18 A study-aid desk staffed by a graduate student has been established to answer students' ques- tions and help in working problems in your OM course. The desk is staffed eight hours per day. The dean wants to know how the facility is working. Statistics show that students arrive at a rate of four per hour, and the distribution is approximately Poisson. Assistance time averages 10 minutes, distributed exponentially. Assume population and line length can be infinite and queue discipline is FCFS.

a. Calculate the percentage utilization of the graduate student.

b. Calculate the average number of students in the system.

c. Calculate the average time in the system.

d. Calculate the probability of four or more students being in line or being served.

e. Before a test, the arrival of students increases to six per hour on the average. What does this do to the average length of the line?