Exact solution to a Lindley-type equation on a bounded support

Abstract

We derive the limiting waiting-time distribution $F_W$ of a model described by the Lindley-type equation $W=\max \{0,B-A-W\}$, where $B$ has a polynomial distribution. This exact solution is applied to derive approximations of $F_W$ when $B$ is generally distributed on a finite support. We provide error bounds for these approximations.

arXiv comment9 pages, 2 figures, 1 table, 11 references