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Categorification of the Müller-Wichards System Performance Estimation Model: Model Symmetries, Invariants, and Closed Forms

1
Electromagnetic and Sensor Systems Department, Naval Surface Warfare Center Dahlgren Division, Dahlgren, VA 22448, USA
2
Strategic and Computing Systems Department, Naval Surface Warfare Center Dahlgren Division, Dahlgren, VA 22448, USA
*
Author to whom correspondence should be addressed.
Received: 25 October 2018 / Revised: 11 December 2018 / Accepted: 11 December 2018 / Published: 24 January 2019
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Abstract

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. View Full-Text
Keywords: system performance modelling; categorification; performance functor; symmetries; invariants; effect of parallelization; system performance stationary action principle system performance modelling; categorification; performance functor; symmetries; invariants; effect of parallelization; system performance stationary action principle
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Parks, A.D.; Marchette, D.J. Categorification of the Müller-Wichards System Performance Estimation Model: Model Symmetries, Invariants, and Closed Forms. Systems 2019, 7, 6.

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