Critical path statistics of max-plus linear systems with Gaussian noise

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
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: http://eprints.maths.manchester.ac.uk/id/eprint/2005

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