12.4 Consider a queueing system in which the server is subject to breakdown and repair. When it...
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12.4 Consider a queueing system in which the server is subject to breakdown and repair. When it is operational, the time until it fails is exponentially distributed with mean 1=η. When it breaks down, the time until it is repaired and brought back to service is also exponentially distributed with mean 1=γ. Customers arrive according to a Poisson process with rate λ. However, it has been found that the behavior of arriving customers depends on the state of the server. Specifically, when it is operational, all arriving customers stay in the system until they are served. But a customer that arrives when the server is down will balk (i.e., leave without receiving service) with probability p. Finally, the time to serve a customer when the system is operational is exponentially distributed with mean 1=μ. Give the state transition rate diagram of the process and determine the Q-matrix, identifying the A and D submatrices.
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