Stochastic Reliability Analysis of Peak Hour Factor Variations and Their Impact on Intersection Signal Delay

Abstract

Traffic signalized intersections form crucial control nodes in urban networks, where fluctuations in vehicle arrival rates during peak periods often produce extended delays and unreliable performance. Traditional deterministic design approaches, based on mean hourly volumes, fail to represent short-term variability inherent in real-world traffic conditions. This paper presents a stochastic reliability analysis framework to quantify the effect of Peak Hour Factor (PHF) variability on intersection delay performance, integrating field traffic data from Palm Beach and Broward Counties, Florida. Using Monte Carlo simulation, delay probability distributions were generated, and key reliability metrics-including the probability of failure (Pf) and reliability index (β)-were evaluated for both morning (AM) and evening (PM) peaks.
Results revealed that intersections with low PHF (< 0.80) exhibited higher probabilities of exceeding the critical 55 s/veh delay threshold, with PM peaks showing Pf ≈ 0.39 and β = 0.28, compared to AM Pf ≈ 0.27 and β = 0.61. Incorporating additional uncertainties-arrival-type randomness and saturation flow variability-increased unreliability by approximately 15%. The proposed framework demonstrates that reliability-based modeling provides a more realistic, risk-informed foundation for traffic signal timing, design evaluation, and urban mobility planning.