Comparison of Variability of Individual Vehicle Delay and Average Control Delay at Signalized Intersections

Two types of delay variability have been commonly referred to at signalized intersections: arrival-time-dependent individual vehicle delay variability and average control delay variability. The former focuses on the delay experienced by individual vehicles, whereas the latter deals with the average consequence of signal control for the entire traffic flow during a given evaluation period. With a number of methods available for estimation, little research has been conducted to enable a comprehensive comparison of these two variability measures. This issue is addressed by a comparison of these two types of delay variability at isolated, fixed-time controlled intersections based on two analytical models accounting for the stochastic nature of traffic arrivals and overflow queues. The results show that in undersaturated conditions, individual vehicle delay tends to have a wider distribution and a larger variance compared with average control delay. In oversaturated conditions, the shapes of both types of delay distributions shift to the higher values with larger variances. Different arrival processes are found to have a significant influence on the pairwise delay distributions. In addition, the width of the delay distribution based on percentiles is used to quantify the delay uncertainty under different degrees of saturation. Compared with average control delay, individual vehicle delay is found to have a larger uncertainty in undersaturated conditions, whereas it becomes relatively certain in oversaturated conditions. All the analyses have special practical implications for enriched knowledge of stochastic arrival and departure processes at signals.