Hook, J
(2012)
*Critical path statistics of max-plus linear systems
with Gaussian noise.*
[MIMS Preprint]

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## Abstract

The critical paths of a max-plus linear systems 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.

Item Type: | MIMS Preprint |
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Uncontrolled Keywords: | max-plus algebra, max-plus linear system, max-plus stochastic, queuing, tropical, stochastic, turnpike, optimization, extreme value theory |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 05 Combinatorics MSC 2010, the AMS's Mathematics Subject Classification > 37 Dynamical systems and ergodic theory MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes MSC 2010, the AMS's Mathematics Subject Classification > 90 Operations research, mathematical programming |

Depositing User: | Mr James Hook |

Date Deposited: | 23 Jul 2013 |

Last Modified: | 08 Nov 2017 18:18 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2005 |

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