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Approximate Behavior of Tandem Queues pp 1–42Cite as

General Theory

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Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 171))

Abstract

Most of the literature relating to the analysis of tandem queues (or more general queueing systems) is limited to the rare situation in which a Poisson arrival stream to one service facility generates a Poisson output stream, which, in turn becomes a Poisson arrival stream for other servers. Furthermore, most of this literature is concerned only with equilibrium queue distributions.[1–3]Many attempts have been made to determine stochastic properties of the output process for more general service systems,[4] but the detailed probability structure of the output is usually so complicated that, even if one knew it, one could not make much progress in analysing any subsequent queues for which this might be the input.

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References-Chapter I

  1. R. R. P. Jackson, “Queueing Systems with Phase Type Service,” Operational Res. Q. 5, 109–120 (1954).

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  2. E. Reich, “Waiting Times When Queues Are in Tandem,” Ann. Math. Stat. 28, 768–773 (1957).

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  3. J. R. Jackson, “Networks of Waiting Lines,” Opns. Res. 5, 518–521 (1957).

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  4. D. J. Daley, “Notes on Queueing Output Processes,” Mathematical Methods of Queueing Theory, Lecture Notes in Economics and Mathematical Systems #98, Springer-Verlag, 19 74.

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  5. G. F. Newell, Applications of Queueing Theory, Chapman & Hall, London, 1971.

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  6. G. F. Newell, “Approximate Stochastic Behavior of n-server Service Systems with Large n,” Lecture Notes in Economic and Mathematical Systems #87, Springer-Verlag, 19 73.

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  7. D. R. Cox and H. D. Miller, The Theory of Stochastic Processes, J. Wiley, New York, 1965.

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Authors and Affiliations

  1. Institute of Transportation Studies, University of California, Berkeley, CA, 94720, USA

    Gordon F. Newell

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  1. Gordon F. Newell
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© 1979 Springer-Verlag Berlin Heidelberg

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Newell, G.F. (1979). General Theory. In: Approximate Behavior of Tandem Queues. Lecture Notes in Economics and Mathematical Systems, vol 171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46410-2_1

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  • DOI: https://doi.org/10.1007/978-3-642-46410-2_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09552-1

  • Online ISBN: 978-3-642-46410-2

  • eBook Packages: Springer Book Archive

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