Problem $3(6$ points$)$

$[$D$/$D$/1$ Queue$]$ Suppose there is a toll plaza between Rosslyn and Foggy

Bottom with a capacity of $2000ve\frac{h}{h}.$ The morning peak starts at $8$:$00$ AM

$($before that, there is no queue at the toll plaza$).$ The traffic between $8$:$00-$

$9$:$00$ AM is $3000ve\frac{h}{h}$ and then reduces to the normal level of $1500ve\frac{h}{h}$

after $9$:$00$ AM$.$ What is the time of queue clearance, the maximum queue

length, the maximum queuing time, and the average queuing delay of

vehicles arriving between $8$:$00$ am and the time of queue clearance

clearance?