Categorification of the Müller-Wichards System Performance Estimation Model: Model Symmetries, Invariants, and Closed Forms
| Autor: | David J. Marchette, Allen D. Parks |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
0209 industrial biotechnology
Information Systems and Management effect of parallelization Computer Networks and Communications Performance estimation Categorification symmetries system performance modelling 02 engineering and technology Symmetry group lcsh:TA168 020901 industrial engineering & automation performance functor lcsh:Technology (General) 0202 electrical engineering electronic engineering information engineering Special case Natural approach Category theory Algebraic method Mathematics system performance stationary action principle Algebra categorification lcsh:Systems engineering Control and Systems Engineering Modeling and Simulation Homogeneous space lcsh:T1-995 020201 artificial intelligence & image processing invariants Software |
| Zdroj: | Systems, Vol 7, Iss 1, p 6 (2019) Systems Volume 7 Issue 1 |
| ISSN: | 2079-8954 |
| DOI: | 10.3390/systems7010006 |
| Popis: | The Müller-Wichards model (MW) is an algebraic method that quantitatively estimates the performance of sequential and/or parallel computer applications. Because of category theory’s expressive power and mathematical precision, a category theoretic reformulation of MW, i.e., CMW, is presented in this paper. The CMW is effectively numerically equivalent to MW and can be used to estimate the performance of any system that can be represented as numerical sequences of arithmetic, data movement, and delay processes. The CMW fundamental symmetry group is introduced and CMW’s category theoretic formalism is used to facilitate the identification of associated model invariants. The formalism also yields a natural approach to dividing systems into subsystems in a manner that preserves performance. Closed form models are developed and studied statistically, and special case closed form models are used to abstractly quantify the effect of parallelization upon processing time vs. loading, as well as to establish a system performance stationary action principle. |
| Databáze: | OpenAIRE |
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