Details
| Original language | English |
|---|---|
| Pages (from-to) | 127-141 |
| Number of pages | 15 |
| Journal | Computer networks |
| Volume | 56 |
| Issue number | 1 |
| Publication status | Published - 5 Sept 2011 |
Abstract
Fractional Brownian motion (fBm) emerged as a useful model for self-similar and long-range dependent aggregate Internet traffic. Asymptotic, respectively, approximate performance measures are known for single queueing systems with fBm through traffic. In this paper end-to-end performance bounds for a through flow in a network of tandem queues under open-loop fBm cross traffic are derived. To this end, a rigorous sample path envelope for fBm is proven that complements previous approximate results. The sample path envelope and the concept of leftover service curves are employed to model the remaining service after scheduling fBm cross traffic at a queuing system. Using composition results for tandem systems from the stochastic network calculus end-to-end statistical performance bounds for individual flows in networks under fBm cross traffic are derived. The discovery is that these bounds grow in On(logn) 1/(2-2H) for n systems in series where H is the Hurst parameter of the cross traffic. Explicit results on the impact of the variability and the burstiness of through and cross traffic on network performance are shown. Our analysis has direct implications on fundamental questions in network planning and service management.
Keywords
- Fractional Brownian motion, Long range dependence, Self-similarity, Stochastic service curve
ASJC Scopus subject areas
- Computer Science(all)
- Computer Networks and Communications
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In: Computer networks, Vol. 56, No. 1, 05.09.2011, p. 127-141.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Non-asymptotic end-to-end performance bounds for networks with long range dependent fBm cross traffic
AU - Rizk, Amr
AU - Fidler, Markus
N1 - Funding information: This work was supported by an Emmy Noether Grant of the German Research Foundation (DFG).
PY - 2011/9/5
Y1 - 2011/9/5
N2 - Fractional Brownian motion (fBm) emerged as a useful model for self-similar and long-range dependent aggregate Internet traffic. Asymptotic, respectively, approximate performance measures are known for single queueing systems with fBm through traffic. In this paper end-to-end performance bounds for a through flow in a network of tandem queues under open-loop fBm cross traffic are derived. To this end, a rigorous sample path envelope for fBm is proven that complements previous approximate results. The sample path envelope and the concept of leftover service curves are employed to model the remaining service after scheduling fBm cross traffic at a queuing system. Using composition results for tandem systems from the stochastic network calculus end-to-end statistical performance bounds for individual flows in networks under fBm cross traffic are derived. The discovery is that these bounds grow in On(logn) 1/(2-2H) for n systems in series where H is the Hurst parameter of the cross traffic. Explicit results on the impact of the variability and the burstiness of through and cross traffic on network performance are shown. Our analysis has direct implications on fundamental questions in network planning and service management.
AB - Fractional Brownian motion (fBm) emerged as a useful model for self-similar and long-range dependent aggregate Internet traffic. Asymptotic, respectively, approximate performance measures are known for single queueing systems with fBm through traffic. In this paper end-to-end performance bounds for a through flow in a network of tandem queues under open-loop fBm cross traffic are derived. To this end, a rigorous sample path envelope for fBm is proven that complements previous approximate results. The sample path envelope and the concept of leftover service curves are employed to model the remaining service after scheduling fBm cross traffic at a queuing system. Using composition results for tandem systems from the stochastic network calculus end-to-end statistical performance bounds for individual flows in networks under fBm cross traffic are derived. The discovery is that these bounds grow in On(logn) 1/(2-2H) for n systems in series where H is the Hurst parameter of the cross traffic. Explicit results on the impact of the variability and the burstiness of through and cross traffic on network performance are shown. Our analysis has direct implications on fundamental questions in network planning and service management.
KW - Fractional Brownian motion
KW - Long range dependence
KW - Self-similarity
KW - Stochastic service curve
UR - http://www.scopus.com/inward/record.url?scp=84655163385&partnerID=8YFLogxK
U2 - 10.1016/j.comnet.2011.07.027
DO - 10.1016/j.comnet.2011.07.027
M3 - Article
AN - SCOPUS:84655163385
VL - 56
SP - 127
EP - 141
JO - Computer networks
JF - Computer networks
SN - 1389-1286
IS - 1
ER -