Question: A queueing network consists of two servers 1 and 2 in series. Server 1 is subject to a homogeneous Poisson input with intensity (lambda=5) an

A queueing network consists of two servers 1 and 2 in series. Server 1 is subject to a homogeneous Poisson input with intensity \(\lambda=5\) an hour. A customer is lost if server 1 is busy. From server 1 a customer goes to server 2 for further service. If server 2 is busy, the customer is lost. The service times of servers 1 and 2 are exponential with respective mean values

\[1 / \mu_{1}=6 \min \text { and } 1 / \mu_{2}=12 \min\]

All arrival and service times are independent.

What percentage of customers (with respect to the total input at server 1) is served by both servers?

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