Question $4(6\mathrm{.}5$ points$)$

Consider the intersection geometry below. For this intersection, lanes with protected throughs have saturation flow of $1800ve\frac{h}{h}r,$ lanes with protected lefts have a saturation flow of $1700ve\frac{h}{h}r,$ lanes with shared through and right have saturation flow of $1600ve\frac{h}{h}r,$ lanes with shared through, right, and permitted lefts have saturation flow of $1000$ and lanes with permitted lefts have saturation flow of $500$ veh$/$hr$.$ Saturation flows for lane groups with more than one lane are the sum of the individual lane saturation flow rates $($ignore weighting$).$ The start$-$up and clearance lost times are both $2$ sec$.$ Assume the displayed flow rates have already been adjusted by the PHF$.$

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A$)$ Using a three$-$phase design $(1-$N$/$S Lefts, $2-$N$/$S Through$/$Right$,3-$All E$/$W$),$ complete the table

$\backslash$table$[[$Approach$,$EB$,$WB$,$NB$,$SB$],[$Lane Group,L$/$T$/$R$,$L$,$T$/$R$,$L$,$T$/$R$,$L$,$T$/$R$],[\backslash$table$[[$Analysis Flow $($v$)]],,,,,,,],[\backslash$table$[[$Saturation Flow$],[($s$)]],,,,,,,],[$Flow Ratio $($v$/$s$),,,,,,,],[\backslash$table$[[$Critical Lane$],[$Group$?($Y or N$)]],,,,,,,]]$

B$)$ Based on the Table from part A$,$ calculate the minimum cycle length using a $90\%$ capacity utilization.

C$)$ Using a minimum cycle length of $30$ s$,$ find the following for WB T$/$R lane group only. Effective green $($g$),$ Capacity $($c$),$ v$/$c $($X$),$ d$1,$ d$2($For analysis duration T$=0\mathrm{.}25$ hrs$)$ and LOS.