My recent trip to Washington D.C. reminded me of how good we have it here in Dalton, GA. The traffic was horrible! Waiting in traffic provided me with ample time to contemplate how queuing theory could be used to evaluate a toll booth operation. During rush hour, I estimate that cars arrive at 1200/hr and there are 7 toll booths that process 177 cars/hr.
A. What is the average number of cars in line waiting for a chance to pay their toll?
B. What would be the average time that a vehicle must wait to get through the system?
C. How many operators would be necessary if 30 seconds is more than enough time to expect to wait in line and pay a toll?
D. If the cost of employing each toll operator is $20/hr and a commuter’s time is valued at $5/hr, what case can you make for employing more operators? Assume this situation exists 8 hours a day 5 days a week with a 50 week work year.