A stochastic computational model for yellow time determination and its application

This paper proposes a stochastic model to determine the yellow time according to the occurring probability of Type‐I dilemma zone (P_DZ). Unlike the conventional methods generally based on the deterministic traffic flow theory, the proposed model fully accounts for the randomness of input variables such as approaching speed, deceleration rate, perception‐and‐reaction time, and distance to stop‐line at the yellow onset. A theoretical model is firstly established, and a computational program incorporating Monte Carlo Simulation is then developed to facilitate its general solution. These two alternative solution approaches to derive P_DZ and Y are proposed, depending upon whether D/V and (τ + V/2d) follow certain analytical distributions or not. In addition, field data at a typical high‐speed highway intersection are collected to validate the model. Based on the validated model, comprehensive sensitivity analysis is conducted to look into the entire picture of the relationship between P_DZ and the distributions as well as correlations of the input variables. To demonstrate the application of the proposed model, the required yellow times for various conditions are calculated based on the acceptable levels of P_DZ, and representative application tables for typical cases are finally provided. With the aid of the proposed methodology, traffic engineers are capable of designing yellow time in a more sophisticated manner. Copyright © 2014 John Wiley & Sons, Ltd.