Exercise 2. Consider the open network of queues shown in Figure 1. Customers enter the network at rate Figure 1: Upen queueing network. immediately reaching queue 1 . Customers leaving queue 1 will choose queue 2 with probability p, and queue 3 with probability (1p). All customers leaving queue 2 return to queue 1 . Let N1,N2 and N3 be the average number of customers in queue 1,2 , and 3 , respectively. A) What is the expected total time spent in the system by a customer (defined as T )? [pt. 10]. B) What is the expected time spent in queue 2 by a customer visiting the queue only once (defined as T2 )? [pt. 10 ]. Exercise 2. Consider the open network of queues shown in Figure 1. Customers enter the network at rate Figure 1: Upen queueing network. immediately reaching queue 1 . Customers leaving queue 1 will choose queue 2 with probability p, and queue 3 with probability (1p). All customers leaving queue 2 return to queue 1 . Let N1,N2 and N3 be the average number of customers in queue 1,2 , and 3 , respectively. A) What is the expected total time spent in the system by a customer (defined as T )? [pt. 10]. B) What is the expected time spent in queue 2 by a customer visiting the queue only once (defined as T2 )? [pt. 10 ]