Question: You have been asked to analyse the book borrowing process (including the queue) at the Library. A. From measuring the librarian's performance you have determined

You have been asked to analyse the book borrowing process (including the queue) at the Library.

A. From measuring the librarian's performance you have determined that when borrowers are waiting, librarians process 30 borrowers per hour on average. Surprisingly, the coefficient of variance of this service process is exactly 2.00. Assuming arrivals are random with a mean arrival rate of 1 every 4 minutes, service times are independent of queue length, the system is in a steady state, borrowers do not leave the queue early, and there is a single librarian processing loans, what is the average time that borrowers will spend queuing?

B. In February the utillsation is expected to reach 100%. Under the same assumptions as above question. What is the new expected number of borrowers in the queue?

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