Analysis of inhomogeneous Markov reward models

M. Telek, A. Horváth, G. Horváth

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

The majority of computational methods applied for the analysis of homogeneous Markov reward models (MRMs) are not applicable for the analysis of inhomogeneous MRMs. By the nature of inhomogeneous models, only forward differential equations can be used to describe the model behaviour. In this paper we provide forward partial differential equations describing the distribution of reward measures of inhomogeneous MRMs. Based on this descriptions, we introduce the set of ordinary differential equations that describes the behaviour of the moments of reward measures when it is possible. This description of moments allows the effective numerical analysis of rather large inhomogeneous MRMs. A numerical example demonstrates the application of inhomogeneous MRMs in practice and the numerical behaviour of the introduced analysis technique.

Original languageEnglish
Pages (from-to)383-405
Number of pages23
JournalLinear Algebra and Its Applications
Volume386
Issue number1-3 SUPPL.
DOIs
Publication statusPublished - Jul 15 2004

Fingerprint

Reward
Model
Moment
Computational methods
Ordinary differential equations
Computational Methods
Partial differential equations
Numerical analysis
Numerical Analysis
Ordinary differential equation
Differential equations
Partial differential equation
Differential equation
Numerical Examples
Demonstrate

Keywords

  • Inhomogeneous Markov reward models
  • Moments of reward measures
  • Ordinary and partial differential equations

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis

Cite this

Analysis of inhomogeneous Markov reward models. / Telek, M.; Horváth, A.; Horváth, G.

In: Linear Algebra and Its Applications, Vol. 386, No. 1-3 SUPPL., 15.07.2004, p. 383-405.

Research output: Contribution to journalArticle

Telek, M. ; Horváth, A. ; Horváth, G. / Analysis of inhomogeneous Markov reward models. In: Linear Algebra and Its Applications. 2004 ; Vol. 386, No. 1-3 SUPPL. pp. 383-405.
@article{dcf7f2445899449ebb2725d09134adc0,
title = "Analysis of inhomogeneous Markov reward models",
abstract = "The majority of computational methods applied for the analysis of homogeneous Markov reward models (MRMs) are not applicable for the analysis of inhomogeneous MRMs. By the nature of inhomogeneous models, only forward differential equations can be used to describe the model behaviour. In this paper we provide forward partial differential equations describing the distribution of reward measures of inhomogeneous MRMs. Based on this descriptions, we introduce the set of ordinary differential equations that describes the behaviour of the moments of reward measures when it is possible. This description of moments allows the effective numerical analysis of rather large inhomogeneous MRMs. A numerical example demonstrates the application of inhomogeneous MRMs in practice and the numerical behaviour of the introduced analysis technique.",
keywords = "Inhomogeneous Markov reward models, Moments of reward measures, Ordinary and partial differential equations",
author = "M. Telek and A. Horv{\'a}th and G. Horv{\'a}th",
year = "2004",
month = "7",
day = "15",
doi = "10.1016/j.laa.2004.02.002",
language = "English",
volume = "386",
pages = "383--405",
journal = "Linear Algebra and Its Applications",
issn = "0024-3795",
publisher = "Elsevier Inc.",
number = "1-3 SUPPL.",

}

TY - JOUR

T1 - Analysis of inhomogeneous Markov reward models

AU - Telek, M.

AU - Horváth, A.

AU - Horváth, G.

PY - 2004/7/15

Y1 - 2004/7/15

N2 - The majority of computational methods applied for the analysis of homogeneous Markov reward models (MRMs) are not applicable for the analysis of inhomogeneous MRMs. By the nature of inhomogeneous models, only forward differential equations can be used to describe the model behaviour. In this paper we provide forward partial differential equations describing the distribution of reward measures of inhomogeneous MRMs. Based on this descriptions, we introduce the set of ordinary differential equations that describes the behaviour of the moments of reward measures when it is possible. This description of moments allows the effective numerical analysis of rather large inhomogeneous MRMs. A numerical example demonstrates the application of inhomogeneous MRMs in practice and the numerical behaviour of the introduced analysis technique.

AB - The majority of computational methods applied for the analysis of homogeneous Markov reward models (MRMs) are not applicable for the analysis of inhomogeneous MRMs. By the nature of inhomogeneous models, only forward differential equations can be used to describe the model behaviour. In this paper we provide forward partial differential equations describing the distribution of reward measures of inhomogeneous MRMs. Based on this descriptions, we introduce the set of ordinary differential equations that describes the behaviour of the moments of reward measures when it is possible. This description of moments allows the effective numerical analysis of rather large inhomogeneous MRMs. A numerical example demonstrates the application of inhomogeneous MRMs in practice and the numerical behaviour of the introduced analysis technique.

KW - Inhomogeneous Markov reward models

KW - Moments of reward measures

KW - Ordinary and partial differential equations

UR - http://www.scopus.com/inward/record.url?scp=2942617143&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=2942617143&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2004.02.002

DO - 10.1016/j.laa.2004.02.002

M3 - Article

VL - 386

SP - 383

EP - 405

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - 1-3 SUPPL.

ER -