An intersection has a three$-$timing$-$stage signal with the movements allowed in each timing stage and corresponding analysis and saturation flow rates shown in the table below.

Calculate the sum of the flow ratios of the critical lane groups.

Determine the minimum cycle length. Also calculate the effective green time for each timing stage. Assume the lost time is $4$ seconds per timing stage and a critical intersection v$/$c of $0\mathrm{.}9$ is desired.

Calculate the optimal cycle length. Assume the lost time is $4$ seconds per timing stage.

$\backslash$table$[[$Timing stage,$1,2,3],[$Allowed movements,NB L$,$ SB L$,$NB T$/$R$,$ SB T$/$R$,$EB L$,$ WB L$,$EB T$/$R$,$ WB T$/$R$],[$Analysis flow rate,$330,365ve\frac{h}{h},1125,1075ve\frac{h}{h},110,80ve\frac{h}{h},250,285ve\frac{h}{h}$