Question: 17. Customers arrive at a two-server station in accordance with a Poisson process with a rate of two per hour. Arrivals finding server 1 free

17. Customers arrive at a two-server station in accordance with a Poisson process with a rate of two per hour. Arrivals finding server 1 free begin service with that server. Arrivals finding server 1 busy and server 2 free begin service with server 2. Arrivals finding both servers busy are lost. When a customer is served by server 1, she then either enters service with server 2 if 2 is free or departs the system if 2 is busy. A customer completing service at server 2 departs the system.

The service times at server 1 and server 2 are exponential random variables with respective rates of four and six per hour.

(a) What fraction of customers do not enter the system?

(b) What is the average amount of time that an entering customer spends in the system?

(c) What fraction of entering customers receives service from server 1?

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