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,
1998

ISSN 0281-1944
ISRN LUNFD6/NFMS--3196--SE

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_Creg during a regenerative cycle C^reg and the asymptotic tail of the stationary random variable L_infty, respectively, of the level process are given and shown to be subexponential, with L_infty having the heavier tail.