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

$$\begin{gathered} D = \sum {\left( {average\;delay\;per\;vehicle} \right) \times flow} \hfill \\ D = \sum\limits_{r = 1}^{r = n} {\left[ {\frac{{c{{\left( {1 - {\lambda _r}} \right)}^2}}}{{2\left( {1 - {\lambda _r}{x_r}} \right)}} + \frac{{x_r^2}}{{2{q_r}\left( {1 - {x_r}} \right)}}} \right]} \;{q_r} \hfill \\ \quad = \sum\limits_1^n {\left[ {\frac{{c{y_r}{s_r}{{\left( {1 - {\lambda _r}} \right)}^2}}}{{2\left( {1 - {y_r}} \right)}} + \frac{{y_r^2}}{{2{q_r}\left( {{\lambda _r} - {y_r}} \right)}}} \right]} \hfill \\ \end{gathered} $$

where y = q/s for any phase.