The aim of this book is the development of the heavy traffic approach to the modeling and analysis of queueing networks, both controlled and uncontrolled, and many applications to computer, communications, and manufacturing systems. The methods exploit the multiscale structure of the physical problem to get approximating models that have the form of reflected diffusion processes, either controlled or uncontrolled. These ap- proximating models have the basic structure of the original problem, but are significantly simpler. Much of inessential detail is eliminated (or "av- eraged out"). They...

Stochastic portfolio theory is a mathematical methodology for constructing stock portfolios, analyzing the behavior of portfolios, and understanding the structure of equity markets. Stochastic portfolio theory has both theoretical and practical applications: as a theoretical tool it can be used to construct examples of theoretical portfolios with specified characteristics, and to determine the distributional component of portfolio return. On a practical level, stochastic portfolio theory has been the basis for strategies used for over a decade by the institutional equity manager INTECH, where...

This book discusses the building blocks of electronic circuits - the microchips, transistors, resistors, condensers, and so forth, and the boards that support them - from the point of view of mechanics: What are the stresses that result from thermal expansion and contraction? What are the elastic parameters that determine whether a component will survive a certain acceleration? After an introduction to the elements of structural analysis and finite-element analysis, the author turns to components, data and testing. A discussion of leadless chip carriers leads to a detailed thermal analysis of...

This is a revised and expanded version of the earlier edition. The new material is on Markov-modulated storage processes arising from queueing and data commu- nication models. The analysis of these models is based on the fluctuation theory of Markov-additive processes and their discrete time analogues, Markov random walks. The workload and queue length processes, omitted from the earlier edition, are also presented. In addition, many sections have been rewritten, with new re- sults and proofs, as well as further examples. The mathematical level and style of presentation, however, remain the...

This book presents the second part of a two-volume series devoted to a sys- tematic exposition of some recent developments in the theory of discrete- time Markov control processes (MCPs). As in the first part, hereafter re- ferred to as "Volume I" (see Hernandez-Lerma and Lasserre 1]), interest is mainly confined to MCPs with Borel state and control spaces, and possibly unbounded costs. However, an important feature of the present volume is that it is essentially self-contained and can be read independently of Volume I. The reason for this independence is that even though both volumes deal...

As is well known, Pontryagin's maximum principle and Bellman's dynamic programming are the two principal and most commonly used approaches in solving stochastic optimal control problems. * An interesting phenomenon one can observe from the literature is that these two approaches have been developed separately and independently. Since both methods are used to investigate the same problems, a natural question one will ask is the fol- lowing: (Q) What is the relationship betwccn the maximum principlc and dy- namic programming in stochastic optimal controls? There did exist some researches (prior...

In a stochastic network, such as those in computer/telecommunications and manufacturing, discrete units move among a network of stations where they are processed or served. Randomness may occur in the servicing and routing of units, and there may be queueing for services. This book describes several basic stochastic network processes, beginning with Jackson networks and ending with spatial queueing systems in which units, such as cellular phones, move in a space or region where they are served. The focus is on network processes that have tractable (closed-form) expressions for the equilibrium...

Both in insurance and in finance applications, questions involving extremal events (such as large insurance claims, large fluctuations in financial data, stock market shocks, risk management, ...) play an increasingly important role. This book sets out to bridge the gap between the existing theory and practical applications both from a probabilistic as well as from a statistical point of view. Whatever new theory is presented is always motivated by relevant real-life examples. The numerous illustrations and examples, and the extensive bibliography make this book an ideal reference text for...

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clas- sical techniques of applied mathematics. This renewal of interest, both in research and teaching, had led to the establishment of the series: Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems,...

Stochastic control theory is a relatively young branch of mathematics. The beginning of its intensive development falls in the late 1950s and early 1960s. During that period an extensive literature appeared on optimal stochastic control using the quadratic performance criterion (see references in W onham 76J). At the same time, Girsanov 25J and Howard 26J made the first steps in constructing a general theory, based on Bellman's technique of dynamic programming, developed by him somewhat earlier 4J. Two types of engineering problems engendered two different parts of stochastic control...