Problem:
During registration at a university, students have their courses approved by the adviser. It takes the adviser an average of 2.8 minutes (exponentially distributed) to approve each schedule, and students arrive at the adviser's office at the rate of 20 per hour (Poisson distributed). You are required to answer the following questions:
1) Compute the average time a student spends in the waiting line.
The registrar has received complaints from students about the length of time they must wait to have their schedules approved. The registrar is considering several ways to reduce the waiting time.
2) One way is to assign some assistants to the adviser. Each such assistant would reduce the average time required to approve a schedule by 0.2 minute, down to a minimum of 1.0 minute. If this option is followed, how many assistants should the registrar assign to the adviser if he feels that a waiting time of 10 minutes is not unreasonable?
3) It has been noted that about one-fifth of the students fall under routine cases which they can themselves identify as routine. These routine cases take 1 minute to be served with negligible variance. Hence one other way to reduce the waiting time is to provide an assistant who handles routine cases, while non-routine cases are handled by the adviser. Will this option be acceptable?
4) Yet another way is to provide additional advisers. Assuming that the average service time for each adviser is the same, how many advisers will be needed to bring the waiting time to 10 minutes or less?