A librarian at a college library, on an average, could process 14.5 students during one hour. On an average, a student arrives to her at every 5 minutes. Assume it is a single-server waiting line model.
(a) Determine the mean arrival rate and the mean service rate.
(b) Determine the probability that a student will have an empty queue.
(c) Determine the average number of students in the queue and the average number of students in the system.
(d) Determine the average waiting time in the queue and the average total time in the system for a student.
(e) Find the utilization factor of the librarian.
(f) Determine the probability that 3 students are in the queuing system. 6.
In Question 5, suppose the librarian can be replaced by a specialist, who must be paid $25 per hour whereas the current librarian is paid $18 per hour. The specialist can process 17 students in one hour. If a students time is considered to be worth $8.50 per hour, is it worth to replace the current librarian with the specialist?