A stochastic delay model for signal-free intersections

This study presents a stochastic delay model that treats signal-free intersections as systems of servers where the probability of conflict between vehicles determines delay. Rather than relying on predetermined major-minor hierarchies, the model builds on interaction between any two approaching vehicles attempting to occupy the same conflict zone simultaneously. This conflict-probability framework applies across many traffic scenarios, from traditional unsignalized multi-modal intersections, merging sections, and roundabouts to signal-free intersections for autonomous vehicles (AVs). The model employs queuing theory formulations where service time depends on conflict probability and clearance time for conflict zones. The model extends to multi-movement intersections through dependent and independent conflict zone networks and accommodates time-varying demand through dynamic parameter adaptation. Theoretical analysis reveals that equal inflows maximize delays due to peak conflict probabilities. Validation using real-world trajectory datasets demonstrates improvements over Highway Capacity Manual and Austroads methods across diverse scenarios. Furthermore, the proposed delay model achieves mean absolute errors of 4.6 to 10.9 s using simulation of signal-free intersections for AVs under first-come first-served and communication-free distributed control algorithm protocols.