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Introduction to Queuing Theory

Bibliographic Details
Main Author: GNEDENKO.
Format: eBook
Language:English
Published: Boston, MA Birkhäuser 1989, 1989
Edition:2nd ed. 1989
Series:Mathematical Modeling
Subjects:
Artificial Intelligence / Data Processing
Algorithms
Computational Mathematics And Numerical Analysis
Mathematics / Data Processing
Computational Science And Engineering
Data Science
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 6.1. Principles of the Monte Carlo Method
  • 6.2. Simulation of Some Classes of Random Processes
  • 6.3. Statistical Problems Associated with Simulation
  • 6.4. Simulation of Queueing Systems
  • 6.5. Calculation of Corrections to Characteristics of Systems
  • to the Second Edition
  • to the First Edition
  • 1. Problems of Queueing Theory under the Simplest Assumptions
  • 1.1. Simple Streams
  • 1.2. Service with Waiting
  • 1.3. Birth and Death Processes
  • 1.4. Applications of Birth and Death Processes in Queueing Theory
  • 1.5. Priority Service
  • 1.6. General Principles of Constructing Markov Models of Systems
  • 1.7. Systems with Limited Waiting Time
  • 1.8. Systems with Bounded Holding Times
  • 2. The Study of the Incoming Customer Stream
  • 2.1. Some Examples
  • 2.2. A Simple Nonstationary Stream
  • 2.3. A Property of Stationary Streams
  • 2.4. General Form of Stationary Streams without Aftereffects
  • 2.5. The Palm-Khinchin Functions
  • 2.6. Characteristics of Stationary Streams and the Lebesgue Integral
  • 2.7. Basic Renewal Theory
  • 2.8. Limit Theorems for Compound Streams
  • 2.9. Direct Probabilistic Methods
  • 2.10. Limit Theorem for Thinning Streams
  • 2.11. Additional Limit Theorems for Thinning Streams
  • 3. Some Classes of Stochastic Processes
  • 3.1. Kendall’s Method: Semi-Markov Processes
  • 3.2. Linear-Type Markov Processes
  • 3.3. Piecewise-Linear Markov Processes
  • 3.4. Other Important Classes of Random Processes
  • 4. Semi-Markov Models of Queueing Systems
  • 4.1. Classification of Queueing Systems
  • 4.2. M?G?1 System
  • 4.3. Nonstationary Characteristics of an M/G/1 System
  • 4.4. A System of the GI?M?m Type
  • 4.5. M/G/1 System with an Unreliable and “Renewable” Server
  • 4.6. Mixed Service Systems
  • 4.7. Systems with Restrictions
  • 4.8. Priority Service
  • 4.9. The Generalized Scheme of Priority Service with a Limited Queue
  • 5. Application of More General Methods
  • 5.1. The GI?G?1 System
  • 5.2. GI?G?m Systems
  • 5.3. The M?G?m?0 System
  • 5.4. More Complex Systems with Losses
  • 5.5. Ergodic Theorems
  • 5.6.Heavily Loaded Queueing Systems
  • 5.7. Underloaded Queueing Systems
  • 5.8. Little’s Theory and its Corollaries
  • 6. Statistical Simulation of Systems

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