Optimization of approach traffic signal control scheduling for four-phase intersections

Abstract This paper proposes an analytical intersection delay function for traffic signal control and network flow assignment. The proposed function incorporates queue length and green capacity, and provides an analytically tractable estimate of vehicle delay at signalized intersections. Based on Wardrop’s principles, a bilevel optimization model is developed in which the lower level determines equilibrium traffic flows for a given signal timing plan and the upper level optimizes the green splits under known travel demand. The framework is first derived for two-phase signal control and is then extended to a four-phase setting incorporating through movements and protected left-turn phases. The bilevel formulation with route choice is solved on a two-path network example. For the empirical part of the study, traffic data were collected at a four-phase signalized intersection in China; because demand is fixed per turning movement at an isolated intersection, the lower-level flow assignment is not a decision variable there and the problem reduces to a single-level nonlinear program. Under that formulation, the optimized green splits reduce the modelled total delay per cycle by 26.16% relative to the as-operated timing plan at the study site for one off-peak hour of measurement, and by 23.58% when a practical minimum displayed green of 15 s per phase is imposed.