LEADER 05256nam 22007815 450 001 9910300155503321 005 20220418225318.0 010 $a3-319-06674-9 024 7 $a10.1007/978-3-319-06674-5 035 $a(CKB)3710000000118039 035 $a(EBL)1731139 035 $a(OCoLC)884584952 035 $a(SSID)ssj0001243819 035 $a(PQKBManifestationID)11699057 035 $a(PQKBTitleCode)TC0001243819 035 $a(PQKBWorkID)11310917 035 $a(PQKB)10383087 035 $a(MiAaPQ)EBC1731139 035 $a(DE-He213)978-3-319-06674-5 035 $a(MiAaPQ)EBC3333735 035 $a(PPN)17878110X 035 $a(EXLCZ)993710000000118039 100 $a20140520d2014 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aInput modeling with phase-type distributions and Markov models $etheory and applications /$fby Peter Buchholz, Jan Kriege, Iryna Felko 205 $a1st ed. 2014. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014. 215 $a1 online resource (137 p.) 225 1 $aSpringerBriefs in Mathematics,$x2191-8198 300 $aDescription based upon print version of record. 311 $a3-319-06673-0 320 $aIncludes bibliographical references and index. 327 $a1. Introduction -- 2. Phase Type Distributions -- 3. Parameter Fitting for Phase Type Distributions -- 4. Markovian Arrival Processes -- 5. Parameter Fitting of MAPs -- 6. Stochastic Models including PH Distributions and MAPs -- 7. Software Tools -- 8. Conclusion -- References -- Index. 330 $aContaining a summary of several recent results on Markov-based input modeling in a coherent notation, this book introduces and compares algorithms for parameter fitting and gives an overview of available software tools in the area. Due to progress made in recent years with respect to new algorithms to generate PH distributions and Markovian arrival processes from measured data, the models outlined are useful alternatives to other distributions or stochastic processes used for input modeling. Graduate students and researchers in applied probability, operations research and computer science along with practitioners using simulation or analytical models for performance analysis and capacity planning will find the unified notation and up-to-date results presented useful. Input modeling is the key step in model based system analysis to adequately describe the load of a system using stochastic models. The goal of input modeling is to find a stochastic model to describe a sequence of measurements from a real system to model for example the inter-arrival times of packets in a computer network or failure times of components in a manufacturing plant. Typical application areas are performance and dependability analysis of computer systems, communication networks, logistics or manufacturing systems but also the analysis of biological or chemical reaction networks and similar problems. Often the measured values have a high variability and are correlated. It?s been known for a long time that Markov based models like phase type distributions or Markovian arrival processes are very general and allow one to capture even complex behaviors. However, the parameterization of these models results often in a complex and non-linear optimization problem. Only recently, several new results about the modeling capabilities of Markov based models and algorithms to fit the parameters of those models have been published. 410 0$aSpringerBriefs in Mathematics,$x2191-8198 606 $aProbabilities 606 $aMathematical models 606 $aComputer software 606 $aComputer science?Mathematics 606 $aComputer mathematics 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aMathematical Modeling and Industrial Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M14068 606 $aMathematical Software$3https://scigraph.springernature.com/ontologies/product-market-codes/M14042 606 $aMathematical Applications in Computer Science$3https://scigraph.springernature.com/ontologies/product-market-codes/M13110 615 0$aProbabilities. 615 0$aMathematical models. 615 0$aComputer software. 615 0$aComputer science?Mathematics. 615 0$aComputer mathematics. 615 14$aProbability Theory and Stochastic Processes. 615 24$aMathematical Modeling and Industrial Mathematics. 615 24$aMathematical Software. 615 24$aMathematical Applications in Computer Science. 676 $a519.233 700 $aBuchholz$b Peter$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721605 702 $aKriege$b Jan$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aFelko$b Iryna$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300155503321 996 $aInput Modeling with Phase-Type Distributions and Markov Models$92534135 997 $aUNINA