SpringerBriefs in Mathematics

Input Modeling with Phase-Type Distributions and Markov Models

Theory and Applications

Authors: Buchholz, Peter, Kriege, Jan, Felko, Iryna

  • Contains an overview of available open source software tools for parameter fitting of PH distributions and MAPs
  • Presents a large number of algorithms to fit the parameters of PH distributions or MAPs according to measured traces
  • Introduces the use of PH distributions and MAPs in stochastic models including simulation models, especially in the network simulator OMNeT++
see more benefits

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-06674-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA
  • ISBN 978-3-319-06673-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this book

Containing a summary of several recent results on Markov-based input modeling in a coherent notation, this book introduces and compares algorithms for parameter fitting and gives an overview of available software tools in the area. Due to progress made in recent years with respect to new algorithms to generate PH distributions and Markovian arrival processes from measured data, the models outlined are useful alternatives to other distributions or stochastic processes used for input modeling. Graduate students and researchers in applied probability, operations research and computer science along with practitioners using simulation or analytical models for performance analysis and capacity planning will find the unified notation and up-to-date results presented useful. Input modeling is the key step in model based system analysis to adequately describe the load of a system using stochastic models.

The goal of input modeling is to find a stochastic model to describe a sequence of measurements from a real system to model for example the inter-arrival times of packets in a computer network or failure times of components in a manufacturing plant. Typical application areas are performance and dependability analysis of computer systems, communication networks, logistics or manufacturing systems but also the analysis of biological or chemical reaction networks and similar problems. Often the measured values have a high variability and are correlated. It’s been known for a long time that Markov based models like phase type distributions or Markovian arrival processes are very general and allow one to capture even complex behaviors. However, the parameterization of these models results often in a complex and non-linear optimization problem. Only recently, several new results about the modeling capabilities of Markov based models and algorithms to fit the parameters of those models have been published.​

Table of contents (8 chapters)

  • Introduction

    Buchholz, Peter (et al.)

    Pages 1-3

  • Phase-Type Distributions

    Buchholz, Peter (et al.)

    Pages 5-28

  • Parameter Fitting for Phase Type Distributions

    Buchholz, Peter (et al.)

    Pages 29-62

  • Markovian Arrival Processes

    Buchholz, Peter (et al.)

    Pages 63-74

  • Parameter Fitting of MAPs

    Buchholz, Peter (et al.)

    Pages 75-93

Buy this book

eBook $39.99
price for USA (gross)
  • ISBN 978-3-319-06674-5
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $54.99
price for USA
  • ISBN 978-3-319-06673-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Input Modeling with Phase-Type Distributions and Markov Models
Book Subtitle
Theory and Applications
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Peter Buchholz, Jan Kriege, Iryna Felko
eBook ISBN
978-3-319-06674-5
DOI
10.1007/978-3-319-06674-5
Softcover ISBN
978-3-319-06673-8
Series ISSN
2191-8198
Edition Number
1
Number of Pages
XII, 127
Number of Illustrations and Tables
7 b/w illustrations, 35 illustrations in colour
Topics