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

TL;DR

This paper derives an exact solution for the limiting waiting-time distribution in a Lindley-type queue model with bounded support, providing useful approximations and error bounds for practical applications.

Contribution

It presents the first exact solution for a Lindley-type equation with polynomially distributed bounded support and develops approximation methods with error bounds.

Findings

Exact limiting waiting-time distribution derived

Approximation methods for general distributions on finite support

Error bounds established for approximations

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.