#### Title

Matrix-Analytics Methods in Stochastic Models

#### Document Type

Book Chapter

#### Publication Date

9-1-1996

#### Publication Title

Execution Time on an Unreliable Server with Latent Breakdowns

#### Abstract

Nicola et al . ( 1992) discussed several reliability characteristics of a system that alternates between up and down states and that reaches a critical condition when the accumulated downtime exceeds a given threshold, say b. They show that the probability distribution of various important measures can be directly derived from the probability distributions of the total execution time, when the job requires given a time units. The approach used is quite general and some early known results have been obtained as particular cases . The probability distributions are derived in terms of multidimensional Laplace transforms. Applications of the matrix-analytic approach with attraction of PH-distributions to the similar models of total execution time can be found in Bobbio and Trivedi ( 1990) and Jereb et al . ( 1995) . Both papers contain review of papers related to this subject . The above review briefly presents the status of this field.

#### First Page

225

#### Last Page

241

#### ISBN

9780824797669

#### Rights

© 1996 Taylor & Francis

#### Recommended Citation

Chukova, Stefanka and Dimitrov, Boyan N., "Matrix-Analytics Methods in Stochastic Models" (1996). *Mathematics Publications*. 71.

https://digitalcommons.kettering.edu/mathematics_facultypubs/71

## Comments

Chapter 12, p 225-240.16 pages. Edited by S. Chakravarthy, Attahiru S. Alfa.