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Optimal cycle length formulas for intersections with or without transit signal priority

TitleOptimal cycle length formulas for intersections with or without transit signal priority
Publication TypeJournal Article
Year of Publication2016
AuthorsWolput B, Christofa E, Tampère CMJ
JournalTransportation Research Record: Journal of the Transportation Research Board
Date Published07/2016
Accession Number 01592101
KeywordsOptimization, Oversaturation (Traffic flow), Traffic delays, Traffic signal cycle, Traffic signal priority, Traffic signal timing

Webster’s formulas for optimal green split and cycle length are a common way for optimizing signal settings at signalized intersections. However, these equations were 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 due to the asymptotical behaviour 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 like green extension or green extension with phase rotation are implemented and/or when the intersection operates under near or oversaturated conditions. A formula for optimal cycle length is developed as a function of lost time and intersection flow ratio. It is applicable both with and without TSP. It appears that for green split, no new formulas are required as the Webster equisaturation approach is near-optimal. The cycle length formula is validated for undersaturated, near-saturated, and oversaturated conditions with and without transit signal priority for two-, three- and four-phase signalized intersections. Compared to Webster’s formula the proposed formula shows a significant improvement in reducing person delay. Compared to the Webster formula there is a 6%, 17% and 22% less average person delay and a 16%, 27% and 35% less average bus delay for two-, three- and four-phase signalized intersections respectively.