Four$-$legged intersection shown in Figure Q$3$ is located in urban area. Each lane has a width of $3\mathrm{.}25m$ for North$-$South movements and $3\mathrm{.}5m$ for East$-$West movements. The characteristic of traffic flow at each approach is presented in Table Q$3.$

$($i$)$ Design a signalized intersection according to ATJ $13/87$ method with the consideration that North and South approaches are in the same Phase $1,$ while East and West approaches are in Phase $2$ and $3$ respectively. Given turning radius, $R=15m$ and the road is sloping $-3\%$ towards South. The average passenger car equivalent is $1\mathrm{.}3$pcu for all vehicles. An all red period may be taken as $3s\frac{ec}{?}$ phase, lost time due to late start is equal to $2$