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Consider two servers. An average of 8 customers per hour arrive from outside at server 1, and an average of 17 customers per hour arrive from outside at server 2. Interarrival times are exponential. Server 1 can serve at an exponential rate of 20 customers per hour, and server 2 can serve at an exponential rate of 30 customers per hour. After completing service at server 1, half of the customers leave the system, and half go to server 2. After completing service at server 2, 3/4 of the customers complete service, and 1/4 return to server 1.
a. What fraction of the time is server 1 idle?
b. Find the expected number of customers at each server.
c. Find the average time a customer spends in the system.
d. How would the answers to parts (1)-(3) change if server 2 could serve only an average of 20 customers per hour?
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