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.

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The Answer is This is an M/M/1 queue with

\lambda

= 20 and

\mu

= 30.E [# of airplanes at the end of the thunderstorm] = E [# of airplanes before thunderstorm] + E[# arrived planes during the thunderstorm] = $This is an M/M/1 queue with \lambda = 20 and \mu = 30.E [# of airplanes at the end of the thunderstorm] = E [# of airplanes before thunderstorm] + E[# arrived planes during the thunderstorm] =$

Airplanes Arrive for Take-Off at the Runway of an Airport