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.
The delay vehicles experience at signalized intersections is one of the most important indicators for measuring intersection performance. The interpretation of delay variability evolvement at intersections gives a comprehensive insight into arterial traffic operation. Thus, an analytical model is proposed to investigate delay variability at coordinated intersections. Two different flow rates are assumed for both effective red and green periods in cumulative curves, through which the effect of signal coordination is incorporated in delay estimation. Then, an analogy of Markov chain process is used to explore the mechanism of stochastic overflow queue at signalized intersections. Numerical case studies show that with the decrease of arrival proportions during green, the shape of delay distribution in both undersaturation and oversaturation cases shifts faster towards higher values, implying that the coordination effect between paired intersections has a great effect on the delay distribution. As for delay fluctuation range, favorable coordination is demonstrated to be able to weaken the variability of delay estimates especially for undersaturation conditions.
