$3\mathrm{.}20.$ I$-96$ Incident and queueing analysis. A truck overturned at $11$:$57$ AM near milepost $138$ on NB

I$-96,$ completely blocking that highway. Fortunately, the incident site is just beyond an off$-$ramp. This

means that most vehicles will see the blockage and exit I$-96$ at the off ramp, avoiding a long backup and

long delay. This also makes the detour of through vehicles simply a matter of using the off$-$ramp and the

on$-$ramp to go around the incident site. For the first ten minutes after the truck's mishap, the ramp

capacities were governed by the stop sign at the end of the off ramp and the priority given to cross traffic,

which did not have a stop sign. The ramp's service rate for detouring traffic was approximately $325vph.$

After ten minutes, state police began controlling traffic at the end of the off$-$ramp, increasing the ramp's

service rate for detouring traffic to $650vph.$ At exactly $1$:$00$ PM$,$ NB I$-96($capacity $=3600vph)$ was

reopened to through traffic. If the NB I$-96$ flow rate at this time of day is $1550vph$ :

A$.$ Draw a queueing diagram that shows the buildup and dissipation of the queue.

B$.$ At approximately what time $($to the nearest minute$)$ does the queue dissipate? Show this event on

your diagram.

C$.$ What was the longest vehicle queue? What was the longest vehicle delay? Show the longest

queue and the longest delay on your diagram.