General Stochastic Processes in the Theory of Queues (eBook)

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.

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