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 02811944
ISRN LUNFD6/NFMS3196SE

Abstract:

Bivariate regenerative Markov modulated queueing processes
{I_{n}, L_{n}} are described.
{I_{n}} is the phaseprocess and {L_{n}} is
the levelprocess. 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.
