Loss Rate Asymptotics for Random Walks with Two Reflecting Barriers
Mats Pihlsgård
Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,
2003
ISSN 14039338

Abstract:

We consider the stationary loss rate l^K of a random walk reflected at 0
and some level K>0. We derive sharp asymptotics for the loss rate in
nonlattice random walks with negative drift. As an

example, we consider the PH/PH/1 case, where we compare the exact loss rate
to the asymptotic one and illustrate our results graphically with the help
of a small MATLAB program.




Key words:

stationary loss rate, asymptotics, random walk, Lundberg's equation, Lundberg's
inequality, Cram\'erLundberg approximation, phasetype distributions
