QUESTION $2$: Vehicles arrive in a single approach for two consecutive cycles at a signalized intersection. The signal has a $60-$second cycle time which consists of a $30-$second green interval and a $30-$second red interval $($ignore yellow interval$).$ The arrival rates are assumed to be constant in both cycies. The arrival rate was $1,080$ vehicles$/$hour in the first cycle and it decreased to $720$ vehicies$/$hour in the second cycle. Assume that all vehicles in the quewe formed on red pass through the intersection during the subsequent green interval at the saturation flow rate of $1,800$ vehicles hour immediately after the start of the green interval. $($a$)$ Sketch a queueing diagram $($cumulative arrival and departure curves over time$)$ the approach during the two cycles. $($b$)$ Calculate the maximum queue length $($maximum number of vehicles in the quewe$).($c$)$ Calculate $1)$ the total vehicle delay and $2)$ the average delay per vehicle during the two cycles.