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

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

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

Scalable analysis of stochastic process algebra models

The performance modelling of large-scale systems using discrete-state approaches is fundamentally hampered by the well-known problem of state-space explosion, which causes exponential growth of the reachable state space as a function of the number of the components which constitute the model. Because they are mapped onto continuous-time Markov chains (CTMCs), models described in the stochastic process algebra PEPA are no exception. This thesis presents a deterministic continuous-state semantics of PEPA which employs ordinary differential equations (ODEs) as the underlying mathematics for the performance evaluation. This is suitable for models consisting of large numbers of replicated components, as the ODE problem size is insensitive to the actual population levels of the system under study. Furthermore, the ODE is given an interpretation as the fluid limit of a properly defined CTMC model when the initial population levels go to infinity. This framework allows the use of existing results which give error bounds to assess the quality of the differential approximation. The computation of performance indices such as throughput, utilisation, and average response time are interpreted deterministically as functions of the ODE solution and are related to corresponding reward structures in the Markovian setting. The differential interpretation of PEPA provides a framework that is conceptually analogous to established approximation methods in queueing networks based on meanvalue analysis, as both approaches aim at reducing the computational cost of the analysis by providing estimates for the expected values of the performance metrics of interest. The relationship between these two techniques is examined in more detail in a comparison between PEPA and the Layered Queueing Network (LQN) model. General patterns of translation of LQN elements into corresponding PEPA components are applied to a substantial case study of a distributed computer system. This model is analysed using stochastic simulation to gauge the soundness of the translation. Furthermore, it is subjected to a series of numerical tests to compare execution runtimes and accuracy of the PEPA differential analysis against the LQN mean-value approximation method. Finally, this thesis discusses the major elements concerning the development of a software toolkit, the PEPA Eclipse Plug-in, which offers a comprehensive modelling environment for PEPA, including modules for static analysis, explicit state-space exploration, numerical solution of the steady-state equilibrium of the Markov chain, stochastic simulation, the differential analysis approach herein presented, and a graphical framework for model editing and visualisation of performance evaluation results

NASA RECON: Course Development, Administration, and Evaluation

The R and D activities addressing the development, administration, and evaluation of a set of transportable, college-level courses to educate science and engineering students in the effective use of automated scientific and technical information storage and retrieval systems, and, in particular, in the use of the NASA RECON system, are discussed. The long-range scope and objectives of these contracted activities are overviewed and the progress which has been made toward these objectives during FY 1983-1984 is highlighted. In addition, the results of a survey of 237 colleges and universities addressing course needs are presented

First Annual Workshop on Space Operations Automation and Robotics (SOAR 87)

Several topics relative to automation and robotics technology are discussed. Automation of checkout, ground support, and logistics; automated software development; man-machine interfaces; neural networks; systems engineering and distributed/parallel processing architectures; and artificial intelligence/expert systems are among the topics covered

Safety and Reliability - Safe Societies in a Changing World

The contributions cover a wide range of methodologies and application areas for safety and reliability that contribute to safe societies in a changing world. These methodologies and applications include: - foundations of risk and reliability assessment and management - mathematical methods in reliability and safety - risk assessment - risk management - system reliability - uncertainty analysis - digitalization and big data - prognostics and system health management - occupational safety - accident and incident modeling - maintenance modeling and applications - simulation for safety and reliability analysis - dynamic risk and barrier management - organizational factors and safety culture - human factors and human reliability - resilience engineering - structural reliability - natural hazards - security - economic analysis in risk managemen

Space Simulation, 7th

Space simulation facilities and techniques are outlined that encompass thermal scale modeling, computerized simulations, reentry materials, spacecraft contamination, solar simulation, vacuum tests, and heat transfer studies