Reference no: EM131130588
We wish to compare two maintenance policies for the airplanes of a certain airline company. In the case of policy A(respectively, B), the airplanes arrive to the maintenance shop according to a Poisson process with rate λA = 1
(resp., λB = 1/4) per day. Moreover, when policy A (resp., B) is used, the service time (in days) is an exponential random variable with parameter μA = 2 (resp., the sum of four independent exponential random variables, each of them with parameter 𝜇B = 2). In both cases, maintenance work is performed on only one airplane at a time.
(a) What is the better policy? Justify your answer by calculating the average number of airplanes in the maintenance shop (in stationary regime) in each case.
Indication. The average number of customers in a queueing system M/G/1 (after a long enough time) is given by
where S is the service time and A is the average arrival rate of customers.
(b) Let N be the number of airplanes in the maintenance shop in stationary regime. Calculate the distribution of N if policy A is used, given that there are two or three airplanes in the shop (at a particular time instant).
(c) If policy A is used, what is the average time that an airplane, which has already been in the maintenance shop for two days, will spend in the shop overall?
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: We wish to compare two maintenance policies for the airplanes of a certain airline company. In the case of policy A(respectively, B), the airplanes arrive to the maintenance shop according to a Poisson process with rate λA = 1
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