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

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 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.

(e)

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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