1. A librarian at a college library, on an
average, could process 18 students during one hour. On an average, a student
arrives to her at every 4 minutes. Assume it is a single-server waiting line
Determine the mean arrival rate and the mean service rate.
Determine the probability that a student will have an empty queue.
Determine the probability that 2 students are in the queuing system.
(d) Determine the average number of students in
the queue and the average number of students in the system.
Determine the average waiting time in the queue and the average total time in
the system for a student.
(f) Find the utilization factor of the librarian.
In Question 1, suppose the librarian can be
replaced by a specialist, who must be paid $32 per hour whereas the current librarian
is paid $22 per hour. The specialist can process 22 students in one hour. If a student’s
time is considered to be worth $10 per hour, is it worth to replace the current
librarian with the specialist?
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