Products of random Max-plus matrices

Hook, J (2011) Products of random Max-plus matrices. [MIMS Preprint]

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Abstract

Max-plus stochastic linear systems describe a wide variety of non-linear queueing processes. The dynamics of these systems are dominated by a Max-plus analogue of the Lyupanov exponent the value of which depends on the structure of the underlying support graphs as well as the properties of the waiting-time distributions. For matrices whose associated weighted graphs have identically distributed edge weights (componentwise homogeneity) we are able to decouple these two effects and provide a sandwich of bounds for the Max-plus Lyupanov exponent relating it to some classical properties of the support graph and some extreme value expectations of the waiting-time distributions. This sandwich inequality is then applied to products of componentwise exponential, Gaussian and uniform matrices.

Item Type: MIMS Preprint
Uncontrolled Keywords: Max-plus algebra, matrices, random matrices, stochastic, petri-net, dynamical systems, graph eigenvalues, markov chains, distributed computing
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 05 Combinatorics
MSC 2010, the AMS's Mathematics Subject Classification > 06 Order, lattices, ordered algebraic structures
MSC 2010, the AMS's Mathematics Subject Classification > 15 Linear and multilinear algebra; matrix theory
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 > 68 Computer science
MSC 2010, the AMS's Mathematics Subject Classification > 90 Operations research, mathematical programming
MSC 2010, the AMS's Mathematics Subject Classification > 91 Game theory, economics, social and behavioral sciences
Depositing User: Mr James Hook
Date Deposited: 11 Dec 2011
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/1728

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