Optimal Cycle-Length Formulas for Intersections With or Without Transit Signal Priority

Webster’s formula for optimal green split and cycle length is a common way to optimize signal settings at signalized intersections. However, these equations are intended to be used for optimizing signal timing plans for fixed-time isolated intersections, balancing phase utilization and minimizing car delay for undersaturated conditions. These formulas are less appropriate for near-saturated and oversaturated conditions because of the asymptotical behavior of the cycle-length formula when the intersection flow ratio approaches one. These formulas were not conceived for operation under transit signal priority (TSP) strategies. The main objective of this paper is to develop formulas for the optimal cycle length that can be applied when mild TSP strategies, such as green extension or green extension with phase rotation, are implemented or when the intersection operates under near-saturated or oversaturated conditions. A formula for optimal cycle length is developed as a function of lost time and intersection flow ratio. The formula is applicable both with and without TSP. It appears that for green split, no new formulas are required because the Webster equisaturation approach is close to optimal. The cycle-length formula is validated for undersaturated, near-saturated, and oversaturated conditions with and without TSP for two-, three-, and four-phase signalized intersections. Compared with Webster’s formula, the proposed formula shows a significant improvement in reducing person delay. Compared with Webster’s formula, average person delay is 6%, 17%, and 22% less and average bus delay is 16%, 27%, and 35% less for two-, three- and four-phase signalized intersections, respectively.