Stochastic Processes in Queueing Theory

The object of queueing theory (or the theory of mass service) is the investigation of stochastic processes of a special form which are called queueing (or service) processes in this book. Two approaches to the definition of these processes are possible depending on the direction of investigation. In...

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Bibliographic Details
Main Author: Borovkov, Alexandr
Format: eBook
Language:English
Published: New York, NY Springer New York 1976, 1976
Edition:1st ed. 1976
Series:Stochastic Modelling and Applied Probability
Subjects:
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • § 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
  • § 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