Question: Consider a facility open 24 hours per day with a single machine that is used to service only one type of job. The company policy is to limit the number of jobs within the facility at any one time to 4. The mean arrival rate of jobs is 120 jobs per day, and the mean processing time for a job is 15 minutes. Both the processing and inter-arrival times are assumed to be exponentially distributed. Answer the following questions regarding the long-run behavior of the facility.
(a) What is the average number of jobs that arrive to the facility (but not necessarily get in) per hour?
(b) What is the probability that there are no jobs at the facility?
(c) What is the average number of jobs within the facility?
(d) What is the average number of jobs lost per day due to the limited capacity of the facility?
(e) What is the average throughput rate per hour?
(f) What is the average amount of time, in minutes, that a job spends within the facility?