Continuous-time Markov chains and applications a two-time-scale approach G. George Yin, Qing Zhang

Format:

Book

Author/Creator:

Yin, George, 1954-

Contributor:

Zhang, Qing, 1959-

Series:

Stochastic modelling and applied probability 37

Stochastic modelling and applied probability 0172-4568 37

Language:

English

Subjects (All):

Markov processes.

Perturbation (Mathematics).

Physical Description:

1 online resource

Edition:

2nd ed.

Place of Publication:

New York Springer 2013

Summary:

This book gives a systematic treatment of singularly perturbed systems that naturally arise in control and optimization, queueing networks, manufacturing systems, and financial engineering. It presents results on asymptotic expansions of solutions of Komogorov forward and backward equations, properties of functional occupation measures, exponential upper bounds, and functional limit results for Markov chains with weak and strong interactions. To bridge the gap between theory and applications, a large portion of the book is devoted to applications in controlled dynamic systems, production planning, and numerical methods for controlled Markovian systems with large-scale and complex structures in the real-world problems. This second edition has been updated throughout and includes two new chapters on asymptotic expansions of solutions for backward equations and hybrid LQG problems. The chapters on analytic and probabilistic properties of two-time-scale Markov chains have been almost completely rewritten and the notation has been streamlined and simplified. This book is written for applied mathematicians, engineers, operations researchers, and applied scientists. Selected material from the book can also be used for a one semester advanced graduate-level course in applied probability and stochastic processes

Contents:

Querying Moving Objects Detected by Sensor Networks

1 Introduction

2 Applications for MOSD

2.1 Application Example 1: Surveillance

2.2 Application Example 2: Animal Tracking

2.3 Scope and Assumptions

3 Background

3.1 Detection Mechanisms

3.2 Moving Object Databases

3.3 Query Processing in Sensor Networks

4 Generic Model of a Sensor Network

5 Point Set Topology for Sensor Networks

6 Deriving Predicate Results

6.1 Detection Scenarios

6.2 Predicate Results for Regions

6.3 Predicate Results for Zones

6.4 Summary.

7 Spatio-Temporal Developments

7.1 Irregularity of Zones and Concatenation

7.2 A Canonical Collection of Spatio-Temporal Developments

7.3 Formal Description of Object Detection Sequences

7.4 Detection Terms

8 Spatio-Temporal Query Processing in SN.

8.1 Data Structures and Algorithms

8.2 Computing Detection Scenarios

8.3 Centralized data collection.

8.4 Distributed data collection

8.5 Impact of Node Failures

9 Evaluation

9.1 Simulation Configuration

9.2 Simulation Results

9.3 Sun SPOT Case Study

10 Conclusions References Energy-Consumption in Sensor Networks

A.1 Experimental Setup

A.2 Results and Analysis

A.2.1 Impact of Communication on node lifetime

A.2.2 Energy consumption of sending and receiving

A.2.3 Impact of energy-aware MAC protocols

A.3 Lessons Learned

Part 1. Prologue and Preliminaries Introduction and Overview Mathematical Preliminaries Markovian Models

Part 2. Two-Time-Scale Markov Chains Asymptotic Expansions of Solutions for Forward Equations Occupation Measures: Asymptotic Properties and Ramification Asymptotic Expansions of Solutions for Backward Equations

Part 3. Applications: MDPs, Near-optimal Controls, Numerical Methods, and LQG with Switching Markov Decision Problems Stochastic Control of Dynamical Systems Numerical Methods for Control and Optimization Hybrid LQG Problems

Notes:

Includes bibliographical references and index

Other Format:

Print version Yin, George, 1954- Continuous-time Markov chains and applications.

ISBN:

9781461443469

1461443466

1461443458

9781461443452

OCLC:

821030935

Publisher Number:

10.1007/978-1-4614-4346-9

Access Restriction:

Restricted for use by site license