QUESTION $2$:

Consider traffic flow in an one$-$lane road. The arrival rate is $1500$ vehicles$/$hour from $9$:$00$ am to $11$:$00$ am and drops to $750$ vehicles$/$hour thereafter. The capacity of the lane is $1250$ vehicles$/$hour$.$

$($a$)$ Sketch a queueing diagram $($cumulative arrival and departure curves over time$)$ from $9$:$00$ am to the time when the queue clears.

$($b$)$ Calculate the maximum queue length $($maximum number of vehicles in the queue$)$ and the maximum waiting time in the queue.

$($c$)$ Calculate $1)$ the total vehicle delay and $2)$ the average delay per vehicle.