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Products of Irreducible Random Matrices in the (Max, +) Algebra

1997
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Advances in Applied Probability
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We consider the recursive equation x(n + 1)= A(n)⊗x(n), where x(n + 1) and x(n) are ℝ k -valued vectors and A(n) is an irreducible random matrix of size k × k. The matrix-vector multiplication in the (max, +) algebra is defined by (A(n)⊗x(n))= maxj (Aij (n) + xj (n)). This type of equation can be used to represent the evolution of stochastic event graphs which include cyclic Jackson networks, some manufacturing models and models with general blocking (such as Kanban). Let us assume that the

doi:10.1017/s0001867800028081
fatcat:vqmdi7peu5f3jfuekzwqkzrewy