Journal ArticleDOI
Computing the phase-type renewal and related functions
TLDR
In this article, a procedure for computing the renewal function, the renewal density, the integral of the renewal functions, and the variance function of phase-type renewal processes is presented, based on the computation of the state probability vector of a continuous-time Markov chain.Citations
More filters
Journal Article
Fitting Phase-type Distributions via the EM Algorithm
TL;DR: An extended EM algorithm is used to minimize the information divergence (maximize the relative entropy) in the density approximation case and fits to Weibull, log normal, and Erlang distributions are used as illustrations of the latter.
Journal ArticleDOI
On the solution of renewal-type integral equations
TL;DR: In this article, a simple method (here called the RS-method) established for solving renewal-type integral equations based on direct numerical Riemann-Stieltjes integration is presented and evaluated.
Journal ArticleDOI
Matrix-analytic Models and their Analysis
TL;DR: In this article, the authors survey phase-type distributions and Markovian point processes, aspects of how to use such models in applied probability calculations and how to fit them to observed data.
Journal ArticleDOI
A simple approximation to the renewal function (reliability theory)
E. Smeitink,Rommert Dekker +1 more
TL;DR: In this article, the authors present a simple, easy-to-understand approximation to the renewal function that is easy to implement on a personal computer and works very well with one term if not too much accuracy is required.
Journal ArticleDOI
An approach for computing tight numerical bounds on renewal functions
TL;DR: This method computes tight lower and upper bounds for the renewal function, based on Riemann-Stieltjes integration, and provides bounds for solving certain renewal equations used in the study of availability.
References
More filters
Journal ArticleDOI
Matrix-geometric solutions in stochastic models : an algorithmic approach
TL;DR: In this paper, a mathematical text suitable for students of engineering and science who are at the third year undergraduate level or beyond is presented, which is a book of applicable mathematics, which avoids the approach of listing only the techniques, followed by a few examples.
Journal ArticleDOI
Elementary numerical analysis: an algorithmic approach (2nd edition), by S. D. Conte and Carl de Boor. Pp x, 396. £4·80 hard covers, £2·70 paperback. 1973 (McGraw-Hill)
TL;DR: Intended for introductory courses in numerical analysis, this book features a comprehensive treatment of major topics in this subject area using an algorithmic approach and provides numerous worked examples with computer output, and flowcharts and programs.
Book
Elementary Numerical Analysis: An Algorithmic Approach
Samuel Daniel Conte,Carl de Boor +1 more
TL;DR: In this article, a comprehensive treatment of major topics in numerical analysis is presented, using an algorithmic approach, providing numerous worked examples with computer output, and flowcharts and programs.
Journal ArticleDOI
Stochastic modelling and analysis: a computational approach
TL;DR: This book uses realistic examples to explore a wide variety of applications, such as inventory and production control, reliability, maintenance, queueing computer and communication systems, and will be of considerable interest to practitioners and researchers in operations research, statistics, computer science and engineering.