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Closed-Form Solution of a LAN Gateway Queueing Model

In: Contributions in Mathematics and Engineering

Author

Listed:
  • Hamed Nassar

    (Suez Canal University, Computer Science Department, Faculty of Computers and Informatics)

  • El-Sayed El-Hady

    (Innsbruck University
    Suez Canal University, Basic Science Department, Faculty of Computers and Informatics)

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.

Suggested Citation

  • Hamed Nassar & El-Sayed El-Hady, 2016. "Closed-Form Solution of a LAN Gateway Queueing Model," Springer Books, in: Panos M. Pardalos & Themistocles M. Rassias (ed.), Contributions in Mathematics and Engineering, pages 393-427, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-31317-7_20
    DOI: 10.1007/978-3-319-31317-7_20
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