A geometric convergence formula for the level-increment-truncation approximation of M/G/1-type Markov chains

TL;DR

This paper derives a geometric convergence formula for the level-increment-truncation approximation of M/G/1-type Markov chains, providing theoretical insights into the approximation's accuracy under light-tailed conditions.

Contribution

It introduces a geometric convergence formula for the difference between the original and truncated Markov chain stationary distributions, assuming light-tailed level-increments.

Findings

Establishes a geometric convergence rate for the approximation

Provides theoretical bounds under light-tailed assumptions

Enhances understanding of approximation accuracy in Markov chains

Abstract

This paper considers an approximation usually used when implementing Ramaswami's recursion for the stationary distribution of the M/G/1-type Markov chain. The approximation is called the level-increment-truncation approximation because it truncates level increment at a given threshold. The main contribution of this paper is to present a geometric convergence formula of the level-wise difference between the respective stationary distributions of the original M/G/1-type Markov chain and its LI truncation approximation under the assumption that the level-increment distribution is light-tailed.