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Markov-renewal fluid queues. (English) Zbl 1063.60127
Summary: We consider a fluid queue controlled by a semi-Markov process and we apply the Markov-renewal approach developed earlier in the context of quasi-birth-and-death processes and of Markovian fluid queues. We analyze two subfamilies of semi-Markov processes. In the first family, we assume that the intervals during which the input rate is negative have an exponential distribution. In the second family, we take the complementary case and assume that the intervals during which the input rate is positive have an exponential distribution. We thoroughly characterize the structure of the stationary distribution in both cases.

MSC:
60K15 Markov renewal processes, semi-Markov processes
60K37 Processes in random environments
60K25 Queueing theory (aspects of probability theory)
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