Introduction to Queuing Theory Mmo (Mathematical Modeling, 5) - Softcover

Introduction to Queuing Theory

Taschenbuch. Zustand: Neu. Druck auf Anfrage Neuware - Printed after ordering - to the Second Edition.- to the First Edition.- 1. Problems of Queueing Theory under the Simplest Assumptions.- 1.1. Simple Streams.- 1.1.1. Historical Remarks.- 1.1.2. The Notion of a Stream of Homogeneous Events.- 1.1.3. Qualitative Assumptions and Their Analysis.- 1.1.4. Derivation of Equations for Simple Streams.- 1.1.5. Solution of the Equations.- 1.1.6. Derivation of the Additional Assumption from the Other Three Assumptions.- 1.1.7. Distribution of Times of Events of a Stream.- 1.1.8. The Intensity and Parameter of a Stream.- 1.2. Service with Waiting.- 1.2.1. Statement of the Problem.- 1.2.2. The Servicing Process as a Markov Process.- 1.2.3. Construction of Equations.- 1.2.4. Determination of the Stationary Solution.- 1.2.5. Some Preliminary Results.- 1.2.6. The Distribution Function of the Waiting Time.- 1.2.7. The Mean Waiting Time.- 1.2.8. Example.- 1.3. Birth and Death Processes.- 1.3.1. Definition.- 1.3.2. Differential Equations for the Process.- 1.3.3. Proof of Feller¿s Theorem.- 1.3.4. Passive Redundancy without Renewal.- 1.3.5. Active Redundancy without Renewal.- 1.3.6. Existence of Solutions for Birth and Death Equations.- 1.3.7. Backward Equations.- 1.4. Applications of Birth and Death Processes in Queueing Theory.- 1.4.1. Systems with Losses.- 1.4.2. Systems with Limited Waiting Facilities.- 1.4.3. Distribution of the Waiting Time until the Commencement of Service.- 1.4.4. Team Servicing of Machines.- 1.4.5. A Numerical Example.- 1.4.6. Duplicated Systems with Renewal (Passive Redundancy).- 1.4.7. Duplicated Systems with Renewal (Active Redundancy).- 1.4.8. Duplicated Systems with Renewal (Partially Active Redundancy).- 1.5. Priority Service.- 1.5.1. Statement of the Problem.- 1.5.2. Problems with Losses.- 1.5.3. Equations for pij(t).- 1.5.4. A Particular Case.- 1.5.5. The Possibility of Failure of the Servers.- 1.6. General Principles of Constructing Markov Models of Systems.- 1.6.1. Homogeneous Markov Processes.- 1.6.2. Characteristics of Functionals.- 1.6.3. A General Scheme for Constructing Markov Models of Service Systems.- 1.6.4. The HyperErlang Approximation.- 1.7. Systems with Limited Waiting Time.- 1.7.1. Statement of the Problem.- 1.7.2. The Stochastic Process Describing the State of a System for = const.- 1.7.3. System of Integro-differential Equations for the Problem.- 1.7.4. Various Characteristics of Service.- 1.7.5. Distribution of the Queue Length.- 1.7.6. Waiting Time Bounded by a Random Variable.- 1.8. Systems with Bounded Holding Times.- 1.8.1. Statement of the Problem and Assumptions.- 1.8.2. A Stochastic Process Describing the Service.- 1.8.3. Stationary Distributions.- 1.8.4. Holding Time in a System Bounded by a Random Variable.- 2. The Study of the Incoming Customer Stream.- 2.1. Some Examples.- 2.1.1. The Notion of the Incoming Stream.- 2.1.2. Feed of Components from a Hopper.- 2.1.3. A Regular Stream of Customers.- 2.1.4. Streams of Customers Served by Successively Positioned Servers.- 2.1.5. A Wider Approach to the Notion of the Incoming Stream.- 2.1.6. Marked Streams.- 2.2. A Simple Nonstationary Stream.- 2.2.1. Definition of a Simple Nonstationary Stream.- 2.2.2. Equations for the Probabilities pk(t0, t).- 2.2.3. Solution of the System (7).- 2.2.4. Instantaneous Intensity of a Stream.- 2.2.5. Examples.- 2.2.6. The General Form of Poisson Streams without Aftereffects.- 2.2.7. A System with Infinitely Many Servers.- 2.3. A Property of Stationary Streams.- 2.3.1. Existence of the Parameter.- 2.3.2. A Lemma.- 2.3.3. Proof of Khinchin¿s Theorem.- 2.3.4. An Example of a Stationary Stream with Aftereffects.- 2.4. General Form of Stationary Streams without Aftereffects.- 2.4.1. Statement of the Problem.- 2.4.2. The Existence of the Limits $$mathop {lim }limits_{t o 0} frac{{{pi _k}(t)}}{t}$$.- 2.4.3. Equations for the General Stationary Stream without Aftereffects.- 2.4.4. Solution of Systems (3) and (4).- 2.4.5. A Special Case.- 2.4.6. The Generating Function of the Stream.- 2.4.7. Concluding Remarks.- 2.5. The Palm-Khinchin Functions.- 2.5.1. Definition of the Palm-Khinchin Functions.- 2.5.2. Proof of the Existence of the Palm-Khinchin Functions.- 2.5.3. The Palm-Khinchin Formulas.- 2.5.4. Intensity of a Stationary Stream.- 2.5.5. Korolyuk¿s Theorem.- 2.5.6. The Case of Nonorderly Streams.- 2.6. Characteristics of Stationary Streams and the Lebesgue Integral.- 2.6.1. A General Definition of Mathematical Expectation.- 2.6.2. A Refinement of the Notion of Orderliness.- 2.6.3. Existence of the Parameter of a Stream.- 2.6.4. Dobrushin¿s Theorem.- 2.6.5. The Existence of the Palm-Khinchin Function.- 2.6.6. The k-Intensity of a Stream.- 2.7. Basic Renewal Theory.- 2.7.1. Definition of Renewal Processes (Renewal Streams).- 2.7.2. A Property of Renewal Streams.- 2.7.3. Relation to the Palm-Khinchin Functions.- 2.7.4. Definition of the Palm-Khinchin Functions for Stationary Renewal Streams.- 2.7.5. Basic Formulas for Renewal Processes.- 2.7.6. Statements of Some Theorems on Stationary Renewal Processes.- 2.8. Limit Theorems for Compound Streams.- 2.8.1. Statement of the Problem.- 2.8.2. Definitions and Notation.- 2.8.3. Statement of the Basic Result and a Proof of Necessity.- 2.8.4. Proof of Sufficiency.- 2.8.5. The Case of Stationary and Orderly Component Streams.- 2.8.6. Additional Remarks.- 2.9. Direct Probabilistic Methods.- 2.10. Limit Theorem for Thinning Streams.- 2.10.1. Statement of the Problem.- 2.10.2. Laplace Transform of Transformed Streams.- 2.10.3. Some Properties of the T-Operation.- 2.10.4. The Tq-Transformation for a Simple Stream.- 2.10.5. R¿i¿s Limit Theorem.- 2.11. Additional Limit Theorems for Thinning Streams.- 2.11.1. Belyaev¿s Theorem and its Generalizations.- 2.11.2. Rare Events in the Scheme of a Regenerative Process.- 3. Some Classes of Stochastic Processes.- 3.1. Kendall¿s Method: Semi-Markov Processes.- 3.1.1. Semi-Markov Processes and Embedded Markov Chains.- 3.1.2. Some R. Artikel-Nr. 9780817634230

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