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Some Problems in Finite Queues

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Mathematical Methods in Queueing Theory

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 98))

Abstract

In this paper computationally convenient analytic methods are developed for the analysis of two classes of finite queueing systems with (1) arrivals with Poisson properties, general state dependent service time distribution and a single server and (2) general state dependent inter-arrival times, exponential service times and s(≥ 1) servers.

Research supported by NSF grant GK-19537.

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References

  1. U. Narayan Bhat and Richard E. Nance (1971), “Busy Period Analysis of a Time-Sharing System Modeled as a Semi-Markov Process” Jour. ACM, Vol. 18, (2), 221–238.

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  2. Kemeny, J. G. and Snell, J. L. (1960). Finite Markov Chains, Princeton, N. J.: D. Van Nostrand.

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  3. Richard E. Nance, U. Narayan Bhat, and Billey G. Claybrook (1972), “Busy Period Analysis of a Time-Sharing System: Transform Inversion”, Jour. ACM Vol. 19 (3), 453–463.

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  4. R. A Pyke (1961a), “Markov Renewal Processes: Definitions and Preliminary Properties”; Ann. Math. Statist. 32, 1231–1242.

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  5. R. A. Pyke (1961b), “Markov Renewal Processes with Finitely Many States,” Ann. Math. Statist. 32, 1243–1259.

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  6. John Riordan (1962), Stochastic Service Systems, New York: John Wiley and Sons, Inc.

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  7. Lajos Takâcs (1962), Introduction to the Theory of Queues, New York: Oxford University Press.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Operations Research, Southern Methodist University, USA

    U. Narayan Bhat

Authors
  1. U. Narayan Bhat
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Western Michigan University, 49001, Kalamazoo, MI, USA

    A. Bruce Clarke

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© 1974 Springer-Verlag Berlin · Heidelberg

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Bhat, U.N. (1974). Some Problems in Finite Queues. In: Clarke, A.B. (eds) Mathematical Methods in Queueing Theory. Lecture Notes in Economics and Mathematical Systems, vol 98. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80838-8_8

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  • DOI: https://doi.org/10.1007/978-3-642-80838-8_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06763-4

  • Online ISBN: 978-3-642-80838-8

  • eBook Packages: Springer Book Archive

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