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020 _a9783319066745
_9978-3-319-06674-5
024 7 _a10.1007/978-3-319-06674-5
_2doi
035 _ato000543316
040 _aSpringer
_cSpringer
_dRU-ToGU
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
082 0 4 _a519.2
_223
100 1 _aBuchholz, Peter.
_eauthor.
_9450287
245 1 0 _aInput Modeling with Phase-Type Distributions and Markov Models
_helectronic resource
_bTheory and Applications /
_cby Peter Buchholz, Jan Kriege, Iryna Felko.
260 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2014.
300 _aXII, 127 p. 42 illus., 35 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aSpringerBriefs in Mathematics,
_x2191-8198
505 0 _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.
520 _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.
650 0 _amathematics.
_9566183
650 0 _aComputer software.
_9303280
650 0 _aDistribution (Probability theory).
_9303731
650 1 4 _aMathematics.
_9566184
650 2 4 _aProbability Theory and Stochastic Processes.
_9303734
650 2 4 _aMathematical Modeling and Industrial Mathematics.
_9303944
650 2 4 _aMathematical Software.
_9303285
650 2 4 _aMathematical Applications in Computer Science.
_9412135
700 1 _aKriege, Jan.
_eauthor.
_9450288
700 1 _aFelko, Iryna.
_eauthor.
_9450289
710 2 _aSpringerLink (Online service)
_9143950
773 0 _tSpringer eBooks
830 0 _aSpringerBriefs in Mathematics,
_9445669
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-06674-5
912 _aZDB-2-SMA
999 _c401238