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A computer system can usually be interpreted as a closed network with two different types of servers. It is then possible to convert the network into a single server system with state-dependent arrivals. This paper investigates the stationary behavior of a single server queue with different classes of jobs. It is assumed that the input process has state-dependent exponential inter-arrival times and preemptions at the server are not allowed. The exact solution is obtained by finding the relationship between the time average probability distribution and the departure average probability distribution. The latter can be derived, based upon an imbedded Markov Chain.
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We-Min Chow (1975) studied this question.
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