New Optimal Cycle Length Formulation for Pretimed Signals at Isolated Intersections

Under near-saturated or saturated conditions, the optimal cycle length formulation proposed by Webster becomes infeasible because (1) it generates an unreasonably large cycle length as the intersection critical flow ratio approaches one, and (2) it becomes inapplicable if the intersection critical flow ratio is equal to or greater than one. An attempt is made here to rectify this deficiency by providing a simplistic but reasonably accurate formulation for optimal cycle length under saturated conditions. Using the optimal timing variables obtained based on the delay minimization criterion, the functional relationship between optimal cycle lengths and traffic flow parameters, including intersection critical flow ratio, total lost time, and duration of analysis period, is established through a nonlinear regression analysis. The resulting formulation generates fairly accurate estimates of optimal cycle length with 5.7% average deviation from the analytical solutions. The corresponding average delay, however, only deteriorates about 0.9%. The timing plans consisting of the proposed optimal cycle estimates and the equalized degree-of-saturation green splits produce near-optimal delay performance with 3.3% degradation from the optimal solutions.