A Closed Queueing Maintenance Network with Two Batch Policies

TL;DR

This paper models a maintenance network as a closed queueing system with two batch policies, using block-structured Markov processes and RG-factorizations to analyze its performance and establish a new product-form solution.

Contribution

It introduces a novel maintenance network model with a new nonlinear matrix equation and extends queueing theory to more general block-structured Markov processes.

Findings

The network can be analyzed using RG-factorizations.

A new nonlinear matrix equation determines relative arrival rates.

The model provides a general product-form solution for performance evaluation.

Abstract

This paper discusses a maintenance network with failed items that can be removed, repaired, redistributed, and reused under two batch policies: one for removing the failed items from each base to a maintenance shop and the other for redistributing the repaired items from the maintenance shop to bases. This maintenance network can be considered a virtual closed queueing network, and the Markov system of each node is described as an elegant block-structured Markov process whose stationary probabilities can be computed by the RG-factorizations. The structure of this maintenance network is novel and interesting. To compute the closed queueing network, we set up a new nonlinear matrix equation to determine the relative arrival rates, in which the nonlinearity comes from two different groups of processes: the failure and removal processes and the repair and redistribution processes. This paper also extends a simple queueing system of a node to a more general block-structured Markov process which can be computed by the RG-factorizations. Based on this, the paper establishes a more general product-form solution for the closed queueing network and provides performance analysis of the maintenance network. Our method will open a new avenue for quantitative evaluation of more general maintenance networks.