# Μ ? p n n 1 μ ? μ ? 29 p n n n n μ ? ρ p 1 p 1

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μ λ - P n n 1 μ λ μ λ - ( 29 0 P n ! n N ! N μ λ - ρ 0 P 1 - 0 P 1 - Solved Example 10: The college of Business Management at Osmania University has a 5 copy machines on the first floor for faculty and students use. Heavy use of the five copy machines causes frequent failures.

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Maintenance records show that a machine fails every 2.5 days. The college has a maintenance contract with the authorized dealer of the copy machines. Because the copy machines fail so frequently, the dealer has assigned one person to the college to repair them. This person can repair an average of 2.5 machines per day. Answer the following questions: a) What is the average utilization of the maintenance person? b) On average, how many copy machines are being repaired or waiting to be repaired? c) What is the average time spent by a copy machine in the repair system (waiting and repaired)? Solution: Given problem is M/M/1 5/FIFO because copy machines are repaired by single person and customers are coming from a finite population i.e., five copy machines. N = 5 Mean arrival of copy machines for repair ( λ ) = 2.5 days/ machine or 0.4 machines/day Mean service rate of maintenance person ( μ ) = 2.5 machines/day Idle rate of maintenance person = 1 N 0 n n 0 )! n N ( ! N P - = μ λ - = 1 5 0 n n 0 5 . 2 4 . 0
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