Telecommunication Systems

, Volume 27, Issue 1, pp 33–45 | Cite as

An Analytical Approach to Obtain the Interdeparture Time Characteristics in a Multistage VoIP Network

  • Veronique Inghelbrecht
  • Bart Steyaert
  • Sabine Wittevrongel
  • Herwig Bruneel


In this paper, we investigate the evolution of the interarrival and interdeparture times between voice packets when they are proceeding through a number of network nodes. We model the arrival process in a node as the superposition of a single tagged stream and an independent background process that aggregates the remaining traffic sources. Because we assume that the load of a single voice stream is very low compared to the load of the aggregate traffic, we can represent the tagged voice packets as markers (packets with size zero). We will establish an expression for the probability generating function (pgf) of the interdeparture time of the voice packets after one stage and use this interdeparture-time pgf as the pgf of the interarrival time of the voice packets in the next stage, in order to assess the evolution of the interarrival-time characteristics throughout the network.

multistage networks interdeparture times queuing generating functions 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    P. Brown and S. Simonian, Perturbation of a periodic flow in a synchronous server, in: Proceedings of the 12th IFIP WG7.3 International Symposium on Computer Performance Modeling, Measurement and Evaluation, Brussels, 1987, pp. 89–112.Google Scholar
  2. [2]
    H. Bruneel and B.G. Kim, Discrete-Time Models for Communication Systems Including ATM (Kluwer Academic, Boston, 1993).Google Scholar
  3. [3]
    F. Guillemin and J.W. Roberts, Jitter and bandwidth enforcement, in: Proceedings GLOBECOM' 91, Phoenix, AZ, 1991, pp. 261–265.Google Scholar
  4. [4]
    V. Inghelbrecht, B. Steyaert and H. Bruneel, Characteristics of switched traffic in a multistage ATM network, in: Proceedings of the Seventh IFIP Workshop on Performance Modelling and Evaluation of ATM and IP Networks, Antwerp, 1999, pp. 1–12.Google Scholar
  5. [5]
    A. Kuczura, Queues with mixed renewal and Poisson inputs, Bell. Syst. Tech. J. 51(2) (1972) 1305–1326.Google Scholar
  6. [6]
    K. Meier-Hellstern, A fitting algorithm for Markov-modulated Poisson process having two arrival rates, European J. Oper. Res. 29 (1987) 370–377.Google Scholar
  7. [7]
    D. Park and H.G. Perros, m-MMBP characterization of the departure process of an m-MMBP/Geo/1/K queue, in: Proceedings of ITC 14, Antibes, Juan-Les-Pins, 1994, pp. 75–84.Google Scholar
  8. [8]
    J.-F. Ren, J. Mark and J. Wong, End-to-end performance in ATM networks, in: Proceedings of ICC'94, Orlando, 1994, pp. 996–1002.Google Scholar
  9. [9]
    J. L. van den Berg, C.P.H.M. Lavrijsen and D. De Vleeschauwer, End-to-end delays in ATM networks: Theory & practice, in: Proceedings of the ATM Developments' 95 Conference, Rennes, 1995, pp. 113–126.Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Veronique Inghelbrecht
    • 1
  • Bart Steyaert
    • 1
  • Sabine Wittevrongel
    • 1
  • Herwig Bruneel
    • 1
  1. 1.SMACS Research Group, Vakgroep TELINGhent UniversityGhentBelgium

Personalised recommendations