4th International ICST Conference on Performance Evaluation Methodologies and Tools

Research Article

Asymptotic End-to-end Stochastic Evaluation for Tandem Networks with Many Flows

Download113 downloads
  • @INPROCEEDINGS{10.4108/ICST.VALUETOOLS2009.7613,
        author={Kazutomo  Kobayashi and Yukio  Takahashi and Hiroyuki Takada},
        title={Asymptotic End-to-end Stochastic Evaluation for Tandem Networks with Many Flows},
        proceedings={4th International ICST Conference on Performance Evaluation Methodologies and Tools},
        publisher={ICST},
        proceedings_a={VALUETOOLS},
        year={2010},
        month={5},
        keywords={Stochastic network calculus Queuing theory Large deviations techniques},
        doi={10.4108/ICST.VALUETOOLS2009.7613}
    }
    
  • Kazutomo Kobayashi
    Yukio Takahashi
    Hiroyuki Takada
    Year: 2010
    Asymptotic End-to-end Stochastic Evaluation for Tandem Networks with Many Flows
    VALUETOOLS
    ICST
    DOI: 10.4108/ICST.VALUETOOLS2009.7613
Kazutomo Kobayashi1,*, Yukio Takahashi2,*, Hiroyuki Takada1,*
  • 1: Department of Computer and Information Sciences, Nagasaki University, Nagasaki 852-8521, Japan.
  • 2: Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 152-8552, Japan.
*Contact email: kobayashi@cis.nagasakiu.ac.jp, yukio@is.titech.ac.jp, htakada@cis.nagasakiu.ac.jp

Abstract

The stochastic network calculus receives much attention as a new methodology for end-to-end performance evaluation of networks, taking account of the effect of statistical multiplexing. In our previous paper, we proposed a new stochastic network calculus for many flows from an approach like large deviations techniques, and obtained asymptotic end-to-end evaluation formulas for output burstiness and backlog. However, we could not obtain the asymptotic evaluation formula for end-to-end delay in this framework.

In this paper, we enhance the calculation in the previous paper. Concretely we enlarge the domain of the deconvolution operator. Then in addition to for the backlog and the output burstiness in tandem networks, for the delay VL(t) of L flows at time t, using min-plus algebra, we obtain a function of d > 0 by which lim supL → ∞ L-1 log P(VL(t) > d) are bounded from above. We then discuss an application of the result to a tandem network with cross traffic and give a numerical result.