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September 2013 Critical path statistics of max-plus linear systems with Gaussian noise
James Hook
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J. Appl. Probab. 50(3): 654-670 (September 2013). DOI: 10.1239/jap/1378401228

Abstract

The critical paths of a max-plus linear system with noise are random variables. In this paper we introduce the edge criticalities which measure how often the critical paths traverse each edge in the precedence graph. We also present the parallel path approximation, a novel method for approximating these new statistics as well as the previously studied max-plus exponent. We show that, for low amplitude noise, the critical paths spend most of their time traversing the deterministic maximally weighted cycle and that, as the noise amplitude is increased, the critical paths become more random and their distribution over the edges in the precedence graph approaches a highly uniform measure of maximal entropy.

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James Hook. "Critical path statistics of max-plus linear systems with Gaussian noise." J. Appl. Probab. 50 (3) 654 - 670, September 2013. https://doi.org/10.1239/jap/1378401228

Information

Published: September 2013
First available in Project Euclid: 5 September 2013

zbMATH: 1274.60170
MathSciNet: MR3102507
Digital Object Identifier: 10.1239/jap/1378401228

Subjects:
Primary: 60G99
Secondary: 15B52

Rights: Copyright © 2013 Applied Probability Trust

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Vol.50 • No. 3 • September 2013
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