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Closed-Form Solution of a LAN Gateway Queueing Model

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Contributions in Mathematics and Engineering

Abstract

In a recent article, an interesting back-to-back queueing model is developed for a gateway linking two LANs. The model ends up with a two-variable functional equation defining the two-dimensional probability generating function (PGF) of the distribution of the gateway occupancy. Unfortunately, however, the article leaves the equation unsolved, citing the traditional difficulty to attack such equations mathematically. In this chapter, we manage to solve the functional equation for the unknown PGF, utilizing to a great extent the knowledge of the physical properties of the underlying gateway. The closed-form solution obtained for the PGF is validated in several ways, both mathematical and physical. Furthermore, we derive expectations for the gateway occupancy and also validate them both mathematically and physically.

In Honor of Constantin Carathéodory

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Author information

Authors and Affiliations

  1. Computer Science Department, Faculty of Computers and Informatics, Suez Canal University, Ismailia, Egypt

    Hamed Nassar

  2. Innsbruck University, Innsbruck, Austria

    El-Sayed El-Hady

  3. Basic Science Department, Faculty of Computers and Informatics, Suez Canal University, Ismailia, Egypt

    El-Sayed El-Hady

Authors
  1. Hamed Nassar
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  2. El-Sayed El-Hady
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Correspondence to El-Sayed El-Hady .

Editor information

Editors and Affiliations

  1. Industrial and Systems Engineering, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

  2. Department of Mathematics, National Technical Unversity of Athens Department of Mathematics, Athens, Greece

    Themistocles M. Rassias

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Nassar, H., El-Hady, ES. (2016). Closed-Form Solution of a LAN Gateway Queueing Model. In: Pardalos, P., Rassias, T. (eds) Contributions in Mathematics and Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-31317-7_20

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