An Elementary Introduction To Queueing Systems
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An Elementary Introduction To Queueing Systems
The book aims to highlight the fundamental concepts of queueing systems. It starts with the mathematical modeling of the arrival process (input) of customers to the system. It is shown that the arrival process can be described mathematically either by the number of arrival customers in a fixed time interval, or by the interarrival time between two consecutive arrivals. In the analysis of queueing systems, the book emphasizes the importance of exponential service time of customers. With this assumption of exponential service time, the analysis can be simplified by using the birth and death process as a model. Many queueing systems can then be analyzed by choosing the proper arrival rate and service rate. This facilitates the analysis of many queueing systems.Drawing on the author's 30 years of experience in teaching and research, the book uses a simple yet effective model of thinking to illustrate the fundamental principles and rationale behind complex mathematical concepts. Explanations of key concepts are provided, while avoiding unnecessary details or extensive mathematical formulas. As a result, the text is easy to read and understand for students wishing to master the core principles of queueing theory.
Sample-Path Analysis of Queueing Systems
Author: Muhammad El-Taha
language: en
Publisher: Springer Science & Business Media
Release Date: 1999
Sample-Path Analysis of Queueing Systems uses a deterministic (sample-path) approach to analyze stochastic systems, primarily queueing systems and more general input-output systems. Among other topics of interest it deals with establishing fundamental relations between asymptotic frequencies and averages, pathwise stability, and insensitivity. These results are utilized to establish useful performance measures. The intuitive deterministic approach of this book will give researchers, teachers, practitioners, and students better insights into many results in queueing theory. The simplicity and intuitive appeal of the arguments will make these results more accessible, with no sacrifice of mathematical rigor. Recent topics such as pathwise stability are also covered in this context. The book consistently takes the point of view of focusing on one sample path of a stochastic process. Hence, it is devoted to providing pure sample-path arguments. With this approach it is possible to separate the issue of the validity of a relationship from issues of existence of limits and/or construction of stationary framework. Generally, in many cases of interest in queueing theory, relations hold, assuming limits exist, and the proofs are elementary and intuitive. In other cases, proofs of the existence of limits will require the heavy machinery of stochastic processes. The authors feel that sample-path analysis can be best used to provide general results that are independent of stochastic assumptions, complemented by use of probabilistic arguments to carry out a more detailed analysis. This book focuses on the first part of the picture. It does however, provide numerous examples that invoke stochastic assumptions, which typically are presented at the ends of the chapters.
Queueing Theory with Applications to Packet Telecommunication
Author: John N. Daigle
language: en
Publisher: Springer Science & Business Media
Release Date: 2005
Queueing Theory with Applications to Packet Telecommunication is an efficient introduction to fundamental concepts and principles underlying the behavior of queueing systems and its application to the design of packet-oriented electrical communication systems. In addition to techniques and approaches found in earlier works, the author presents a thoroughly modern computational approach based on Schur decomposition. This approach facilitates solution of broad classes of problems wherein a number of practical modeling issues may be explored. Key features of communication systems, such as correlation in packet arrival processes at IP switches and variability in service rates due to fading wireless links are introduced. Numerous exercises embedded within the text and problems at the end of certain chapters that integrate lessons learned across multiple sections are also included. In all cases, including systems having priority, developments lead to procedures or formulae that yield numerical results from which sensitivity of queueing behavior to parameter variation can be explored. In several cases multiple approaches to computing distributions are presented. Queueing Theory with Applications to Packet Telecommunication is intended both for self study and for use as a primary text in graduate courses in queueing theory in electrical engineering, computer science, operations research, and mathematics. Professionals will also find this work invaluable because the author discusses applications such as statistical multiplexing, IP switch design, and wireless communication systems. In addition, numerous modeling issues, such as the suitability of Erlang-k and Pade approximations are addressed.