Simple lower and upper bounds on mean cycle time in stochastic acyclic fork-join queueing networks are derived using a (max,+)algebra based representation of network dynamics. The behaviour of the bounds under various assumptions concerning the service times in the networks is discussed, and related numerical examples are presented. Key-Words: (max,+)-algebra, dynamic state equation, acyclic fo...

The eigenspace structure for a given n × n concave Monge matrix in a max-plus algebra is described. Based on the description, an O(n) algorithm for computing the eigenspace dimension is formulated, which is faster than the previously known algorithms. Analogous results for convex Monge matrices have been published in [M. Gavalec, J. Plavka, Structure of the eigenspace of a Monge matrix in max-p...

The aim of this chapter is to present a system of linear equation and inequalities in max-al‐ gebra. Max-algebra is an analogue of linear algebra developed on the pair of operations (⊕ , ⊗ ) extended to matrices and vectors, where a⊕ b = max(a, b) and a⊗ b = a + b for a, b ∈ R. The system of equations A⊗ x = c and inequalities B⊗ x ≤ d have each been stud‐ ied in the literature. We will present...

Based on max-plus algebra, a class of discrete event processes can be described by linear recursive equations[1]. Such a system exhibits asymptotic periodic behavior, and its performance can be evaluated by calculating the eigenvalue of the system matrix in max-plus algebra. On the other hand, control techniques based on switching among different controllers have been explored extensively in re...

Let a⊕b = max(a, b) and a⊗b = a+b for a, b ∈ R and extend the pair of operations to matrices and vectors in the same way as in linear algebra. The homogeneous twosided system in max-algebra is of the form A⊗ x = B ⊗ x. No polynomial method for solving homogeneous system is known. In this paper, we consider homogeneous twosided linear systems in max-algebra in a special case. We show that it can...

Eigenvectors of a max-min matrix characterize stable states of the corresponding discrete-events system. Investigation of the max-min eigenvectors of a given matrix is therefore of a great practical importance. The eigenproblem in max-min algebra has been studied by many authors. Interesting results were found in describing the structure of the eigenspace, and algorithms for computing the maxim...