Question $5(35$ points$)$: An approach at a pretimed signalized intersection has a constant saturation flow rate of $2400ve\frac{h}{h}$ and is allocated $24$ seconds of effective green time in an $80$second signal cycle. If the total approach flow rate is $500ve\frac{h}{h}$ and arrivals are uniform throughout the cycle, please calculate the following metrics assuming D$/$D$/1$ queueing.

Time to queue clearance after the start of the effective green

Proportion of the cycle with a queue

Proportion of the vehicle stopped

Maximum number of vehicles in the queue

Total vehicle delay per cycle

Average delay per vehicle

Maximum delay of any vehicle