Problem:

A study-aid desk staffed by a graduate student has been established to answer students' questions and help in working problems in your OSCM 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 three per hour, and the distribution is approximately Poisson. Assistance time averages 8 minutes, distributed exponentially. Assume population and line length can be infinite and queue discipline is FCFS.

Required:

Question 1) Calculate the percentage utilization of the graduate student.

Question 2) Calculate the average number of students in the system (excluding the graduate student server).(Round your answer to 3 decimal places.)

Question 3) Calculate the average time in the system. (Round your answer to 2 decimal places.)

Question 4) Calculate the probability of four or more students being in line or being served. (Round your answer to 4 decimal places.)

Question 5) Before a test, the arrival of students increases to six per hour on the average. What will the new line length be?

Solve the given numerical problem and illustrate step by step calculation.