Palm Probabilities and Stationary Queues (Lecture Notes in Statistics 41)
Baccelli, Francois; Bremaud, Pierre
ISBN 10: 0387965149 ISBN 13: 9780387965147
Published by Springer (edition Softcover reprint of the original 1st ed. 1987), 1987
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The item might be beaten up but readable. May contain markings or highlighting, as well as stains, bent corners, or any other major defect, but the text is not obscured in any way. Softcover reprint of the original 1st ed. 1987. Seller Inventory # 0387965149-7-1
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Part 1 is devoted to a detailed review of the basic results concerning Palm probabilities and useful to Queueing Theory. Part 2 features the queueing formulae of all kinds, the existence of stationary states, and the insensitivity theory.
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Title: Palm Probabilities and Stationary Queues (...
Publisher: Springer (edition Softcover reprint of the original 1st ed. 1987)
Publication Date: 1987
Binding: Paperback
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Tables of Contents.- 1. Stationary point processes and Palm probabilities.- 1. Stationary marked point processes.- 1.1. The canonical space of point processes on IR.- 1.2. Stationary point processes.- 1.3. Stationary marked point processes.- 1.4. Two proper. Seller Inventory # 5912760
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Palm Probabilities and Stationary Queues
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Springer, Springer Apr 1987, 1987
ISBN 10: 0387965149
ISBN 13: 9780387965147
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Taschenbuch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -Tables of Contents.- 1. Stationary point processes and Palm probabilities.- 1. Stationary marked point processes.- 2. Intensity.- 3. Palm probability.- 4. From Palm probability to stationary probability.- 5. Examples.- 6. Local aspects of Palm probability.- 7. Characterization of Poisson processes.- 8. Ergodicity of point processes.- References for Part 1: Palm probabilities.- 2. Stationary queueuing systems.- 1. The G/G/1/ queue : construction of the customer stationary state.- 2. Formulae for the G/G/1/ queue.- 3. The G/G/s/ queue.- 4. The G/G/1/0 queue.- 5. Other queueing systems.- 6. The Bedienungssysteme.- 7. The insensitivity balance equations.- 8. The insensitivity theorem.- 9. Insensitivity balance equations are necessary for insensitivity.- 10. Poisson streams.- References for part 2: Stationary queueing systems.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 120 pp. Englisch. Seller Inventory # 9780387965147
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Palm Probabilities and Stationary Queues (Lecture Notes in Statistics 41)
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Palm Probabilities and Stationary Queues
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Springer New York Apr 1987, 1987
ISBN 10: 0387965149
ISBN 13: 9780387965147
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Tables of Contents.- 1. Stationary point processes and Palm probabilities.- 1. Stationary marked point processes.- 1.1. The canonical space of point processes on IR.- 1.2. Stationary point processes.- 1.3. Stationary marked point processes.- 1.4. Two properties of stationary point processes.- 2. Intensity.- 2.1. Intensity of a stationary point process.- 2.2. Intensity measure of a stationary marked point process.- 3. Palm probability.- 3.1. Mecke¿ s definition.- 3.2. Invariance of the Palm probability.- 3.3. Campbell¿ s formula.- 3.4. The exchange formula (or cycle formula) and Wald¿ s equality.- 4. From Palm probability to stationary probability.- 4.1. The inversion formula.- 4.2. Feller¿ s paradox.- 4.3. The mean value formulae.- 4.4. The inverse construction.- 5. Examples.- 5.1. Palm probability of a superposition of independent point processes.- 5.2. Palm probability associated with selected marks.- 5.3. Palm probability of selected transitions of a Markov chain.- 6. Local aspects of Palm probability.- 6.1. Korolyuk and Dobrushin¿ s infinitesimal estimates.- 6.2. Conditioning at a point.- 7. Characterization of Poisson processes.- 7.1. Predictable -fields.- 7.2. Stochastic intensity and Radon-Nikodym derivatives.- 7.3. Palm view at Watanabe¿ s characterization theorem.- 8. Ergodicity of point processes.- 8.1. Invariant events.- 8.2. Ergodicity under the stationary probability and its Palm probability.- 8.3. The cross ergodic theorem.- References for Part 1: Palm probabilities.- 2. Stationary queueuing systems.- 1. The G/G/1/ queue : construction of the customer stationary state.- 1.1. Loynes¿ problem.- 1.2. Existence of a finite stationary load.- 1.3. Uniqueness of the stationary load.- 1.4. Construction points.- 1.5. Initial workload and long term behaviour.- 2. Formulae for the G/G/1/ queue.- 2.1. Construction of the time-stationary workload.- 2.2. Little¿ s formulae: the FIFO case.- 2.3. Probability of emptiness.- 2.4. Takacs formulae.- 3. The G/G/s/ queue.- 3.1. The ordered workload vector.- 3.2. Existence of a finite stationary workload vector.- 3.3. Construction points.- 3.4. The busy cycle formulae.- 4. The G/G/1/0 queue.- 4.1. Definition and examples.- 4.2. Construction of an enriched probability space.- 4.3. Construction of a stationary solution.- 5. Other queueing systems.- 5.1. The G/G/ pure delay system.- 5.2. The G/G/1/ queue in random environment.- 5.3. Priorities in G/G/1/ : the vector of residual service times.- 5.4. Optimality properties of the SPRT rule.- 6. The Bedienungssysteme.- 6.1. The mechanism and the input.- 6.2. A heuristic description of the dynamics.- 6.3. The initial generalized state.- 6.4. The evolution.- 6.5. Examples.- 7. The insensitivity balance equations.- 7.1. Stability and regularity assumptions.- 7.2. Insensitivity balance equations.- 7.3. Examples.- 7.4. Assumption on the input.- 7.5. Two immediate consequences of the insensitivity balance equations.- 8. The insensitivity theorem.- 8.1. The Palm version.- 8.2. From Palm to stationary.- 8.3. The stationary version and Matthes product form.- 9. Insensitivity balance equations are necessary for insensitivity.- 9.1. The converse theorem.- 9.2. The method of stages.- 9.3. Proof of the converse theorem.- 9.4. Example.- 10. Poisson streams.- 10.1. Privileged transitions.- 10.2. Sufficient conditions for Poissonian streams.- 1. Change of scale.- 2. Proof of insensitivity.- 3. The transition marks.- 4. Proof of (8.3.5).- 5. Proof of (9.1.3).- 6. Proof of the converse theorem in the general case.- References for part 2: Stationary queueing systems. 120 pp. Englisch. Seller Inventory # 9780387965147
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