Vaclav E. Benes - General Stochastic Processes in the Theory of Queues

Identifiers: LCCN 2017013597| ISBN 9780486820309 | ISBN 0486820300 Subjects: LCSH: Queuing theory. | Stochastic processes. Classification: LCC QA273 .B45 2017 | DDC 519.8/2dc23 LC record available at https://lccn.loc.gov/2017013597 Manufactured in the United States by LSC Communications
82030001 2017
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In this monograph I attempt such a task for the topic of delays in queueing systems with one server. Delays in queues with one server and order of arrival service are considered without any restrictions on the statistical character of the offered traffic. Elementary methods establish formulas and equations describing probabilities of delay. These methods de-emphasize special statistical models and yield a general theory. In spite of the generality of this approach, intuitive proofs and extensive explanations of the physical significance of formulas are given, as well as rigorous derivations. The theory is applied to specific models to obtain illustrative new results.

Under mild conditions of stationarity, the asymptotic behavior in time of the delay is studied and is shown to be governed by a functional equation closely analogous to the fundamental equation of branching processes, already used in special queueing models. A generalization of the Pollaczek-Khinchin formula is derived for the case in which delays do not build up. So many monographs, surveys, and books on the theory of queues are currently appearing that I have made no effort to canvass the vast extant literature of queueing. References to it have been included only insofar as they arose naturally in the text. For the benefit of the reader, therefore, I cite the following books: J. D. R. Cox and W. L. L.

Smith, Queues. New York: John Wiley and Sons, 1961. T. L. Saaty, Elements of Queueing Theory. New York: McGraw-Hill Book Co., 1961. L. Takcs, Introduction to the Theory of Queues. New York: Oxford University Press, 1962.

I would like to express my gratitude to Bell Telephone Laboratories for providing a milieu in which advanced theoretical work on practical topics can be pursued, and for supplying all the secretarial work involved in completion of the manuscript. Also, it is a pleasure to acknowledge that a careful reading of the manuscript by my colleague E. Wolman resulted in many corrections and improvements. Murray Hill, New Jersey V. E. November 5, 1962.