1 research outputs found
Buffer-overflows: joint limit laws of undershoots and overshoots of reflected processes
Let be the epoch of first entry into the interval ,
, of the reflected process of a L\'evy process , and define the
overshoot and undershoot of
at the first-passage time over the level . In this paper we establish,
separately under the Cram\'{e}r and positive drift assumptions, the existence
of the weak limit of as tends to infinity and provide
explicit formulae for their joint CDFs in terms of the L\'{e}vy measure of
and the renewal measure of the dual of . We apply our results to analyse the
behaviour of the classical M/G/1 queueing system at the buffer-overflow, both
in a stable and unstable case.Comment: 11 pages, no figure