Problem $4.$ Use a queueing diagram to analyze the following situation. When a concert ends at the Moody Center, traffic builds up at the traffic signal where MLK Blvd$.$ intersects the I$-35$ frontage road. For this approach, the signal is green for $30$ seconds, and red for $90$ seconds; and the capacity during a green light is $1800$ vehicles per hour. While the concert is in progress, vehicles arrive at the signal at a rate of $100$ vehicles per hour. Vehicles leaving the concert first arrive at the signal at $11$ PM$,$ right as it turns red. For the next $5$ minutes, the demand jumps to a rate of $600$ vehicles per hour, before falling back to $120$ vehicles per hour.

What is the greatest number of vehicles in queue at this signal?

What is the longest any vehicle has to wait?

At what time does the queue finally clear?

What is the total delay experienced at the signal, from $11$ PM until the queue clears?