A Comprehensive Performance Evaluation on Iterative Algorithms for Sensitivity Analysis of Continuous-Time Markov Chains

• CHENG Yepeng

  Department of Information Engineering, Graduate School of Engineering, Hiroshima University

• OKAMURA Hiroyuki

  Department of Information Engineering, Graduate School of Engineering, Hiroshima University

• DOHI Tadashi

  Department of Information Engineering, Graduate School of Engineering, Hiroshima University

Abstract

This paper discusses how to compute the parametric sensitivity function in continuous-time Markov chains (CTMC). The sensitivity function is the first derivative of the steady-state probability vector regarding a CTMC parameter. Since the sensitivity function is given as a solution of linear equations with a sparse matrix, several linear equation solvers are available to obtain it. In this paper, we consider Jacobi and successive-over relaxation as variants of the Gauss-Seidel algorithm. In addition, we develop an algorithm based on the Takahashi method for the sensitivity function. In numerical experiments, we comprehensively evaluate the performance of these algorithms from the viewpoint of computation time and accuracy.

Journal

• IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

  IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E103.A (11), 1252-1259, 2020-11-01

  The Institute of Electronics, Information and Communication Engineers

Keywords

• CTMC
• steady-state probability
• sensitivity function
• algorithm

Details

• CRID: 1391975276372054400
• NII Article ID: 130007933455
• DOI: 10.1587/transfun.2019eap1171
• ISSN: 17451337
• ISSN: 09168508
• Web Site: https://www.jstage.jst.go.jp/article/transfun/E103.A/11/E103.A_2019EAP1171/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed