RECAL a new efficient algorithm for the exact analysis of multiple-chain closed queueing networks

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A note on integrating products of linear forms over the unit simplex

Integrating a product of linear forms over the unit simplex can be done in polynomial time if the number of variables n is fixed (V. Baldoni et al., 2011). In this note, we highlight that this problem is equivalent to obtaining the normalizing constant of state probabilities for a popular class of Markov processes used in queueing network theory. In light of this equivalence, we survey existing computational algorithms developed in queueing theory that can be used for exact integration. For example, under some regularity conditions, queueing theory algorithms can exactly integrate a product of linear forms of total degree N by solving N systems of linear equations

Queueing networks: solutions and applications

During the pasttwo decades queueing network models have proven to be a versatile tool for computer system and computer communication system performance evaluation. This chapter provides a survey of th field with a particular emphasis on applications. We start with a brief historical retrospective which also servesto introduce the majr issues and application areas. Formal results for product form queuenig networks are reviewed with particular emphasis on the implications for computer systems modeling. Computation algorithms, sensitivity analysis and optimization techniques are among the topics covered. Many of the important applicationsof queueing networks are not amenableto exact analysis and an (often confusing) array of approximation methods have been developed over the years. A taxonomy of approximation methods is given and used as the basis for for surveing the major approximation methods that have been studied. The application of queueing network to a number of areas is surveyed, including computer system cpacity planning, packet switching networks, parallel processing, database systems and availability modeling.Durante as últimas duas décadas modelos de redes de filas provaram ser uma ferramenta versátil para avaliação de desempenho de sistemas de computação e sistemas de comunicação. Este capítulo faz um apanhado geral da área, com ênfase em aplicações. Começamos com uma breve retrospectiva histórica que serve também para introduzir os pontos mais importantes e as áreas de aplicação. Resultados formais para redes de filas em forma de produto são revisados com ênfase na modelagem de sistemas de computação. Algoritmos de computação, análise de sensibilidade e técnicas de otimização estão entre os tópicos revistos. Muitas dentre importantes aplicações de redes de filas não são tratáveis por análise exata e uma série (frequentemente confusa) de métodos de aproximação tem sido desenvolvida. Uma taxonomia de métodos de aproximação é dada e usada como base para revisão dos mais importantes métodos de aproximação propostos. Uma revisão das aplicações de redes de filas em um número de áreas é feita, incluindo planejamento de capacidade de sistemas de computação, redes de comunicação por chaveamento de pacotes, processamento paralelo, sistemas de bancos de dados e modelagem de confiabilidade

PDAC: A Data Parallel Algorithm for the Performance Analysis of Closed Queueing Networks

Abstract. A parallel distribution analysis by chain algorithm (PDAC) is presented for the performance analysis of closed, multiple class queueing networks. The PDAC algorithm uses data parallel computation of the summation indices needed to compute the joint queue length probabilities. The computational cost of the PDAC algorithm is shown to be of polynomial order with a lower degree than the cost of the serial implementation of the DAC algorithm. Examples are presented comparing the PDAC algorithm with the DAC algorithm to illustrate its advantages and limitations

Applying BCMP multi-class queueing networks for the performance evaluation of hierarchical and modular software systems

Queueing networks with multiple classes of customers play a fundamental role for evaluating the performance of both software and hardware architectures. The main strength of product-form models, in particular of BCMP queueing networks, is that they combine a flexible formalism with efficient analysis techniques and solution algorithms. In this paper we provide an algorithm that starting from a high-level description of a system, and from the definition of its components in terms of interacting sub-systems, computes a multiple-class and multiple-chain BCMP queueing network. We believe that the strength of this approach is twofold. First, the modeller deals with simplified models, which are defined in a modular and hierarchical way. Hence, we can carry on sensitivity analysis that may easily include structural changes (and not only on the time parameters). Second, maintaining the product-form property allows one to derive the average system performance indices very efficiently. The paper also discusses the application of the algorithm for the performance evaluation of websites with modular architectures, such as those based on content management systems.Queueing networks with multiple classes of customers play a fundamental role for evaluating the performance of both software and hardware architectures. The main strength of product-form models, in particular of BCMP queueing networks, is that they combine a flexible formalism with efficient analysis techniques and solution algorithms. In this paper we provide an algorithm that starting from a high-level description of a system, and from the definition of its components in terms of interacting sub-systems, computes a multiple-class and multiple-chain BCMP queueing network. We believe that the strength of this approach is twofold. First, the modeller deals with simplified models, which are defined in a modular and hierarchical way. Hence, we can carry on sensitivity analysis that may easily include structural changes (and not only on the time parameters). Second, maintaining the product-form property allows one to derive the average system performance indices very efficiently. The paper also discusses the application of the algorithm for the performance evaluation of websites with modular architectures, such as those based on content management systems

XSnap : a queueing network analysis package

Bibliography: pages 114-116.This dissertation describes the design and implementation of a sophisticated X-Windows based modelling package called XSnap, which can be used to solve product-form mixed multi-class queueing networks. A Graphical User Interface allows interactive network specification, whilst the modeller can also define complex network experiments and request customised output through the use of a language called SnapL. The solution modules used by XSnap are grouped together to form the Calculation Modules ToolBox (CMTB), which can be easily integrated into any modelling package which provides an appropriate user interface. Solution statistics are found using Reiser's Mean Value Analysis (MVA) algorithm, which has been extended to allow for the approximate solution of networks with PRIORITY servers or non-integral closed chain populations. A routing validation algorithm is used to validate the routing information for the network to be solved, and equations defining the relative throughput (or visit ratio) of each class at each centre in the network, are solved using a version of LU-Decomposition called Crout's method with partial pivoting. The dissertation also includes a study of a number of other available modelling packages. The choice of features included in the XSnap GUI has been largely influenced by this study. A number of different algorithms for solving product-form queueing networks are also discussed, and relevant points from this discussion are presented as part of the motivation for using the MVA algorithm for finding solution statistics

CoMoM: Efficient Class-Oriented Evaluation of Multiclass Performance Models

We introduce the Class-oriented Method of Moments (CoMoM), a new exact algorithm to compute performance indexes in closed multiclass queueing networks. Closed models are important for performance evaluation of multi-tier applications, but when the number of service classes is large they become too expensive to solve with exact methods such as Mean Value Analysis (MVA). CoMoM addresses this limitation by a new recursion that scales efficiently with the number of classes. Compared to the MVA algorithm, which recursively computes mean queue-lengths, CoMoM carries on in the recursion also information on higher-order moments of queue-lengths. We show that this additional information greatly reduces the number of operations needed to solve the model and makes CoMoM the best-available algorithm for networks with several classes. We conclude the paper by generalizing CoMoM to the efficient computation of marginal queue-length probabilities, which finds application in the evaluation of state-dependent attributes such as energy consumption or quality-of-service metrics