Reference no: EM132967387

A university, installed a single telephone booth in the student affair office, to provide students with no mobile phone or unwilling to use their mobile phone, the capacity to make a call whenever needed. The arrivals at the telephone booth are considered to be Poisson at an average time of 8 min between our arrival and the next. The length of the phone call is distributed exponentially, with a mean of 4 min. The student affair office stays open 10 hours per day.

Determine for this scenario 1:

1. The arrival rate per hour
2. The service rate per hour
3. Expected in percentage the fraction of the day that the phone will be in use.
4. Expected time in hours the phone will be used per day.
5. Expected number of students in the queue
6. Expected waiting time in the queue.
7. Expected number of students in the system.
8. Expected time spent in the system
9. What is the probability that an arrival will have to wait in queue for service?
10. What is the probability that there are 3 or more persons in the system?
11. What is the probability that more than 5 persons are in system?
12. What is the probability that an arrival will directly enter for service?