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

Yepeng CHENG  Hiroyuki OKAMURA  Tadashi DOHI  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E103-A   No.11   pp.1252-1259
Publication Date: 2020/11/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.2019EAP1171
Type of Manuscript: PAPER
Category: Numerical Analysis and Optimization
Keyword: 
CTMC,  steady-state probability,  sensitivity function,  algorithm,  

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Summary: 
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.