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Exercise Ceansider the open network of quus shown in Figwe 2. ht comists of theee M/Al/l quetes Figure 2. Open queuring network Customers enter the network at rate A immediately teaching queuel. Customers leaving queue I will choose queue 2 with probability, and quete 3 with probability (1-P) All customers having queue 2 return to quete i All customers leaving queur 3 leave the network forever. The service times at the quues are independent and exponentially distributed with mean 1/2 - 1/8, 1/2 - 1/, and 1/3 - 1/. A) Find the stability conditions of the network of quus B) Find the expected total number of customers in the entire network c) Find the average time spent in the system by a ciastomer 65% H2 75% - I-O OTTI 25% Drop 35% 14 I- 10 Exercise Consider the openi network of quas shown in Figure 2. It consists of three M/MI/1quetes Figure 2 Open queueing network Customers enter the network at rate : immediately reaching queue 1. Customers leaving queue I will choose queue 2 with probability P, and queue 3 with probability (1 - p). All customers leaving quete 2 return to queue 1. All customers leaving queue 3 leave the network forever. The service times at the quarters are independent and exponentially distributed with mean 1/1 = 1/4, 1/3 - 1/7, and 1/13 - 1/1 A) Find the stability conditions of the network of queues B) Find the expected total mumber of cistomers in the entire network C) Find the average time spent in the system by a ctastomer HS II- 65% H. He 75% -- II- TIOT INIO 25% Drop 35% II-- Exercise Ceansider the open network of quus shown in Figwe 2. ht comists of theee M/Al/l quetes Figure 2. Open queuring network Customers enter the network at rate A immediately teaching queuel. Customers leaving queue I will choose queue 2 with probability, and quete 3 with probability (1-P) All customers having queue 2 return to quete i All customers leaving queur 3 leave the network forever. The service times at the quues are independent and exponentially distributed with mean 1/2 - 1/8, 1/2 - 1/, and 1/3 - 1/. A) Find the stability conditions of the network of quus B) Find the expected total number of customers in the entire network c) Find the average time spent in the system by a ciastomer 65% H2 75% - I-O OTTI 25% Drop 35% 14 I- 10 Exercise Consider the openi network of quas shown in Figure 2. It consists of three M/MI/1quetes Figure 2 Open queueing network Customers enter the network at rate : immediately reaching queue 1. Customers leaving queue I will choose queue 2 with probability P, and queue 3 with probability (1 - p). All customers leaving quete 2 return to queue 1. All customers leaving queue 3 leave the network forever. The service times at the quarters are independent and exponentially distributed with mean 1/1 = 1/4, 1/3 - 1/7, and 1/13 - 1/1 A) Find the stability conditions of the network of queues B) Find the expected total mumber of cistomers in the entire network C) Find the average time spent in the system by a ctastomer HS II- 65% H. He 75% -- II- TIOT INIO 25% Drop 35% II-