Dilemma zone (DZ), also called decision zone in other literature, is an area where drivers face an indecisiveness of stopping or crossing at the yellow onset. The DZ issue is a major reason for the crashes at high-speed signalized intersections. As a result, how to prevent approaching vehicles from being caught in the DZ is a widely concerning issue. In this dissertation, the author addressed several DZ-associated issues, including the new stochastic safety measure, namely dilemma hazard, that indicates the vehicles' changing unsafe levels when they are approaching intersections, the optimal advance detector configurations for the multi-detector green extension systems, the new dilemma zone protection algorithm based on the Markov process, and the simulation-based optimization of traffic signal systems with the retrospective approximation concept. The findings include: the dilemma hazard reaches the maximum when a vehicle moves in the dilemma zone and it can be calculated according the caught vehicles' time to the intersection; the new (optimized) GES design can significantly improve the safety, but slightly improve the efficiency; the Markov process can be used in the dilemma zone protection, and the Markov-process-based dilemma zone protection system can outperform the prevailing dilemma zone protection system, the detection-control system (D-CS). When the data collection has higher fidelity, the new system will have an even better performance. The retrospective approximation technique can identify the sufficient, but not excessive, simulation efforts to model the true system and the new optimization algorithm can converge fast, as well as accommodate the requirements by the RA technique. / Ph. D.