Analysis of delay variability at isolated signalized intersections

On urban arterials, travel time variability is largely dependent on the variability in the delays vehicles experience at signalized intersections. The interpretation of delay evolvement at intersections will give a comprehensive insight into arterial travel time variability and provide more possibilities for travel time estimation. Accordingly, an analytical model is proposed to study delay variability at isolated, fixed-time controlled intersections. Classic cumulative curves are utilized to derive average delay (per cycle) formulas by assuming a deterministic overflow queue. Then, an analogy with the Markov chain process is made to clarify the mechanism of stochastic delays and overflow queues at signalized intersections. It was found that, in undersaturated cases, the shape of the delay distribution changes very little over time, whereas for saturated and oversaturated cases the delay distribution is time-dependent and becomes flatter with an increasing number of cycles. The analysis of arrival distributions, e.g., Poisson and binomial, produces the conclusion that the variability of arrivals has a significant effect on delay estimates in both undersaturated and oversaturated conditions. A larger variance of arrival flow results in a larger variance of delay distribution. All of these analyses can help road authorities to gain insights into arterial travel time variability.