Author | Borovkov, A. A. author |
---|---|
Title | Stochastic Processes in Queueing Theory [electronic resource] / by A. A. Borovkov |
Imprint | New York, NY : Springer New York, 1976 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-9866-3 |
Descript | XI, 280 p. online resource |
ยง 1. Classifications. Some Notation -- 1. Systems with Queues and Service of Type One -- ยง 2. Cases in Which the Systems โนGโบ Can be Described by Means of Recursion Equations. Equivalence to the System โนG, G, G, 1โบ -- ยง 3. The Basic Equation. Properties of the Solution as a Process. Ergodic Theorems -- ยง 4. Interrupted Governing Sequences -- ยง 5. On Systems Governed by Sequences of Independent Random Variables -- ยง 6. The Virtual Waiting Time. A Continuous Analogue of the System Equation. Properties of the Solution -- ยง 7. Further Properties of the Process w(t). Beneลกโ Equation -- ยง 8. The Stationary Solution of Beneลกโ Equation. Approximation Formulae for Heavy and Light Traffic -- ยง 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 -- ยง 10. Estimates of the Rate of Convergence of the Distributions of wn and w(t) to Stationarity. Connection with the Queue Length -- ยง 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) -- ยง 12. Boundary Problems for Processes Continuous from below with Independent Increments -- ยง 13. Properties of the Distribution of w(t). The Busy Period -- ยง 14. Discrete Time -- 3. Boundary Problems for Sequences with Independent Increments and Factorization Identities -- ยง 15. Preliminary Remarks -- ยง 16. The First Factorization Identity and Its Consequences -- ยง 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 -- ยง 18. Uniqueness Theorems -- ยง 19. Methods of Finding the Distribution of $$\bar{Y}$$ -- ยง 20. Explicit Formulae for the Distribution of $$\bar{Y}$$ under the Conditions of Queueing Theory -- ยง 21. Stability Theorems. The Rate of Convergence -- ยง 22. Asymptotic Properties of the Distributions of $$\bar{Y}$$ and ? -- ยง 23. Inequalities for the Distributions of $$\bar{Y}_n$$ and $$\bar{Y}$$. The Rate of Approach of the Distributions of wn and w1 -- ยง 24. Comparison Theorems -- ยง 25. Conditions for Heavy Traffic. Transitional Phenomena -- ยง 26. The Relation between the Waiting Time and Queue Length Distributions -- 5. Multi-Channel Queueing Systems -- ยง 27. Classes of Systems Which Can Be Described by Recursion Equations. Existence Theorems for a Stationary Solution in the Systems โนG, G,G/m, 1โบ. The Relation between the Waiting Time and the Queue Length -- ยง 28. The Systems โนGI, GIGI/m, 1โบ. Stability Theorems. Connection between the Waiting Time and Queue Length. Estimates of Rates of Convergence -- ยง 29. The Systems โนGI 1, E/m, 1โบ and โนE, GI, GI/m, 1โบ -- 6. The Systems โนG, G, G/?, 1) with an Infinite Number of Service Channels -- ยง 30. Theorems on Convergence to Stationary Processes -- ยง 31. Stability Theorems -- ยง 32. The Systems โน GI, G, GI/?, 1โบ -- ยง 33. The Systems โนE, 1, GI/?, 1โบ -- ยง 34. The Systems โนGโ 1, EI/?, 1โบ -- 7. Systems with Refusals -- ยง 35. The Systems โนG, G, G/m, 1โบR. General Theorems -- ยง 36. Stability Theorems -- ยง 37. The Systems โนGI, 1, GI/m, 1โบR -- ยง 38. The Systems โนGI GI, E/m, GIโบR -- ยง 39. The Systems โนGโบR -- ยง 40. Asymptotic Analysis of Multi-Channel Systems -- 8. Systems with Autonomous Service -- ยง 41. General Properties -- ยง 42. Methods of Calculating the Stationary Distributions -- Appendices -- Appendix 1. Some Theorems from Renewal Theory -- Appendix 3. The Wiener-Lรฉvy 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