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In an immigration department, only selected clerks are allowed to locate files in certain boxes. When the department officers want to access a file, they must queue until a clerk becomes available. Suppose interarrival times between the officers re-questing for files are iid exponential with a mean of 10 mins, the time for a clerk to locate a file is also an exponential random variable with a mean of 15 mins. Suppose that there are 2 clerks available to locate the files in certain boxes. (a) Find the probability that all clerks are busy when an officer comes to find a file. (b) Find the expected number of the officers waiting to be served. (c) How much time, on average, does an officer spend in finding a file? (d) If the immigration department opens from 9 am to 3 pm on weekdays, how many hours does a clerk expect to be idle on Monday?
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