Determination of the optimum cycle from a consideration of delays on the approach

Abstract

Minimisation of delay for a complete intersection has been investigated in Appendix 3 Road Research Technical Paper 39 by considering the first two terms in equation 43.1. The total delay for the intersection is given by

$$\begin{array}{*{20}{c}} {D = \sum (average\,delay\,per\,vehicle)x\,flow} \\ {D = \sum\limits_{r - 1}^{r - n} {\left[ {\frac{{c{{(1 - {\lambda _r})}^2}}}{{2(1 - {\lambda _r}{x_r})}} + \frac{{x_r^2}}{{2{q_r}(1 - {x_r})}}} \right]{q_r}} } \\ { = \sum\limits_1^n {\left[ {\frac{{c{y_r}{s_r}{{(1 - {\lambda _r})}^2}}}{{2(1 - {y_r})}} + \frac{{y_r^2}}{{2{q_r}({\lambda _r} - {y_r})}}} \right]} } \end{array}$$

where y = q/s for any phase.