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A dynamical system which is described in terms of an idempotent algebra by means of a vector equation with random irreducible matrix is considered. An approach based on approximation of the matrix of the system by means of matrices of simple structure is applied to evaluate bounds on the mean rate of growth of the state vector of the system. The process of(More)
We consider a multidimensional extremal problem formulated in terms of tropical mathematics. The problem is to minimize a nonlinear objective function, which is defined on a finite-dimensional semimodule over an idempotent semifield, subject to linear inequality constraints. An efficient solution approach is developed which reduces the problem to that of(More)
Max-algebra models of tandem single-server queueing systems with both finite and infinite buffers are developed. The dynamics of each system is described by a linear vector state equation similar to those in the conventional linear systems theory, and it is determined by a transition matrix inherent in the system. The departure epochs of a customer from the(More)