Customers arrive at a two-server station in accordance with a Poisson process having rate . Upon arriving,
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Customers arrive at a two-server station in accordance with a Poisson process having rate λ. Upon arriving, they join a single queue. Whenever a server completes a service, the person first in line enters service. The service times of server i are exponential with rate μi, i = 1, 2, where μ1 + μ2 >λ. An arrival finding both servers free is equally likely to go to either one. Define an appropriate continuous-time Markov chain for this model, show it is time reversible, and find the limiting probabilities.
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