Queue with limited volume, a diffusion approximation approach

  • Tadeusz Czachórski
  • Tomasz Nycz
  • Ferhan Pekergin
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 62)


The article presents a di_usion approximation model applied to investigate queues with _nite capacity. Usually it is assumed that the size of a queue is limited by the maximum number of customers allowed to the system. Here, we assume that the size of customers is random (i.e. we consider batch arrivals with an arbitrary batch size distribution) and the constraint is given by the total volume of the queue. It is more adequate if we consider the queues of packets in e.g. IP routers where the volume of a bu_er where packets are stored is limited and the size of packets is variable.


Input Rate Limited Volume Interarrival Time Input Stream Service Time Distribution 
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  1. 1.
    Czachórski, T.: A method to solve diffiusion equation with instantaneous return processes acting as boundary conditions. Bulletin of Polish Academy of Sciences, Technical Sciences 41 (1993) 417–451Google Scholar
  2. 2.
    Czachórski, T., Fourneau, J.-M., Nycz, T., Pekergin, F.: Diffusion approximation model of multiserver stations with losses. Electronic Notes in Theoretical Computer Science 232 (2009) 125–143CrossRefGoogle Scholar
  3. 3.
    Gelenbe, E.: On Approximate Computer Systems Models. Journal of ACM, 22 (1975), 261–269zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Gelenbe, E., Pujolle, G.: The Behaviour of a Single Queue in a General Queueing Network. Acta Informatica, 7 (1976) 123–136zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Gelenbe E.: Diffusion approximations: waiting times and batch arrival. Acta Informatica 12 (1979) 285–303CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Tadeusz Czachórski
    • 1
    • 2
  • Tomasz Nycz
    • 2
  • Ferhan Pekergin
    • 3
  1. 1.Institute of Theoretical and Applied InformaticsPolish Academy of SciencesGliwicePoland
  2. 2.Silesian University of TechnologyGliwicePoland
  3. 3.LIPNUniversité Paris-NordVilletaneuseFrance

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