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
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245 0 0 |a Stochastic Processes in Queueing Theory  |h Elektronische Ressource  |c by Alexandr Borovkov 
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505 0 |a § 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 --  
505 0 |a § 19. Methods of Finding the Distribution of 
505 0 |a § 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 --  
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520 |a 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 accordance with this fact, the exposition of the subject can be broken up into two self-contained parts. The first of these forms the content of this monograph. . The definition of the queueing processes (systems) to be used here is dose to the traditional one and is connected with the introduction of so-called governing random sequences. We will introduce algorithms which describe the governing of a system with the aid of such sequences. Such a definition inevitably becomes rather qualitative since under these conditions a completely formal construction of a stochastic process uniquely describing the evolution of the system would require introduction of a complicated phase space not to mention the difficulties of giving the distribution of such a process on this phase space