In a certain system a customer must first be served by server 1 and then by either server 2 or server 3. The routing of customers is random (upon completing service with server 1, each customer will be routed to server 2 probability 0.5 and to server 3 otherwise). Upon completing service with server 2 or 3, the customer leaves the system. Each server (1, 2, or 3) serves customers in the order that they arrive (to the server), and an arrival finding a server busy waits in line for that server. Assume that service times with each serveri {1,2,3}are exponentially distributed with rate_i, and that all service times and routing decisions are independent of one another.

Suppose that when customerBarrives, there is one customer in the system (customerA) who is being served by server 2. Determine the expected total amount of time customerBwill spend in the system. Explain.

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