Registration Line Queuing Model

5. (10 points) It is time for students to register for classes, and a line is forming at the registrar's office for those who need assistance. It takes the registrar an exponentially distributed amount of time to service each student, on average two minutes. Students arrive at the office and get in line according to a Poisson process at the rate of one student every 3 minutes. The arrival times of the students are independent of the registrar's service time. (a) What is the long-term probability that there are not more than 3 students at the registrar's office? (b) How long, on average in the long run, is a student at the registar's office? (c) What is the long-term expected number of students at the registar's office waiting to be served by the registrar? 5. (10 points) It is time for students to register for classes, and a line is forming at the registrar's office for those who need assistance. It takes the registrar an exponentially distributed amount of time to service each student, on average two minutes. Students arrive at the office and get in line according to a Poisson process at the rate of one student every 3 minutes. The arrival times of the students are independent of the registrar's service time. (a) What is the long-term probability that there are not more than 3 students at the registrar's office? (b) How long, on average in the long run, is a student at the registar's office? (c) What is the long-term expected number of students at the registar's office waiting to be served by the registrar