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Analysis of fluid models with Markov modulated rates

Ferrandiz, Josep

HPL-92-101

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Abstract: We analyze both with finite and infinite capacity fluid buffer models with input and output rates modulated by a Markov chain. For the infinite capacity system we obtain the laws of the buffer content, busy period, idle period, system delay, volume processed in a busy period, and perform level crossing analysis. For the finite capacity system we obtain the laws of the buffer content, blocking period distribution as well as the blocking loss distribution during a blocking period. The results obtained are based on the properties of fluctuating Markov additive functionals. In particular, it is worth mentioning a matrix quadratic equation similar to those encountered when analyzing quasi-birth-and-death processes in matrix-geometric stochastic models.

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