Products of random matrices and queueing system performance evaluation

N. K. Krivulin

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arXiv · 1212.5291

Products of random matrices and queueing system performance evaluation

N. K. Krivulin

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Abstract

We consider (max,+)-algebra products of random matrices, which arise from performance evaluation of acyclic fork-join queueing networks. A new algebraic technique to examine properties of the product and investigate its limiting behaviour is proposed based on an extension of the standard matrix (max,+)-algebra by endowing it with the ordinary matrix addition as an external operation. As an application, we derive bounds on the (max,+)-algebra maximal Lyapunov exponent which can be considered as the cycle time of the networks.

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N. K. Krivulin. 2012-12-20. Products of random matrices and queueing system performance evaluation. https://arxiv.org/abs/1212.5291

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