Non-asymptotic delay bounds for networks with heavy-tailed traffic

Non-asymptotic delay bounds for networks with heavy-tailed traffic (2010)

by J Liebeherr, A Burchard, F Ciucu

Venue:

In Proc. IEEE Infocom

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On expressing networks with flow transformation in convolution-form

by Florin Ciucu, T-labs Tu Berlin, Jens Schmitt, Hao Wang, Tu Kaiserslautern - In Proceedings of IEEE INFOCOM , 1979

"... Abstract—Convolution-form networks have the property that the end-to-end service of network flows can be expressed in terms of a (min;+)-convolution of the per-node services. This property is instrumental for deriving end-to-end queueing results which fundamentally improve upon alternative results d ..."

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Abstract—Convolution-form networks have the property that the end-to-end service of network flows can be expressed in terms of a (min;+)-convolution of the per-node services. This property is instrumental for deriving end-to-end queueing results which fundamentally improve upon alternative results derived by a node-by-node analysis. This paper extends the class of convolution-form networks with stochastic settings to scenarios with flow transformations, e.g., by loss, dynamic routing or retransmissions. In these networks, it is shown that by using the tools developed in this paper end-to-end delays grow as O(n) in the number of nodes n; in contrast, by using the alternative node-by-node analysis, end-to-end delays grow as O (n2). I.

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On the scaling of non-asymptotic capacity in multiaccess networks with bursty traffic

by Florin Ciucu - IN PROC. IEEE ISIT , 2011

"... The practicality of available (throughput) capacity results in multi-access networks, which dispense with coding schemes, is often questioned for several reasons including 1) the underlying asymptotic regimes, and 2) the assumption of saturated traffic sources. This paper jointly addresses these li ..."

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The practicality of available (throughput) capacity results in multi-access networks, which dispense with coding schemes, is often questioned for several reasons including 1) the underlying asymptotic regimes, and 2) the assumption of saturated traffic sources. This paper jointly addresses these lim-itations by providing capacity results in non-asymptotic regimes, i.e., holding at all time scales and network sizes, for the very broad class of exponentially bounded burstiness (EBB) traffic sources. Both upper and lower bounds on capacity are derived in terms of probability distributions, which immediately yield all the moments. The explicit and closed-form nature of the results enable the investigation of the impact of burstiness on non-asymptotic network capacity. In particular, the results show that for the EBB class the non-asymptotic end-to-end capacity rate decays linearly in the number of hops.

The impact of link scheduling on long paths: Statistical analysis and optimal bounds

by Yashar Ghiassi-farrokhfal, Jörg Liebeherr, Almut Burchard - IN PROC. OF IEEE INFOCOM , 2011

"... We study how the choice of packet scheduling algorithms influences end-to-end performance on long network paths. Taking a network calculus approach, we consider both deterministic and statistical performance metrics. A key enabling contribution for our analysis is a significantly sharpened method f ..."

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We study how the choice of packet scheduling algorithms influences end-to-end performance on long network paths. Taking a network calculus approach, we consider both deterministic and statistical performance metrics. A key enabling contribution for our analysis is a significantly sharpened method for computing a statistical bound for the service given to a flow by the network as a whole. For a suitably parsimonious traffic model we develop closed-form expressions for end-to-end delays, backlog, and output burstiness. The deterministic versions of our bounds yield optimal bounds on end-to-end backlog and output burstiness for some schedulers, and are highly accurate for endto-end delay bounds.

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Statistical Analysis of Link Scheduling on Long Paths

by Yashar Ghiassi-farrokhfal, Jörg Liebeherr, Almut Burchard , 2011

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On the Convergence to Fairness in Overloaded FIFO Systems

by Florin Ciucu, Oliver Hohlfeld, Lydia Y. Chen

"... Many of today’s computing and communication systems are based on FIFO queues whose performance, e.g., in terms of throughput and fairness, is highly impacted by load fluctuations, especially in the case of short-term overload. This paper analytically proves that overloaded FIFO queues are fair in th ..."

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Many of today’s computing and communication systems are based on FIFO queues whose performance, e.g., in terms of throughput and fairness, is highly impacted by load fluctuations, especially in the case of short-term overload. This paper analytically proves that overloaded FIFO queues are fair in the sense that each flow or aggregate of flows receives a proportional fair share of the service rate. The convergence rate is evaluated with respect to flow sizes and intensity of overutilization for two broad and distinctive arrival classes: Markovian and heavy-tailed/self-similar. For the former class the paper shows smaller convergence times at higher utilizations, which is exactly the opposite behavior characteristic to underloaded queueing systems.

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This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON SMART GRID 1 Toward a Realistic Performance Analysis of Storage Systems in Smart Grids

by Yashar Ghiassi-farrokhfal, Srinivasan Keshav, Catherine Rosenberg

"... Abstract—Energy storage devices (ESDs) have the potential to revolutionize the electricity grid by allowing the smoothing of variable-energy generator output and the time-shifting of demand away from peak times. A common approach to study the impact of ESDs on energy systems is by modeling them as e ..."

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Abstract—Energy storage devices (ESDs) have the potential to revolutionize the electricity grid by allowing the smoothing of variable-energy generator output and the time-shifting of demand away from peak times. A common approach to study the impact of ESDs on energy systems is by modeling them as electric cir-cuits in simulations. Although recent circuit models are becoming more accurate, to obtain statistically valid results, extensive sim-ulations need to be run. In some cases, existing datasets are not large enough to obtain statistically significant results. The impact of ESDs on energy systems has also been recently studied using analytical methods, but usually by assuming ideal ESD behavior, such as infinite ESD charging and discharging rates, and zero self-discharge. However, real-life ESDs are far from ideal. We investigate the effect of nonideal ESD behavior on system per-formance, presenting an analytical ESD model that retains much of the simplicity of an ideal ESD, yet captures many (though not all) nonideal behaviors for a class of ESDs that includes all battery technologies and compressed air energy storage systems. This allows us to compute performance bounds for systems with nonideal ESDs using standard teletraffic techniques. We pro-vide performance results for five widely used ESD technologies and show that our models can closely approximate numerically computed performance bounds. Index Terms—Analytical models, energy storage, performance analysis, renewable energy sources. I.

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