Using Markov chains for modelling networks

The paper contains the review and the discussion on modelling communication networks with the use of queuing models and Markov chains. It shows how to take into account various characteristics of real systems - like some control mechanisms and the traffic self-similarity. There are presented two mechanisms modelled with Markov chains: the RED algorithm in TCP/IP and a self-similar traffic shaping

A Markovian model of the RED mechanism solved with a cluster of computers

The paper presents a working example of distributed application which can be used to find stationary probabilities of states for queuing models - by generating a transition rate matrix and solving a linear system. The presented example is connected to the RED mechanism which can be used in the TCP/IP protocol to control packets flow. The paper also shows efficiency of the application with the use of a various number of computers connected with Ethernet

Markowitz scheme for the sparse WZ factorization

In this paper the authors present problems which can appear when a sparse square matrix(without any special structure) is factorized to a product of matrices W and Z. The fill-in problemis considered, and the manners of its solving – by permuting both rows and columns with amodified Markowitz scheme among others. The results of numerical experiments for sparsematrices of various sizes are presented and they show the Markowitz scheme applicability

The role of the students' and teachers' activities in the adoption and continued use of an e-learning platform

This paper identifies and examines an impact of students' and teachers' activities on possibility of using and adapting e-learning platform in postgraduate studies. The paper aims at experimental survey of students' satisfaction level, their opinions concerning implementing e-learning at work as well as correlation students' activity, teachers' activity and e-learning results. Our hypotheses are tested with 160 students of postgraduate studies using e-learning educational platform

Distributed generation of Markov chains infinitesimal generator matrices for queuing network models

In this paper we want to present problems connected with the generation and storing of huge sparse matrices, arising during modelling the queuing networks with the use of Markov chains. We also want to present an algorithm for distributed generation of such matrices

Solving linear systems with vectorized WZ factorization

In the paper we present a vectorized algorithm for WZ factorization of a matrix which was implemented with the BLAS1 library. We present the results of numerical experiments which show that vectorization accelerates the sequential WZ factorization. Next, we parallelized both algorithms for a two-processor shared memory machine using the OpenMP standard. We present performances of these four algorithms on a two-Pentium III machine with a Linux system (the parallelized sequential algorithm is better than the normal sequential one, but the parallelized vectorized algorithm is very similar in its performance to the non-parallelized vectorized one)

The inverse iteration with the WZ factorization used to the Markovian models

In the article a new approach for solving Markovian linear systems is presented. It is the inverse iteration with the use of the WZ factorization. The paper contains the theoretical base of the method and numerical experiment results where the accuracy and the performance time were investigated. A modified (with the use of the SBLAS library and the Harwell-Boeing sparse matrix storage scheme) method was also presented. The experiments were carried out with the matrices generated for a Markovian model of a leaky bucket with tokens

Assessment of Two Task Frameworks with Dependencies for Matrix Factorizations on a Multicore Architecture

In this study, we evaluate two task frameworks with dependencies for important application kernels coming from the numerical linear algebra. In this approach, the algorithms of the matrix factorization are considered, namely the tiled LU and the WZ factorizations both without pivoting. In tiled algorithms, the operations are represented as a sequence of small tasks which operate on square blocks (tiles) of the data. The dependencies among tasks are expressed as a direct acyclic graph and the runtime system runs the graph on a multicore architecture. The performance of applications based on the task dependencies is related to efficient compilers and the runtime systems. We report the performance and the scalability of two task frameworks with dependencies on the multicore architecture for the matrix factorizations. Namely, we compare OpenMP and Intel Thread Building Blocks. Our results show that the number of tiles in both factorizations always have an impact on the performance and the speedup. Both the frameworks show their suitability for efficient parallelization of such applications, although both have their own merits and flaws

Distributed solving of Markov chains for computer network models

In this paper a distributed iterative GMRES algorithm for solving huge and sparse linear systems (that appear in the Markov chain analysis of queueing network models) is considered. It is implemented using the MPI standard on a collection of Linux machines and the emphasis is put upon the size of linear systems being solved and possibility of storing huge and sparse matrices as well as huge vectors on distributed systems