Marginal Delay: New Measure for Quality of Service at Signalized Intersections

Most existing analytical models determine signal settings at intersections by minimizing total delay. The main problem with these methods is that when green split is based on minimum total intersection delay, low-volume approaches are penalized. Although this may be appropriate, the extent of this penalty has never been theoretically resolved. A new concept and its methodology for determining traffic signal settings were proposed to provide a theoretical basis for this issue. This new concept, marginal delay, has its inception in marginal analysis and is defined as the increase in total delay resulting from a one-vehicle increase in the approach volume. Given the nature of the existing delay equations, marginal delay also represents the measure of the maximum individual vehicle delay for a given cycle. Three marginal delay equations were derived and analyzed over a range of 265 cases. Marginal delay analysis was applied to signal-setting calculations and compared with existing delay models. The work concluded that marginal delay is a significant variable in the calculation of signal settings, especially when large differences exist between the volumes of the different approaches. Furthermore, marginal delay used in conjunction with total delay can improve current signal-timing methods by quantifying the penalty applied to light-volume approaches and by providing a measure of variance between real-time flow and design flow.