-based experimental design using the urban road network of Chania, Greece, which consists of 16 signalized junctions and 60 links. The traffic flow dynamics are modeled using a store-and-forward approach, where the control problem is formulated as a quadratic-programming problem aimed at minimizing link occupancies. This optimization is embedded in a rolling-horizon (model-predictive) control scheme, solving for an optimal control sequence over a finite horizon but applying only the immediate control action. The QPC strategy is compared against the Linear-Quadratic (LQ) approach used in the Traffic-responsive Urban Control (TUC) strategy and optimized fixed-time control settings. Five demand scenarios ranging from very low to high, fluctuating demand were tested. Performance was evaluated using two criteria: Total Time Spent (TTS) and Relative Queue Balance (RQB). The results demonstrate that the QPC approach significantly outperforms both fixed-time control and the LQ-based TUC strategy, particularly under congested conditions. Optimized fixed-time plans (FT-B) performed better than field-applied fixed plans (FT-A) but were still inferior to the adaptive strategies. Among the adaptive methods, QPC achieved lower TTS and RQB values than LQ across all scenarios, indicating superior ability to balance queues and prevent spillback. The study also found that the performance of QPC depends on the optimization horizon and the availability of demand predictions; longer horizons generally improved performance, though the benefit was contingent on accurate demand forecasts. The fundamental diagram for urban networks was used to illustrate how QPC extends the saturation region and mitigates the drop in network flow associated with oversaturation. The significance of this work lies in providing a computationally feasible, real-time solution for network-wide signal control in congested urban environments. By integrating constraints directly into the quadratic programming formulation and using a rolling-horizon framework, the method offers a robust alternative to existing strategies that either lack real-time feasibility or fail under heavy congestion. The findings suggest that balancing link queues through QPC is an effective mechanism for maintaining network throughput and preventing gridlock, offering a practical tool for traffic management systems in large cities.

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• traffic density