Estimating Vehicles in the Dilemma Zone and Application to Fixed-Time Coordinated Signal Optimization

Most traffic accidents are related to driving behaviors. Dangerous driving behaviors may occur if a vehicle is trapped in the dilemma zone. Traditional methods for calculating the number of vehicles in the dilemma zone (NVDZ) are usually based on field data collection and postanalysis and require a great deal of time and human resources. This paper proposes an analytical model for estimating NVDZ on the basis of signal timing, arterial geometry, traffic demand, and driving characteristics. Through application of Robertson's platoon dispersion model, the proposed model calculates the flow rate in the dilemma zone area at yellow onset as well as queue lengths under a discrete time horizon. A VISSIM-based microscopic simulation is then calibrated to validate the NVDZ calculation. The mathematical framework for signal optimization is implemented. Most of the current signal optimization methodologies do not consider safety measures such as NVDZ to be an objective. In this paper, delay and NVDZ are formulated as a multi-objective optimization problem addressing efficiency and safety together. Examples show that delay and NVDZ are competing objectives and cannot be optimized at the same time. Finally, an economic model is applied to quantify both delay and NVDZ in monetary values. The optimal solution considering both factors reduces NVDZ by more than 20% with a less than 2% increase in delay compared with minimizing only delay. The total cost is reduced.