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Computation of the limiting distribution in queueing systems with repeated attempts and disasters

J. R. Artalejo, A. Gómez-Corral (2010)

RAIRO - Operations Research

Single server queues with repeated attempts are useful in the modeling of computer and telecommunication systems. In addition, we consider in this paper the possibility of disasters. When a disaster occurs, all the customers present in the system are destroyed immediately. Using a regenerative approach, we derive a numerically stable recursion scheme for the state probabilities. This model can be employed to analyze the behaviour of a buffer in computers with virus infections.

Computational schemes for two exponential servers where the first has a finite buffer

Moshe Haviv, Rita Zlotnikov (2011)

RAIRO - Operations Research - Recherche Opérationnelle

We consider a system consisting of two not necessarily identical exponential servers having a common Poisson arrival process. Upon arrival, customers inspect the first queue and join it if it is shorter than some threshold n. Otherwise, they join the second queue. This model was dealt with, among others, by Altman et al. [Stochastic Models20 (2004) 149–172]. We first derive an explicit expression for the Laplace-Stieltjes transform of the distribution underlying the arrival (renewal) process to...

Computational schemes for two exponential servers where the first has a finite buffer

Moshe Haviv, Rita Zlotnikov (2011)

RAIRO - Operations Research

We consider a system consisting of two not necessarily identical exponential servers having a common Poisson arrival process. Upon arrival, customers inspect the first queue and join it if it is shorter than some threshold n. Otherwise, they join the second queue. This model was dealt with, among others, by Altman et al. [Stochastic Models20 (2004) 149–172]. We first derive an explicit expression for the Laplace-Stieltjes transform of the distribution underlying the arrival (renewal) process to...

Computing and proving with pivots

Frédéric Meunier (2013)

RAIRO - Operations Research - Recherche Opérationnelle

A simple idea used in many combinatorial algorithms is the idea of pivoting. Originally, it comes from the method proposed by Gauss in the 19th century for solving systems of linear equations. This method had been extended in 1947 by Dantzig for the famous simplex algorithm used for solving linear programs. From since, a pivoting algorithm is a method exploring subsets of a ground set and going from one subset σ to a new one σ′ by deleting an element inside σ and adding an element outside σ: σ′ = σv}  ∪  {u},...

Computing minimum norm solution of a specific constrained convex nonlinear problem

Saeed Ketabchi, Hossein Moosaei (2012)

Kybernetika

The characterization of the solution set of a convex constrained problem is a well-known attempt. In this paper, we focus on the minimum norm solution of a specific constrained convex nonlinear problem and reformulate this problem as an unconstrained minimization problem by using the alternative theorem.The objective function of this problem is piecewise quadratic, convex, and once differentiable. To minimize this function, we will provide a new Newton-type method with global convergence properties....

Computing the greatest 𝐗 -eigenvector of a matrix in max-min algebra

Ján Plavka (2016)

Kybernetika

A vector x is said to be an eigenvector of a square max-min matrix A if A ⊗ x = x . An eigenvector x of A is called the greatest 𝐗 -eigenvector of A if x ∈ 𝐗 = { x ; x ̲ ≤ x ≤ x ¯ } and y ≤ x for each eigenvector y ∈ 𝐗 . A max-min matrix A is called strongly 𝐗 -robust if the orbit x , A ⊗ x , A 2 ⊗ x , ⋯ reaches the greatest 𝐗 -eigenvector with any starting vector of 𝐗 . We suggest an O ( n 3 ) algorithm for computing the greatest 𝐗 -eigenvector of A and study the strong 𝐗 -robustness. The necessary and sufficient conditions for strong 𝐗 -robustness are introduced and an efficient...

Computing the Stackelberg/Nash equilibria using the extraproximal method: Convergence analysis and implementation details for Markov chains games

Kristal K. Trejo, Julio B. Clempner, Alexander S. Poznyak (2015)

International Journal of Applied Mathematics and Computer Science

In this paper we present the extraproximal method for computing the Stackelberg/Nash equilibria in a class of ergodic controlled finite Markov chains games. We exemplify the original game formulation in terms of coupled nonlinear programming problems implementing the Lagrange principle. In addition, Tikhonov's regularization method is employed to ensure the convergence of the cost-functions to a Stackelberg/Nash equilibrium point. Then, we transform the problem into a system of equations in the...

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