Consider the open network of queues shown in Figure 2. It consists of three M/M/1 queues....

 

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Consider the open network of queues shown in Figure 2. It consists of three M/M/1 queues. Queue 1 TIO P 1-p Queue 2 Queue 3 IC H3 Figure 2 Open queueing network. Customers enter the network at rate A immediately reaching queue 1. Customers leaving queue 1 will choose queue 2 with probability p, and queue 3 with probability (1-p). All customers leaving queue 2 return to queue 1. All customers leaving queue 3 leave the network forever. The service times at the queues are independent and exponentially distributed with mean 1/ =1/p, 1/=1/, and 1/3 = 1/. A) Find the stability conditions of the network of queues B) Find the expected total number of customers in the entire network C) Find the average time spent in the system by a customer Consider the open network of queues shown in Figure 2. It consists of three M/M/1 queues. Queue 1 TIO P 1-p Queue 2 Queue 3 IC H3 Figure 2 Open queueing network. Customers enter the network at rate A immediately reaching queue 1. Customers leaving queue 1 will choose queue 2 with probability p, and queue 3 with probability (1-p). All customers leaving queue 2 return to queue 1. All customers leaving queue 3 leave the network forever. The service times at the queues are independent and exponentially distributed with mean 1/ =1/p, 1/=1/, and 1/3 = 1/. A) Find the stability conditions of the network of queues B) Find the expected total number of customers in the entire network C) Find the average time spent in the system by a customer