Theory of Probability and Mathematical Statistics

У навчальному посібнику розглянуто основні поняття теорії ймовірностей та множин, алгебру множин, доповнено основами теорії множин та графів. Наведені закони розподілу та числові характеристики випадкових величин та їх функцій. Також подані основи потоків подій, марковських процесів та систем масового обслуговування, що дуже актуальні у віртуальних обчислюваннях та хмарних технологіях. Розглянуті початкові статистичні формулювання, вирівнювання і узгодження статистичних розподілів та оцінки їх параметрів. Посібник двомовний – українсько-англійський. Матеріал лекцій представлий у вигляді «два стовпці тексту на одній сторінці» (так звана «книгасорочечка», Англійською «vein book»). Посібник призначений для здобувачів ступеня бакалавра за спеціальностями 121 «Інженерія програмного забезпечення», 126 «Інформаційні системи та технології». Також може бути запропонований для студентів закладів вищої освіти для самостійного (без підказки перекладу) опрацювання з англомовними текстами за фахом, особливо в магістратурі

Performance of Computer Systems; Proceedings of the 4th International Symposium on Modelling and Performance Evaluation of Computer Systems, Vienna, Austria, February 6-8, 1979

These proceedings are a collection of contributions to computer system performance, selected by the usual refereeing process from papers submitted to the symposium, as well as a few invited papers representing significant novel contributions made during the last year. They represent the thrust and vitality of the subject as well as its capacity to identify important basic problems and major application areas. The main methodological problems appear in the underlying queueing theoretic aspects, in the deterministic analysis of waiting time phenomena, in workload characterization and representation, in the algorithmic aspects of model processing, and in the analysis of measurement data. Major areas for applications are computer architectures, data bases, computer networks, and capacity planning. The international importance of the area of computer system performance was well reflected at the symposium by participants from 19 countries. The mixture of participants was also evident in the institutions which they represented: 35% from universities, 25% from governmental research organizations, but also 30% from industry and 10% from non-research government bodies. This proves that the area is reaching a stage of maturity where it can contribute directly to progress in practical problems

Stochastic Approximation and Optimization for Markov Chains

We study the convergence properties of the projected stochasticapproximation (SA) algorithm which may be used to find the root of an unknown steady state function of a parameterized family of Markov chains. The analysis is based on the ODE Method and we develop a set of application-oriented conditions which imply almost sure convergence and are verifiable in terms of typically available model data. Specific results are obtained for geometrically ergodic Markov chains satisfying a uniform Foster-Lyapunov drift inequality.Stochastic optimization is a direct application of the above root finding problem if the SA is driven by a gradient estimate of steady state performance. We study the convergence properties of an SA driven by agradient estimator which observes an increasing number of samples from the Markov chain at each step of the SA's recursion. To show almost sure convergence to the optimizer, a framework of verifiable conditions is introduced which builds on the general SA conditions proposed for the root finding problem.We also consider a difficulty sometimes encountered in applicationswhen selecting the set used in the projection operator of the SA algorithm.Suppose there exists a well-behaved positive recurrent region of the state process parameter space where the convergence conditions are satisfied; this being the ideal set to project on. Unfortunately, the boundaries of this projection set are not known a priori when implementing the SA. Therefore, we consider the convergence properties when the projection set is chosen to include regions outside the well-behaved region. Specifically, we consider an SA applied to an M/M/1 which adjusts the service rate parameter when the projection set includes parameters that cause the queue to be transient.Finally, we consider an alternative SA where the recursion is driven by a sample average of observations. We develop conditions implying convergence for this algorithm which are based on a uniform large deviation upper bound and we present specialized conditions implyingthis property for finite state Markov chains

Energy aware performance evaluation of WSNs

Distributed sensor networks have been discussed for more than 30 years, but the vision of Wireless Sensor Networks (WSNs) has been brought into reality only by the rapid advancements in the areas of sensor design, information technologies, and wireless networks that have paved the way for the proliferation of WSNs. The unique characteristics of sensor networks introduce new challenges, amongst which prolonging the sensor lifetime is the most important. Energy-efficient solutions are required for each aspect of WSN design to deliver the potential advantages of the WSN phenomenon, hence in both existing and future solutions for WSNs, energy efficiency is a grand challenge. The main contribution of this thesis is to present an approach considering the collaborative nature of WSNs and its correlation characteristics, providing a tool which considers issues from physical to application layer together as entities to enable the framework which facilitates the performance evaluation of WSNs. The simulation approach considered provides a clear separation of concerns amongst software architecture of the applications, the hardware configuration and the WSN deployment unlike the existing tools for evaluation. The reuse of models across projects and organizations is also promoted while realistic WSN lifetime estimations and performance evaluations are possible in attempts of improving performance and maximizing the lifetime of the network. In this study, simulations are carried out with careful assumptions for various layers taking into account the real time characteristics of WSN. The sensitivity of WSN systems are mainly due to their fragile nature when energy consumption is considered. The case studies presented demonstrate the importance of various parameters considered in this study. Simulation-based studies are presented, taking into account the realistic settings from each layer of the protocol stack. Physical environment is considered as well. The performance of the layered protocol stack in realistic settings reveals several important interactions between different layers. These interactions are especially important for the design of WSNs in terms of maximizing the lifetime of the network