Introduction to Queuing Theory

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.