A single runway according to a poisson process

Reference no: EM131130602

Airplanes arrive at an airport having a single runway according to a Poisson process with rate λ = 18 per hour. The time during which the runway is used by a landing airplane has an exponential distribution with mean equal to two minutes (from the moment it receives the landing authorization).

(a) Knowing that there is at most one airplane in the system (at a given time instant), what is the probability that an arriving airplane will have to wait before being allowed to land?

(b) Given that an airplane has been waiting for the authorization to land for the last 5 minutes, what is the probability that it will have landed and cleared the runway in the next 10 minutes?

Reference no: EM131130602

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