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In: Statistics and Probability

Consider three servers. An average of 12 customers per hour arrive from outside at server 1,...

Consider three servers. An average of 12 customers per hour arrive from outside at server 1, an average of 36 customers per hour arrive from outside at server 2 and an average of 24 customers per hour arrive from outside at server 3. Interarrival times are exponential. Servers 1, 2 and 3 can serve at exponential rates of 100, 120 and 80 customers per hour respectively. After completing service at server 1, 25% of the customers leave the system and 75% of the customers go to server 2. After completing service at server 2, 50% of the customers go to server 3 and 50% of the customers go to server 1. After completing service at server 3, 25% of the customers go to server 2 and 75% of the customers leave the system.

(a) Find the arrival rates: λ1, λ2 and λ3 of the customers at the servers 1,2 and 3 respectively.

(b) Find the expected number of customers at each server. (c) Find the average time a customer spends in the system.

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orchestra answered 1 year ago
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