Lost Time and Cycle Length for Actuated Traffic Signal

Abstract

Time within an actuated signal cycle can be decomposed into time that is fully used, which is the saturation headway multiplied by the number of passing vehicles, and time that is wasted or lost. Activity network modeling is used to show the interaction between signal timing events and traffic flow transitions. Seven components of generalized lost time are identified: those associated with start-up, minimum green, parallel queue discharge (for simultaneous gap-out), extension green, parallel extension (for nonsimultaneous gap-out), the passing of the critical gap, and phase end. Simple formulas can be used to estimate all of these components for many practical cases, allowing one to estimate average cycle length without iteration. The modeling framework accounts for the dual-ring structure with minimum green and maximum green constraints and on–off settings for recall and simultaneous gap-out. Experiments with microsimulation software verify the formulas developed. The formulas show the sensitivity of lost time, and therefore average cycle length, to parameters that a designer can control including detector setback, critical gap, gap-out settings, and number of lanes. They also show sensitivity to total demand and to the ratio of noncritical to critical phase volumes.