Dynamic Signal Timing at Urban Intersections: Cycle-Based Delay Classification and Multi-Period Optimization

Zhao Guo (), Alexander Y. Krylatov and Dan Wang
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Zhao Guo: Applied Mathematics and Control Processes, Saint Petersburg State University, 35 Universitetskaya Prospekt, Saint Petersburg 198504, Russia
Alexander Y. Krylatov: Applied Mathematics and Control Processes, Saint Petersburg State University, 35 Universitetskaya Prospekt, Saint Petersburg 198504, Russia
Dan Wang: Applied Mathematics and Control Processes, Saint Petersburg State University, 35 Universitetskaya Prospekt, Saint Petersburg 198504, Russia

Mathematics, 2025, vol. 13, issue 21, 1-20

Abstract: This paper addresses the optimization of traffic signal timing at urban intersections by introducing a dynamic green ratio allocation framework based on cycle-based delay classification. Conventional methods such as the Webster delay model often fail to capture the asymmetric delay characteristics and the impact of fluctuating flows across multiple cycles. We propose a novel approach that classifies cycles into undersaturated and oversaturated states and develops dedicated optimization models for each type. For undersaturated cycles, a new delay function is derived to accurately capture the interaction between queue dissipation and green time allocation, enabling multi-period minimization of total vehicle delay. For oversaturated cycles, queue minimization at the end of each phase is adopted to accelerate congestion dissipation. The framework is validated through simulation and compared with existing methods, demonstrating superior performance in congestion clearance and delay minimization. The results show improved adaptability to changing traffic conditions and enhanced practicality for real-time signal control in smart transportation systems.

Keywords: signal timing optimization; dynamic green ratio allocation; cycle-based delay classification; queue minimization; smart transportation systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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