Airplanes arrive for take-off at the runway of an airport according to a Poisson process at a mean rate of 20 per hour. The time required for an airplane to take off has an exponential distribution with a mean of 2 minutes, and this process must be completed before the next airplane can begin to take off.
Because a brief thunderstorm has just begun, all airplanes which have not commenced take-off have just been grounded temporarily. However, airplanes continue to arrive at the runway during the thunderstorm to await its end.
Assuming steady-state operation before the thunderstorm, determine the expected number of airplanes that will be waiting to take off at the end of the thunderstorm if it lasts 30 minutes.