Abstract
Bivariate regenerative Markov modulated queueing processes {I n ,L n } are described. {I n } is the phase process, and {L n } is the level process. Increments in the level process have subexponential distributions. A general boundary behavior at the level 0 is allowed. The asymptotic tail of the cycle maximum, \(M_{C^{{reg}} } \), during a regenerative cycle, \(C^{{reg}} \), and the asymptotic tail of the stationary random variable L ∞, respectively, of the level process are given and shown to be subexponential with L ∞ having the heavier tail.
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Asmussen, S., Møller, J.R. Tail asymptotics for M/G/1 type queueing processes with subexponential increments. Queueing Systems 33, 153–176 (1999). https://doi.org/10.1023/A:1019172028316
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DOI: https://doi.org/10.1023/A:1019172028316