Question $3(50$ points$)$

For the geometric and traffic characteristics shown below determine a suitable signal phasing system and phase lengths for the intersection using the Webster method. Show a detailed layout of the phasing system and the intersection geometry used.

$\backslash$table$[[$Approach$,$North Bound,South Bound,East Bound,West Bound$],[$Width $($ft$),56,56,68,68],[$Left turn,$133,73,168,134],[$Through movement,$420,373,563,516],[$Right turn,$140,135,169,178],[$Conflicting pedestrian volumes,$900,1200,1200,900],[$PHF$,0\mathrm{.}95,0\mathrm{.}95,0\mathrm{.}95,0\mathrm{.}95]]$

Assume the following saturation flows:

Through lanes: $1600$ veh$/$h$/$In

Through $+$ right$-$turn lanes: $1400$ veh$/$h$/$In

Left$-$turn lanes: $1000$ veh$/$h$/$In

Left$-$tun $+$ through lanes: $1200$ veh$/$h$/$In

Left$-$turn $+$ through $+$ right$-$turn lanes: $1000$ veh$/$h$/$In