Cycle-Length Optimization of Isolated Signalized Intersection with Mixed-Traffic Condition

For signalized intersections with mixed traffic conditions, pedestrians and bicyclists (P&Bs) affect the vehicle saturation flow rate (SFR), which further influences the cycle length. However, existing studies always consider the effect of P&Bs on vehicle SFR as a constant, which is actually time-variant according to the P&Bs crossing state. Thus, it is necessary to consider this characteristic when determining the cycle length. This study developed a cycle-length model that considers the time-variant effect of P&Bs. The vehicle SFR is first modified using the adjustment factor method. By substituting the modified vehicle SFR into Webster's delay formula, the numerical solutions of the optimal cycle were derived by considering the minimum vehicle delay as the target. Thereafter, using linear regression of the optimal and minimum cycles, the model was simplified, and an analytical solution of the optimal cycle was derived. The average deviation caused by simplification was 1.95%. The optimality of the model was validated by simulation, with significant reduction in vehicle delay compared with the traditional highway capacity manual (HCM) method.