Investigating Parameter Interactions with the Factorial Design Method: Webster's Optimal Cycle Length Model

Accurate estimation of cycle length is an important factor in the performance of a signalized intersection. Cycle length is determined by employing some parameters such as arrival flow, number of phase, lost time etc., but each parameter has different effects on a cycle length model. If the effects of parameters and their interactions in the cycle length model are known, the performance of the model can be effectively increased. In this study, the sensitivity of optimal cycle length model proposed by Webster and its parameters were analysed with the factorial design method. The reason for selecting this model is that the model has still been used in signal timing practice and has lead many studies of researchers over 50 years. The evaluation of sensitivity analysis shows that while arrival flow as single parameter has a major effect on the optimal cycle length model, the remaining single parameters of the model (i.e., the number of phase in a cycle length, saturation flow and lost time) have secondary importance. Additionally, two parameter interactions of arrival flow-saturation flow have major effect on the model results. For three parameter interactions, the number of phase-arrival flow-saturation flow interaction has a slightly larger effect than the other three-parameter interactions. As a result, the factorial design method is an effective tool to determine the importance of the model parameters for researchers, and it can be employed to other traffic engineering applications.