$5.$ The intersection shown in the figure is to be analysed using the HCM $2000$ methodology. The following additional information is available

$[10$ marks$]$

$-\backslash (\backslash$mathrm$\{$PHF$\}=0\mathrm{.}9\backslash )$

$-$ Arrival types: $\backslash (5-\backslash$mathrm$\{$WB$\},2-\backslash$mathrm$\{$EB$\},3-\backslash$mathrm$\{$NB$\}\backslash )$

$-\backslash (\backslash \%\backslash$mathrm$\{$HV$\}=10\backslash \%\backslash )$ in all movements

$-$ No pedestrians

a$)$ Determine the existing $\backslash (\backslash$mathrm$\{$v$\}/\backslash$mathrm$\{$c$\}\backslash )$ ratio and LOS for each lane group in the intersection

b$)$ Determine the LOS for each approach and for the intersection as a whole

c$)$ Make recommendations for improvements in the signal timing if your results indicate that this is needed