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