Brownian Models Of Performance And Control

Direct and to the point, this book from one of the field's leaders covers Brownian motion and stochastic calculus at the graduate level, and illustrates the use of that theory in various application domains, emphasizing business and economics. The mathematical development is narrowly focused and briskly paced, with many concrete calculations and a minimum of abstract notation. The applications discussed include: the role of reflected Brownian motion as a storage model, queuing model, or inventory model; optimal stopping problems for Brownian motion, including the influential McDonald-Siegel investment model; optimal control of Brownian motion via barrier policies, including optimal control of Brownian storage systems; and Brownian models of dynamic inference, also called Brownian learning models or Brownian filtering models.

Direct and to the point, this book from one of the field's leaders covers Brownian motion and stochastic calculus at the graduate level, and illustrates the use of that theory in various application domains, emphasizing business and economics. The mathematical development is narrowly focused and briskly paced, with many concrete calculations and a minimum of abstract notation. The applications discussed include: the role of reflected Brownian motion as a storage model, queuing model, or inventory model; optimal stopping problems for Brownian motion, including the influential McDonald–Siegel investment model; optimal control of Brownian motion via barrier policies, including optimal control of Brownian storage systems; and Brownian models of dynamic inference, also called Brownian learning models or Brownian filtering models.

This state-of-the-art account unifies material developed in journal articles over the last 35 years, with two central thrusts: It describes a broad class of system models that the authors call 'stochastic processing networks' (SPNs), which include queueing networks and bandwidth sharing networks as prominent special cases; and in that context it explains and illustrates a method for stability analysis based on fluid models. The central mathematical result is a theorem that can be paraphrased as follows: If the fluid model derived from an SPN is stable, then the SPN itself is stable. Two topics discussed in detail are (a) the derivation of fluid models by means of fluid limit analysis, and (b) stability analysis for fluid models using Lyapunov functions. With regard to applications, there are chapters devoted to max-weight and back-pressure control, proportionally fair resource allocation, data center operations, and flow management in packet networks. Geared toward researchers and graduate students in engineering and applied mathematics, especially in electrical engineering and computer science, this compact text gives readers full command of the methods.

Here is a systematic discussion of Brownian motion and Ito stochastic calculus. Develops the mathematical methods needed to analyze stochastic processes related to Brownian motion and shows how these methods are used to model and analyze various stochastic flow systems such as queueing and inventory systems. Emphasizes stochastic calculus and models used in engineering, economics, and operations research. Topics include stochastic models of buffered flow, the backward and forward equations, hitting time problems, regulated Brownian motion, optimal control of Brownian motion, and optimizing flow system performance.

A graduate text on theory and methods using applied probability techniques for scheduling service, manufacturing, and information networks.

This volume consists of the proceedings of the Workshop on Analysis and Simulation of Communication Networks held at The Fields Institute (Toronto). The workshop was divided into two main themes, entitled "Stability and Load Balancing of a Network of Call Centres" and "Traffic and Performance". The call centre industry is large and fast-growing. In order to provide top-notch customer service, it needs good mathematical models. The first part of the volume focuses on probabilistic issues involved in optimizing the performance of a call centre. While this was the motivating application, many of the papers are also applicable to more general distributed queueing networks. The second part of the volume discusses the characterization of traffic streams and how to estimate their impact on the performance of a queueing system. The performance of queues under worst-case traffic flows or flows with long bursts is treated. These studies are motivated by questions about buffer dimensioning and call admission control in ATM or IP networks. This volume will serve researchers as a comprehensive, state-of-the-art reference source on developments in this rapidly expanding field.

This books covers the broad range of research in stochastic models and optimization. Applications presented include networks, financial engineering, production planning, and supply chain management. Each contribution is aimed at graduate students working in operations research, probability, and statistics.

This book constitutes the refereed proceedings of the Third European Performance Engineering Workshop, EPEW 2006, held in Budapest, Hungary in June 2006. The 16 revised full papers presented were carefully reviewed and selected from 40 submissions. The papers are organized in topical sections on stochastic process algebra, workloads and benchmarks, theory of stochastic processes, formal dependability and performance evaluation, as well as queues, theory and practice.