Loss Rate Asymptotics for Random Walks with Two Reflecting Barriers

Mats Pihlsgård

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,

ISSN 1403-9338
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 non-lattice 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\'er--Lundberg approximation, phase--type distributions