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Towards an FBM Model Based Network Calculus Framework with Service Differentiation

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Abstract

In this paper, we exploit traffic modeling with the fractional Brownian motion (FBM) process to develop a network calculus framework for end-to-end performance analysis over a network provisioning differentiated services (DiffServ). The fundamental elements constituting the framework include accurate single-hop queueing analysis and three network calculuses that describe the stochastic behaviors when the traffic process is multiplexed, randomly split, or goes through a buffering system, respectively. Specifically, we develop a generic FBM based analysis for multiclass single-hop analysis where both inter-buffer priority and intra-buffer priority are used for service differentiation. Moreover, we present both theoretical and simulation studies to demonstrate that the output from the multiplexing, splitting, and buffering calculuses can still be modeled or well approximated by a properly parameterized FBM process. It is such preservation of the FBM characteristics that enables the concatenation of FBM based single-hop analysis into a network-wide performance analysis.

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Notes

  1. In this paper, X(t) is defined as the traffic volume, measured in packets or bits, arriving in the tth time unit. We use A(t) to denote the cumulative process indicating the total traffic volume from time 0 up to time t. X(t) is also termed as the increment process of A(t) as X(t) = A(t) − A(t − 1).

  2. The Bernoulli random variable V takes the values of 1 and 0 with the probability of p and 1 − p, respectively, with mean value E[V] = p and variance \(\operatorname{var}[V]=p(1-p)\).

  3. The second-hop link capacity is set slightly smaller in order to observe overflow in the second-hop buffer in simulations, as the first-hop output rate is limited by the link capacity c.

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Acknowledgements

The first author would like to thank his students Xiaohua Tian and Hongkun Li for their help in generating the NS2 simulation results.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Illinois Institute of Technology, Chicago, IL, USA

    Yu Cheng

  2. Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON, Canada

    Weihua Zhuang & Xinhua Ling

Authors
  1. Yu Cheng
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  2. Weihua Zhuang
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  3. Xinhua Ling
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Corresponding author

Correspondence to Yu Cheng.

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Cheng, Y., Zhuang, W. & Ling, X. Towards an FBM Model Based Network Calculus Framework with Service Differentiation. Mobile Netw Appl 12, 335–346 (2007). https://doi.org/10.1007/s11036-008-0040-x

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