## 2011.108: Products of random Max-plus matrices

2011.108:
J Hook
(2011)
*Products of random Max-plus matrices.*

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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 |
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Uncontrolled Keywords: | Max-plus algebra, matrices, random matrices, stochastic, petri-net, dynamical systems, graph eigenvalues, markov chains, distributed computing |

Subjects: | MSC 2000 > 05 Combinatorics MSC 2000 > 06 Order, lattices, ordered algebraic structures MSC 2000 > 15 Linear and multilinear algebra; matrix theory MSC 2000 > 37 Dynamical systems and ergodic theory MSC 2000 > 60 Probability theory and stochastic processes MSC 2000 > 68 Computer science MSC 2000 > 90 Operations research, mathematical programming MSC 2000 > 91 Game theory, economics, social and behavioral sciences |

MIMS number: | 2011.108 |

Deposited By: | Mr James Hook |

Deposited On: | 11 December 2011 |

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