Sep 19, 2017

TRAVELERS ARRIVE INDIVIDUALLY AT THE SINGLE CHECK-IN COUNTER OPERATED BY A LOCAL AIRLINE COMPANY….

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Travelers arrive individually at the single check-in counter operated by a local airline company. Coach-class travelers arrive at a rate of 15 per hour and each requires exactly 2 minutes to get boarding tickets and luggage checked in. First-class customers arrive at a rate of four per hour and since they need be pampered, require a fixed time of 5 minutes to check-in. Lastly, at a rate of two per hour, late-arriving customers, about to miss their flights, require an exponentially distributed amount of time with a mean check-in time of 1 minute. The arrival process for all types of customers is Poisson.

(a) The airline company, in the interest of fairness to all, at first operated on a first-come, first-served basis. Determine the mean time spent by a traveler at the check-in facility while this policy was enforced.

(b) As the airline company began to lose money, it decided to implement a priority policy whereby firstclass customers have non preemptive priority over coach travelers and late-arriving customers have preemptive priority over both first- and coach-class customers. Find the mean time spent at the checkin facility by an arbitrary traveler under this new system.


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