Problem $1)$ Temporary capacity reduction

There is a three$-$lane automobile dedicated road, which is designed to have a free$-$flow speed of $80($km$/$h$),$ a capacity of $2000($veh$/$h$/$lane$),$ and a maximum density of $150($veh$/$km$/$lane$).$ The demand for vehicles is constant at $2500($veh$/$h$).$ At this time, an accident occurred at a point $10$ km $($x$=10$ km$)$ at the time point $30$ minutes after observation $($t$=0\mathrm{.}5),$ and the road capacity was limited to $1000($veh$/$h$)$ for one hour $($t$=0\mathrm{.}5$ to $1\mathrm{.}5$ h$).$

A$.$ When the engineer's area in charge is between $0$ and $15$ km$,$ mark the traffic state, shock wave, and the vehicle's trajectory on the time$-$space diagram.

$($ Please draw time$-$ space diagram$)$

B$.$ Discuss the characteristics of the congestion caused by the occurrence of an accident.

E$.$g$.$ The length of the delay in the accident, the timing of the resolution of the delay, etc.

Problem $2)$ Queue Analysis

Solve the problem described above in terms of queue analysis. Draw the Arrival curve and the Department curve at the accident point $($x$=10$ km$)$ on the N$-$curve over time and discuss the characteristics of the congestion.

E$.$g$.$ The length of the delay in an accident, the timing of the delay, etc.

Hint: Arrival rate is $2500($veh$/$h$),$ and the number of vehicles that can actually pass through the section $($departure rate$)$ varies depending on the situation