Day-to-Day Signal Retiming Scheme for Single-Destination Traffic Networks Based on a Flow Splitting Approach

Traffic signal retiming usually requires engineers to fine-tune the signal plan several times to accommodate the traffic pattern changes because the retiming process itself can be considered as a perturbation to the traffic network. To facilitate the signal retiming process, this paper presents a discrete day-to-day signal retiming problem for fine-tuning the green splits in a single-destination traffic network to mitigate the congestion induced by travelers’ adaptation to the new signal plan. The proposed optimal control formulation applies a predictive scheme, rather than a reactive scheme, to fine-tune signals proactively. The embedded day-to-day traffic dynamics model captures travelers’ tendency of swapping to less congested routes, which is formulated as flow splitting at the node level that prevents the difficulties of path enumeration and flow conservation in traditional day-to-day models. The underlying flow splitting approach ensures flow conservation endogenously while preserving properties of the node-level cost functions, including Lipschitz continuity and strong monotonicity. Based on the proposed optimal control formulation built upon the day-to-day model, this study constructs an effective solution algorithm by leveraging the necessary conditions of optimality for the discrete day-to-day signal retiming problem. Numerical examples demonstrate that the proposed signal retiming scheme can reduce the total system travel time over the traffic equilibration period.