QUESTION $3$:

Vehicles in a single approach arrive at a signalized intersection at a rate of $12$ vehicles

per minute. The signal has a $60-$second cycle time with a $30-$second green interval and a

$30-$second red interval $($ignore yellow interval$).$ Assume that all the vehicles in the queue

formed on red pass through the intersection during the subsequent green interval at the

saturation flow rate of $30$ vehicles per minute. Thus, the queue does not spill over to the

next cycle. Ignore driver reaction time and vehicle acceleration time at the start of the

green interval.

$($a$)$ Sketch a queueing diagram $($cumulative arrival and departure curves over time$)$ for

the approach in one cycle $(60$ seconds$).$ Find the time when the queue clears after the

start of the green interval.

$($b$)$ Calculate the maximum queue length $($maximum number of vehicles in the queue$)$

during one cycle.

$($c$)$ Calculate the waiting time of the vehicle that arrives at the end of red interval.

$($d$)$ For one cycle, calculate $1)$ the total vehicle delay and $2)$ the average delay per

vehicle.