Delay at signal-controlled intersections

Abstract

As has been briefly mentioned in chapter 36, the delay to vehicles on a traffic-signal approach has been investigated by F. V. Webster and reported in Road Research Technical Paper 39. By a combination of queueing theory and digital computer simulation it has been shown that the average delay per vehicle on a particular intersection arm is given by

$$d = \frac{{c{{(1 - \lambda )}^2}}}{{2(1 - \lambda x)}} + \frac{{{x^2}}}{{2q(1 - x)}} - 0.65{\left( {\frac{c}{{{q^2}}}} \right)^{1/3}}{x^{(2 + 5\lambda )}}$$

where d = average delay per vehicle, c = cycle time, λ = proportion of the cycle that is effectively green for the phase under consideration (that is, effective green time/cycle time), q = flow, s = saturation flow, x = degree of saturation, which is the ratio of actual flow to the maximum flow that can be passed through the approach (that is q/λs).