Question $1$

The analysis findings for a four phase, pretimed intersection are summarized in the Table below. Pedestrians were not considered in the analysis.

$\backslash$table$[[$Phase$,\backslash$table$[[$C$],[$length$]],$Yellow $+$ Red clearance,Available cycle length,Flow ratios,CS$,\backslash$table$[[$Green$],[($sec$)]]],[$A$,125,3+1,\backslash$table$[[109$ sec$],[($a$)]],0\mathrm{.}282,0\mathrm{.}809,37\mathrm{.}995],[$B$,3+1,0\mathrm{.}218,29\mathrm{.}372],[$C$,3+1,0\mathrm{.}162,21\mathrm{.}827],[$D$,3+1,0\mathrm{.}147,19\mathrm{.}806($b$)]]$

C $=$ optimal cycle length calculated using Webster's equation.

CS $=$ sum of the critical flow ratios.

$1\mathrm{.}1$ Show the calculations leading to the values marked as $($a$)$ and $($b$).$

$(4)$

$1\mathrm{.}2$ What is the total time allocated to phase B $($explain your answer$)?$

$(2)$

$1\mathrm{.}3$ Assume the green times for Phase A$,$ B$,$ C$,$ and D are rounded to $38,29,22,$ and $20$ sec $.,$ respectively. Draw a neat, labelled signalization strip diagram.

$(4)$

$[10$ marks$]$