25. Customers arrive at a service station, manned by a single server who serves at an exponential...
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25. Customers arrive at a service station, manned by a single server who serves at an exponential rate μ1, at a Poisson rate λ. After completion of service the customer then joins a second system where the server serves at an exponential rate μ2. Such a system is called a tandem or sequential queueing system. Assuming that λ < μi , i = 1, 2, determine the limiting probabilities.
Hint: Try a solution of the form Pn,m = Cαnβm, and determine C, α, β.
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