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3. Customers arrive at a two-server service station according to a Poisson process with rate A. Whenever a new customer arrives, any customer in

  

3. Customers arrive at a two-server service station according to a Poisson process with rate A. Whenever a new customer arrives, any customer in the system immediately departs. A new arrival enters service first with server 1 and then with server 2. If the service times at the servers are independent exponentials with respective rates and 2, what proportion of entering customers completes their service with server 2? (Hint: Let S, denote the service time at server i, i = 1,2 and let X denote the time until the next arrival. A customer's service with server 2 is complete if X > S + S2. Then use conditioning and the memoryless property.)

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