Estimating the minimum delay optimal cycle length based on a time-dependent delay formula

For fixed time traffic signal control, the well-known Webster's formula is widely used to estimate the minimum delay optimal cycle length. However, this formula overestimates the cycle length for high degrees of saturation. In this paper, we propose two regression formulas for estimating the minimum delay optimal cycle length based on a time-dependent delay formula as used in the Canadian Capacity Guide and the Highway Capacity Manual (HCM). For this purpose, we develop a search algorithm to determine the minimum delay optimal cycle length required for the regression analysis. Numerical results show that the proposed formulas give a better estimation for the optimal cycle length at high intersection flow ratios compared to Webster's formula.