1. Classifications. Some Notation. - 1. Systems with Queues and Service of Type One. - 2. Cases in Which the Systems G Can be Described by Means of Recursion Equations. Equivalence to the System G G G 1. - 3. The Basic Equation. Properties of the Solution as a Process. Ergodic Theorems. - 4. Interrupted Governing Sequences. - 5. On Systems Governed by Sequences of Independent Random Variables. - 6. The Virtual Waiting Time. A Continuous Analogue of the System Equation. Properties of the Solution. - 7. Further Properties of the Process w(t). Beneš' Equation. - 8. The Stationary Solution of Beneš' Equation. Approximation Formulae for Heavy and Light Traffic. - 9. The Processes X(t) and Y(t) with Stationary Increments Corresponding to Governing Sequences with Independent Terms. The Connection between the Distributions of wc(t) and wk. - 10. Estimates of the Rate of Convergence of the Distributions of wn and w(t) to Stationarity. Connection with the Queue Length. - 11. Theorems on the Stability of the Stationary Waiting Time under a Change of the Governing Sequences. - 2. Some Boundary Problems for Processes Continuous from below with Independent Increments. Their Connection with the Distribution of w(t). - 12. Boundary Problems for Processes Continuous from below with Independent Increments. - 13. Properties of the Distribution of w(t). The Busy Period. - 14. Discrete Time. - 3. Boundary Problems for Sequences with Independent Increments and Factorization Identities. - 15. Preliminary Remarks. - 16. The First Factorization Identity and Its Consequences. - 17. The Second Factorization Identity and Its Consequences. - 4. Properties of the Supremum of Sums of Independent Random Variables and Related Problems of QueueingTheory. - 18. Uniqueness Theorems. - 19. Methods of Finding the Distribution of $$\bar{Y}$$. - 20. Explicit Formulae for the Distribution of $$\bar{Y}$$ under the Conditions of Queueing Theory. - 21. Stability Theorems. The Rate of Convergence. - 22. Asymptotic Properties of the Distributions of $$\bar{Y}$$ and ?. - 23. Inequalities for the Distributions of $$\bar{Y}_n$$ and $$\bar{Y}$$. The Rate of Approach of the Distributions of wn and w1. - 24. Comparison Theorems. - 25. Conditions for Heavy Traffic. Transitional Phenomena. - 26. The Relation between the Waiting Time and Queue Length Distributions. - 5. Multi-Channel Queueing Systems. - 27. Classes of Systems Which Can Be Described by Recursion Equations. Existence Theorems for a Stationary Solution in the Systems G GG/m 1. The Relation between the Waiting Time and the Queue Length. - 28. The Systems GI GIGI/m 1. Stability Theorems. Connection between the Waiting Time and Queue Length. Estimates of Rates of Convergence. - 29. The Systems GI 1 E/m 1 and E GI GI/m 1. - 6. The Systems G G G/? 1) with an Infinite Number of Service Channels. - 30. Theorems on Convergence to Stationary Processes. - 31. Stability Theorems. - 32. The Systems GI G GI/? 1. - 33. The Systems E 1 GI/? 1. - 34. The Systems G 1 EI/? 1. - 7. Systems with Refusals. - 35. The Systems G G G/m 1R. General Theorems. - 36. Stability Theorems. - 37. The Systems GI 1 GI/m 1R. - 38. The Systems GI GI E/m GIR. - 39. The Systems GR. - 40. Asymptotic Analysis of Multi-Channel Systems. - 8. Systems with Autonomous Service. - 41. General Properties. - 42. Methods of Calculating the StationaryDistributions. - Appendices. - Appendix 1. Some Theorems from Renewal Theory. - Appendix 3. The Wiener-Lévy Theorems and the Asymptotic Behavior of the Coefficients of Absolutely Convergent Series. - Appendix 4. Estimates for the Distributions of Sums of Independent Random Variables. - List of Basic Notation. - Bibliographical Notes. - Author Index. Language: English