Tail asymptotics for M/G/1 type queueing processes with subexponential increments

Sören Asmussen and Jakob R. Möller

Department of Mathematical Statistics,
Lund Institute of Technology,
Lund University,

ISSN 0281-1944

Bivariate regenerative Markov modulated queueing processes {In, Ln} are described. {In} is the phase-process and {Ln} 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 MCreg during a regenerative cycle Creg and the asymptotic tail of the stationary random variable Linfty, respectively, of the level process are given and shown to be subexponential, with Linfty having the heavier tail.