At a toll booth, vehicles arrive and are processed (tolls collected) at uniform deterministic rates λ and μ, respectively. The arrival rate is 3 veh/min.
Processing begins 15 minutes after the arrival of the first vehicle and the queue dissipates t minutes after the arrival of the first vehicle.
Letting the number of vehicles that must actually wait in a queue be x, develop an expression for determining processing rates in terms of x.