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ANALYSIS OF FINITE OSCILLATING GIX/M(m)//N QUEUEING SYSTEMS

In: Recent Advances In Stochastic Operations Research II

Author

Listed:
  • FÁTIMA FERREIRA

    (Department of Mathematics and CEMAT, University of Trás-os-Montes e Alto Douro, Quinta dos Prados, 5001-911 Vila Real, Portugal)

  • ANTÓNIO PACHECO

    (Department of Mathematics and CEMAT, Instituto Superior Técnico, Technical University of Lisbon, Av. Rovisco Pais, 1049-001 Lisboa, Portugal)

  • HELENA RIBEIRO

    (Department of Mathematics and CEMAT, School of Technology and Management, Polytechnic Institute of Leiria, Campus 2, Morro do Lena - Alto do Vieiro, 2411-901 Leiria, Portugal)

Abstract

In this work we investigate oscillating GIX/M(m)//N systems, which are queueing systems whose service mechanism reacts to the congestion of the system; namely, the service rates oscillate between two forms according to the evolution of the number of customers in the system. Resorting to Markov chain embedding, we address the time-dependent and limit analysis of the number of customers in the system at batch prearrivals and seen by customers at their arrival to the system. These results are then used to derive the continuous-time limit distribution of the number of customers in the system. In addition, we provide some numerical examples that illustrate our approach.

Suggested Citation

  • Fátima Ferreira & António Pacheco & Helena Ribeiro, 2009. "ANALYSIS OF FINITE OSCILLATING GIX/M(m)//N QUEUEING SYSTEMS," World Scientific Book Chapters, in: Tadashi Dohi & Shunji Osaki & Katsushige Sawaki (ed.), Recent Advances In Stochastic Operations Research II, chapter 7, pages 79-98, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812791672_0007
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