Analysis and Modelling of the Relationship between Stopped and Control Delays by Differential Evolution Algorithm

Akgüngör, Ali Payıdar; Korkmaz, Ersin · 2016 · Crossref

DOI: 10.2174/1874149501610010266

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Summary

This study addresses the relationship between stopped delay and control delay at signalized intersections, challenging the conventional assumption that the conversion ratio ($D_s/D_c$) is a constant value of 0.76. While stopped delay is easily measurable in the field, control delay is the preferred metric for determining intersection level of service. Previous literature has debated whether the ratio between these two metrics is fixed or variable. This research aims to develop models that relate stopped delay to control delay using the Differential Evolution (DE) algorithm, a metaheuristic optimization technique, and to evaluate the sensitivity of the conversion ratio to traffic volume, cycle length, and green ratio. The methodology employed CORSIM simulation software to generate data for a four-leg signalized intersection. The simulations varied traffic volumes from 600 to 1400 vehicles per hour (vph), cycle lengths from 60 to 150 seconds, and green ratios from 0.35 to 0.60, with a constant saturation flow of 1800 vph. A total of 2700 simulation runs were conducted, yielding 270 data points for model development. The DE algorithm was used to optimize weighting factors for four mathematical model forms: linear without intercept, linear with intercept, power, and exponential. The objective function minimized the sum of squared errors between simulated and estimated control delays. The dataset was split into training (230 data points) and testing (40 data points) subsets. Additionally, a one-factor-at-a-time approach was used to isolate the effects of specific parameters on the conversion ratio. The results demonstrated that all four models achieved high coefficients of determination ($R^2$ ranging from 0.983 to 0.992), with the power model yielding the lowest mean square error. The average conversion ratio derived from the models was 0.74, close to the traditional 0.76 value, but the study confirmed that the ratio is not constant. Sensitivity analysis revealed that the conversion ratio decreases as traffic volume increases (dropping from 0.787 at 600 vph to 0.687 at 1400 vph) and as the green ratio increases (dropping from 0.781 at a green ratio of 0.40 to 0.646 at 0.60). Conversely, the conversion ratio increases with longer cycle lengths, rising from 0.731 at 60 seconds to 0.784 at 150 seconds. The significance of this work lies in its demonstration that using a fixed conversion ratio for delay estimation is inaccurate due to the stochastic nature of traffic and varying signalization parameters. The study concludes that the relationship between stopped and control delays is dependent on operational conditions, specifically volume, cycle length, and green ratio. Therefore, practitioners should utilize variable models rather than constant coefficients to accurately estimate control delay from field-measured stopped delay. The authors suggest future research incorporate additional parameters such as approach speed and saturation flow to further refine these models.

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