Introduction to Queuing Theory [electronic resource] /

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.