b$)$ The following traffic counts summarised in Table $3$ were made at an approach for a TWSC junction.

Table $3.$ Traffic counts during morning and evening periods

$\backslash$table$[[$Movement$,$Traffic volume $($veh$/$hr$)],[$Morning period,Evening period$],[$Left turn $($LT$),66,52],[$Through movement $($TH$),44,122],[$Right turn $($RT$),90,52]]$

Determine the following:

$($i$)$ The potential capacity for each movement given the conflicting volumes, critical gap and follow$-$up times summarised in Table $4.(6$ marks$)$

Table $4.$ Conflicting volumes, critical gap and follow$-$up times

$\backslash$table$[[$Movement$,$ Critical gap,

$t_{cs}(s),$Follow$-$up time, $t_f($s$),$Conflicting volumes, $ve{r}_{cl}($veh$/$hr$)],[$Morning period,Evening period$],[$Left turn $($LT$),6\mathrm{.}26,3\mathrm{.}33,399,334],[$Through movement $($TH$),6\mathrm{.}56,4\mathrm{.}03,2071,2298],[$Right turn $($RD$),7\mathrm{.}16,3\mathrm{.}53,1576,1742]]$

Page $2$ of $3$Given: Potential capacity, $c_{px}=v_{cx}[\frac{e^{-v_{cx}\frac{t_{cx}}{3600}}}{1-e^{-v_{cx}\frac{t_{fx}}{3600}}}]$

$($ii$)$ The shared lane capacity for the approach during the different time periods. $(3$ marks$)$ Given: Shared Lane capacity, $c_{SH}=\frac{{\displaystyle \underset{y^{\text{'}}}{\overset{?}{}}}{v}_{y^{\text{'}}}}{{\displaystyle \underset{y}{\overset{?}{}}}(\frac{v_{y^{\text{'}}}}{c_{my}})}$;

$v_y=$ flow rate for movement $y$ sharing a lane with another minor street flow,

$c_{my}=$ potential capacity for movement $y$ sharing a lane with another minor street flow

$($iii$)$ The delay for the approach during the different time periods. $(6$ marks$)$ Given:

delay, $d_x=5+\frac{3600}{c_{px}}+900T[\frac{v_x}{c_{px}}-1+\sqrt[\phantom{2}]{(\frac{v_x}{c_{px}}-1{)}^2+\frac{(\frac{3600}{c_{px}})(\frac{v_x}{c_{px}})}{450T}}],$

$T=0\mathrm{.}25,v_x=$ demand flow rate for shared lane in veh$/$hr$.$