Part: Waiting-Line Models

At the University Student Central, students wait in line to register for classes before the start of fall semester classes. Students arrive at the rate of 10 per hour and it takes the single clerk on duty an average of 3 minutes to check their student status and register them for classes. The student's dissatisfaction would potentially cost $10 per hour, while the clerk's salary is $15 per hour.

a) If the students arrive in a steady stream (e.g., Poisson distribution) and the service time is exponentially distributed, apply the appropriate waiting-line model to determine the system performance and costs, including :

- average number of students in such registration system (waiting and being registered)

- average time a student spends in the system (waiting and registration)

- average number of students waiting in the line

- average time a student spends waiting in the line

- average utilization of the system

- probability that the clerk is not serving any students

- probability of more than 1, 2 and 3 students in the system, respectively

- total expected cost of this registration system

b) The university is now considering if more clerks are needed for the registration service. Formulate the registration system with two clerks, given other information no change. Determine the new system performance and costs, and justify if the university should hire two clerks for the registration service.