Introduction to Queuing Theory

Inhaltsverzeichnis

• 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.
• 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.