The general form linearizer algorithms: A new family of approximate mean value analysis algorithms
Approximate Mean Value Analysis (AMVA) is a popular technique for analyzing queueing network models due to the accuracy and efficiency that it affords. Currently, there is no algorithm that is more accurate than, and yet has the same computational cost as, the Linearizer algorithm, one of the most popular among different AMVA algorithms that trade off accuracy and efficiency. In this paper, we present a new family of AMVA algorithms, termed the General Form Linearizer (GFL) algorithms, for analyzing product-form queueing networks. The Linearizer algorithm is a special instance of this family. We show that some GFL algorithms yield more accurate solutions than, and have the same numerical properties and computational complexities as, the Linearizer algorithm. We also examine the numerical properties and computational costs of different implementations of the new and existing AMVA algorithms.
The study of the stability of many stochastic processes as Markov chains needs sometimes to use eigenvalues and eigenvectors of the transition matrix. This paper is an investigation on a methodology which computes fuzzy eigenvalues and fuzzy eigenvectors within the context of a fuzzy Markov chain transition matrix, under max-min composition.