Smoothing the Input Process in a Batch Queue

  • F. Ait Salaht
  • H. Castel Taleb
  • J. M. FourneauEmail author
  • T. Mautor
  • N. Pekergin
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 363)


We state some stochastic comparison results for the loss probabilities and the time to live in a tandem network with two queues. We consider such a network under batch arrivals and constant service time. We show that making the service capacity of the first queue finite will improve the performance. More precisely, we derive stochastic bounds for the accumulated number of losses without any assumptions on the input traffic.


  1. 1.
    Aït-Salaht, F., Castel-Taleb, H., Fourneau, J., Pekergin, N.: Stochastic bounds and histograms for network performance analysis. In: Computer Performance Engineering—10th European Workshop, EPEW Italy, volume 8168 of Lecture Notes in Computer Science, pp. 13–27. Springer, New York (2013)Google Scholar
  2. 2.
    Chang, C.-S.: Smoothing point processes as a means to increase throughput. Oper. Res. 43(1), 117–129 (1995)CrossRefGoogle Scholar
  3. 3.
    Dupuis, A., Hébuterne, G.: Dimensioning the continuous state leaky bucket for geometric arrivals. In: Data Communications and their Performance, Proceedings of the Sixth IFIP WG6.3 Conference on Performance of Computer Networks, Istanbul, Turkey, (1995), volume 36 of IFIP Conference Proceedings, pp. 289–301. Chapman and Hall (1995)Google Scholar
  4. 4.
    Fourneau, J.-M., Le Coz, M., Pekergin, N., Quessette, F.: An open tool to compute stochastic bounds on steady-state distributions and rewards. In: 11th International Workshop on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems (MASCOTS: Orlando. IEEE Computer Society, FL (2003)Google Scholar
  5. 5.
    Friedman, H.D.: Reduction methods for tandem queuing systems. Oper. Res. 13(1), 121–131 (1965)CrossRefzbMATHGoogle Scholar
  6. 6.
    Hernández-Orallo, E., Vila-Carbó, J.: Network queue and loss analysis using histogram-based traffic models. Comput. Commun. 33(2), 190–201 (2010)CrossRefGoogle Scholar
  7. 7.
    Muller, A., Stoyan, D.: Comparison Methods for Stochastic Models and Risks. Wiley, New York (2002)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • F. Ait Salaht
    • 1
  • H. Castel Taleb
    • 1
  • J. M. Fourneau
    • 2
    Email author
  • T. Mautor
    • 2
  • N. Pekergin
    • 3
  1. 1.SAMOVAR, CNRS Télécom Sud ParisÉvry CedexFrance
  2. 2.PRiSM, UVSQ, CNRSVersaillesFrance
  3. 3.LACL, Université de Paris Est CréteilCréteilFrance

Personalised recommendations