Performance of Fixed-time Signal Control at Isolated Intersections in a Connected and Automated Environment: an Analytic Approach

Fixed-time control is the most extensively deployed traffic control method at intersections, thanks to its practicality and robustness. The emerging of connected and automated vehicle (CAV) technologies can further improve the performance of traditional fixed-time control with sophisticated trajectory planning and smaller vehicular gap. However, existing studies have not paid enough attention to the investigation of the potential improvement. This paper presents an analysis method on two key performance metrics, i.e., average vehicle delay and intersection throughput at isolated intersections under a CAV environment. We concentrate on Poisson arrival pattern and model the vehicle arrival as a discrete Markov process. With elaborate derivations using conditional expectation and computation of a higher order heterogeneous ordinary differential equation, the average vehicle delay is expressed as a function of Poisson intensity. The throughput can be derived based on a classic conclusion of rate stability. In addition, numerical simulation is conducted to verify correctness of the theoretical results of delay and throughput.