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.