For the situation described in Problem $1,$ construct a plot of cumulative arrivals and departures versus time $($in minutes$),$ starting at $7$:$00$ AM and ending at $1$:$00$ PM$.,$ that is$,$ t $0\mathrm{.}0$ min at $7$:$00$ AM and t $=240\mathrm{.}0$ min at $1$ PM$.$ From this plot: $($a$)$ identify the maximum size of the queue that forms.

$($b$)$ identify the longest waiting time for a vehicle during the study time period.