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A Min-Plus Algebra System Theory for Traffic Networks

Mathematics, 2023
In this article, we introduce a comprehensive system theory based on the min-plus algebra of 2×2 matrices of functions. This novel approach enables the algebraic construction of traffic networks and the analytical derivation of performance bounds for ...
Nadir Farhi
doaj   +4 more sources

Asymptotic Identity in Min-Plus Algebra: A Report on CPNS [PDF]

Computational and Mathematical Methods in Medicine, 2012
Network calculus is a theory initiated primarily in computer communication networks, especially in the aspect of real-time communications, where min-plus algebra plays a role. Cyber-physical networking systems (CPNSs) are recently developing fast and models in data flows as well as systems in CPNS are, accordingly, greatly desired.

exaly   +5 more sources

Characteristic Min-Polynomial and Eigen Problem of a Matrix over Min-Plus Algebra

JTAM (Jurnal Teori dan Aplikasi Matematika), 2023
Let R_ε=R∪{-∞}, with R being a set of all real numbers. The algebraic structure (R_ε,⊕,⊗) is called max-plus algebra. The task of finding the eigenvalue and eigenvector is called the eigenproblem.
Sahmura Maula Al Maghribi, Siswanto Siswanto, Sutrima Sutrima   +2 more
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CRAMER’S RULE IN MIN-PLUS ALGEBRA

Barekeng
Cramer’s rule is one of a method for solving a system of linear equations in conventional algebra. The system of linear equation  can be solved using Cramer’s rule if .
Zakia Nur Ramadhani Putri, Siswanto Siswanto, Vika Yugi Kurniawan   +2 more
doaj   +2 more sources

Interval min-plus algebraic structure and matrices over interval min-plus algebra

Journal of Physics: Conference Series, 2020
Abstract Max-plus algebra is the set ℝ max
A R Awallia, null Siswanto, V Y Kurniawan   +2 more
exaly   +2 more sources

CRAMER’S RULE IN INTERVAL MIN-PLUS ALGEBRA

Barekeng
A min-plus algebra is a set ,  where  is the set of all real numbers, equipped with the minimum  and addition  operations. The system of linear equations  in min-plus algebra can be solved using Cramer's rule.
Siswanto Siswanto, Ade Safira Septiany
doaj   +2 more sources

Determining the Inverse of a Matrix over Min-Plus Algebra

JTAM (Jurnal Teori dan Aplikasi Matematika)
Linear algebra over the semiring  R_ε with ⊗ (plus) and ⨁ (maximum) operations which is known as max-plus algebra. One of the isomorphic with this algebra is a min-plus algebra.
Siswanto Siswanto, Anggrina Gusmizain
doaj   +2 more sources

PERMANENT AND DOMINANT OF MATRIX OVER INTERVAL MIN-PLUS ALGEBRA

Barekeng
A min-plus algebra is a set , where is the set of all real numbers equipped with two binary operations, namely minimum and addition . Every square matrix in min-plus algebra can always be calculated as a permanent and dominant matrix.
Ade Safira Septiany, Siswanto Siswanto, Vika Yugi Kurniawan   +2 more
doaj   +2 more sources

Independent [1, 2]-domination of grids via min-plus algebra

Electronic Notes in Discrete Mathematics, 2016
Abstract Domination of grids has been proved to be a demanding task and with the addition of independence it becomes more challenging. It is known that no grid with m , n ≥ 5 has a perfect code, that is an independent vertex set such that each vertex not in it has exactly one neighbor in that set. So it is interesting to study the existence
M L Puertas
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Characteristic Polynomial and Eigenproblem of Triangular Matrix over Interval Min-Plus Algebra

JTAM (Jurnal Teori dan Aplikasi Matematika)
A min-plus algebra is a linear algebra over the semiring R_ε', equipped with the operations “"⊕'=min" ” and “⊗=+”. In min-plus algebra, there is the concept of characteristic polynomial obtained from permanent of matrix.
Anita Dwi Rahmawati, Siswanto Siswanto, Supriyadi Wibowo   +2 more
doaj   +2 more sources