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.