Consider a single-line, single-server waiting line system. Suppose that customers arrive
according to a Poisson distribution at an average rate of 60 per hour, and the average
(exponentially distributed) service time is 45 seconds per customer. What is the average
utilization of the system?
The university replication facility provides copier repair service for the university and
for local businesses. Over the last year the mean arrival rate is 55 copiers a month. The
repair facility uses two identical repair technicians who can repair an average of 30
copiers each month. The university is considering changing out the copiers and expects
that the average arrival time will drop to 25 copiers per month. This will allow them to
reassign one of the technicians to other tasks. Assume the change has occurred and the
system is set up as a single channel; first come first serve, single server system.
•What is the utilization of the service center?
•What is the average number of copiers waiting in the system?
•What is the average number of copiers in the waiting line?
•What is the average time a copier is waiting to be repaired
•What is the average time the copier is in the waiting line?
•What is the probability that 6 copiers will be in the system at a given time?
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