Autorentext
Václav E. Bene? 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.
Klappentext
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.
Dover (2017) republication of the edition originally published by the Addison-Wesley Publishing Company, Reading, Massachusetts, 1963.
www.doverpublications.com
Inhalt
Chapter 1: Virtual Delay
1. Introduction
2. The system to be studied
3. Character of the results to be proven
Chapter 2: Delay Formulas: A Direct Approach
1. Probabilities of delay
2. Proofs of delay formulas
3. Example: Poisson arrivals, independent service times
4. An elementary probabilistic derivation
Chapter 3: Delay Formulas: An Approach Using Transforms
1. Summary
2. Measurability of W (x)
3. A representation ofr exp {-sW(t)}
4. General stochastic analogues of Takacs' equation
5. A Volterra equation of p(t, 0)
6. Probabilites and expectations
Chapter 4: Weak Stationarity: Preliminary Results
1. The compound Poisson case: a paradigm
2. Basic assumptins and notations
3. Summary of Chapters 4 and 5
4. Solution for Pr{W (x) = 0} by transforms
5. Preliminary lemmata
6. The transform II (x) of Pr{W (x) = 0}
7. Asymptotic relationships and characterization of the serive factor p
Chapter 5: Weak Stationarity: Convergence Theorems
1. Convergence of Pr{W (x) = 0}: Mercerian methods
2. Convergence of Pr{W (x) = 0}: Tauberian methods
3. Limit theorems for Pr {W (t) [greater than or equal to] w}
Chapter 6: Weak Markov Assumptions
1. Generalized irrelevance conditions
2. A particular irrelevance assumption
3. The transform II (x) of Pr {W (x) = 0}
4. The distribution of the first zero z
References
Index
