Signal Timing Optimization for Mixed Connected Automated Traffic Based on a Markov Delay Approximation

Connected automated vehicles (CAVs) offer unparalleled opportunities to revolutionize existing transportation systems. In the near future, CAVs and human-driven vehicles (HDVs) are expected to coexist, forming a mixed traffic system. Although several prototype traffic signal systems leveraging CAVs have been developed, a simple yet realistic approximation of mixed traffic delay and optimal signal timing at intersections remains elusive. This paper presents an analytical approximation for delay and optimal cycle length at an isolated intersection of mixed traffic using a stochastic framework that combines Markov chain analysis, a car following model, and queuing theory. Given the intricate nature of mixed traffic delay, the proposed framework systematically incorporates the impacts of multiple factors, such as the distinct arrival and departure behaviors and headway characteristics of CAVs and HDVs, through mathematical derivations to ensure both realism and analytical tractability. Subsequently, closed-form expressions for intersection delay and optimal cycle length are derived. Numerical experiments are then conducted to validate the model and provide insights into the dynamics of mixed traffic delays at signalized intersections.