General Stochastic Processes in the Theory of Queues (eBook)

Vaclav E. Benes (Autor)

eBook Download: EPUB

2017
96 Seiten
Dover Publications (Verlag)
978-0-486-82337-9 (ISBN)

Infos

Mathematicians and engineers will appreciate this general, rigorous presentation of mathematical theory and understandable, practical account of applications. Topics include virtual delay, delay formulas, weak stationarity, weak Markov assumptions. 1963 edition.

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This concise, widely referenced monograph addresses an important topic in queuing theory: delays in queuing systems with one server. The book offers a general, rigorous presentation of mathematical theory in addition to an understandable, practical account of applications. This balanced treatment is suitable for advanced undergraduates and graduate students in applied mathematics, operations research, and electrical engineering as well as professional electrical engineers.The text examines delays in queues with one server and order of arrival service without any restrictions on the statistical character of the offered traffic. Formulas and equations describing probabilities of delay and loss are established by elementary methods. Despite the generality of the approach, intuitive proofs and extensive applications of the physical significance of formulas are given, along with rigorous derivations. The theory is then applied to specific models to obtain illustrative new results.

Autor

Václav E. Beneš is a Czech-American mathematician whose work centers on stochastic processes, queueing theory, and the design of telecommunication switches. He was affiliated with Bell Labs and was on the faculty of Columbia University for many years.

Inhalt

Chapter 1: Virtual Delay1. Introduction2. The system to be studied3. Character of the results to be proven Chapter 2: Delay Formulas: A Direct Approach1. Probabilities of delay2. Proofs of delay formulas3. Example: Poisson arrivals, independent service times4. An elementary probabilistic derivation Chapter 3: Delay Formulas: An Approach Using Transforms1. Summary2. Measurability of W (x)3. A representation ofr exp {-sW(t)}4. General stochastic analogues of Takacs' equation5. A Volterra equation of p(t, 0)6. Probabilites and expectations Chapter 4: Weak Stationarity: Preliminary Results1. The compound Poisson case: a paradigm2. Basic assumptins and notations3. Summary of Chapters 4 and 54. Solution for Pr{W (x) = 0} by transforms5. Preliminary lemmata6. The transform II (x) of Pr{W (x) = 0}7. Asymptotic relationships and characterization of the serive factor p Chapter 5: Weak Stationarity: Convergence Theorems1. Convergence of Pr{W (x) = 0}: Mercerian methods2. Convergence of Pr{W (x) = 0}: Tauberian methods3. Limit theorems for Pr {W (t) [greater than or equal to] w} Chapter 6: Weak Markov Assumptions1. Generalized irrelevance conditions2. A particular irrelevance assumption3. The transform II (x) of Pr {W (x) = 0}4. The distribution of the first zero zReferencesIndex      

Produkt-Details

• Erscheint lt. Verlag: 15.6.2017
• Sprache: englisch
• Maße: 140 x 140 mm
• Gewicht: 132 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Schlagworte: advanced math • applied math • Applied mathematics • applied theory • books about math • Convergenve Theorems • Delay Formulas • describing probabilities • graduate math • intuitive proof • learning math • Markov theory • math and queues • math book • mathematical studies • Mathematical Theory • Mathematics • math equations • math formula • Monograph • Non-fiction • practical application • probability & statistics • Queueing Theory • queues in math • Queuing Systems • queuing theory • signals & signal processing • significant formulas • Stochasic processes. • Stochastic Processes • undergrad math • Virtual delay • Weak Stationarity
• ISBN-10: 0-486-82337-7 / 0486823377
• ISBN-13: 978-0-486-82337-9 / 9780486823379