Iterative solution methods for obtaining the steady-state probability distributions of Markovian multi-echelon repairable item inventory systems

Iterative solution methods for obtaining the steady-state probability distributions of Markovian multi-echelon repairable item inventory systems

0.00 Avg rating0 Votes
Article ID: iaor1994825
Country: United Kingdom
Volume: 20
Issue: 8
Start Page Number: 817
End Page Number: 828
Publication Date: Oct 1993
Journal: Computers and Operations Research
Authors: , ,
Keywords: markov processes
Abstract:

The Jacobi, Gauss-Seidel, and bi-conjugate gradient methods are used to compute the steady-state probability distributions for finite state-space continuous time Markov processes (closed queueing networks) that arise in the modeling of two- and three-echelon repairable item inventory systems. Alternative systems of linear equations that express the steady-state conditions are examined, generation and storage of the transition rate matrix are discussed briefly, and various initializations and stopping criteria are tested. Numerical results are given for problems with up to one million states. Good results are obtained with a two-phase algorithm that uses the Guass-Seidel method first and the bi-conjugate gradient method subsequently.

Reviews

Required fields are marked *. Your email address will not be published.