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The problem of characterizing the relationship between packet size and network delay has received little attention in the field. Research in that area has been limited to either simulation studies or empirical observations that are detached from analytic traffic modeling. From a queueing viewpoint, it is simple to show that these three variables are inter-related, which necessitates a more careful study. We present a traffic model of a router fed by ON/OFF-type sources with heavy-tailed burst sizes. The traffic model considered is consistent with the evidence that Web traffic is heavy-tailed. The analysis cases that are considered establish a quantitative characterization of the complex relationship among packet payload and header sizes, traffic burstiness, and router queueing delay. © 2004 IEEE.
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Understanding the impact of network traffic properties on performance behavior in bottleneck links or larger networks is of primary interest to traffic analysts and network designers. Among the contributing factors, variance and correlation properties have been thoroughly studied and a large set of individual results have been obtained. However, these individual contributing factors are not sufficient to predict performance behavior. In this paper we review a unifying and versatile class of ON/OFF models through which the relationship among these parameters can be characterized and their influence on network performance be understood. The analytic performance results from the model show that there is a radically different queueing behavior when the ON period duration follows truncated power-tail distributions (even if truncated), as opposed to model variants where these distribution types are used for the OFF periods. All these models create correlation functions that only decay slowly. This motivates the development of a simple data analysis scheme to distinguish performance relevant correlation. The scheme is described both for interarrival and count processes of traffic data and its effectiveness is shown using real data traces.
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Measurements of parameters in electricity grids are frequently average values over some time interval. In scenarios of distributed measurements such as in distribution grids, offsets of local clocks can result in the averaging interval being misaligned. This paper investigates the properties of the so-called time alignment error of such measurands that is caused by shifts of the averaging interval. A Markov model is derived that allows for numerically calculating the expected value and other distribution properties of this error. Actual consumption measurements of an office building are used to study the behavior of this time alignment error, and to compare the results from the trace with numerical results and simulations from a fitted Markov model. For increasing averaging interval offset, the time alignment error approaches a normal distribution, whose parameters can be calculated or approximated from the Markov model.
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The operation and planning of distribution grids require the joint processing of measurements from different grid locations. Since measurement devices in low-and medium-voltage grids lack precise clock synchronization, it is important for data management platforms of distribution system operators to be able to account for the impact of nonideal clocks on measurement data. This paper formally introduces a metric termed Additive Alignment Error to capture the impact of misaligned averaging intervals of electrical measurements. A trace-driven approach for retrieval of this metric would be computationally costly for measurement devices, and therefore, it requires an online estimation procedure in the data collection platform. To overcome the need of transmission of high-resolution measurement data, this paper proposes and assesses an extension of a Markov-modulated process to model electrical traces, from which a closed-form matrix analytic formula for the Additive Alignment Error is derived. A trace-driven assessment confirms the accuracy of the model-based approach. In addition, the paper describes practical settings where the model can be utilized in data management platforms with significant reductions in computational demands on measurement devices. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.
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We consider the problem of propagating an update to nodes in a distributed system using two gossiping protocols. The first is an idealized algorithm with static and dynamic knowledge of the system, and the second is a simple randomized algorithm. We construct a theoretical model that allows us to derive work and completion time statistics under varying transmission delay distributions. Numerical results are obtained for both exponential and nonexponential transmission times using linear-algebraic queueing theory techniques. Additionally, we present the results of simulation experiments showing that under node churn assumptions, the randomized algorithm's performance is qualitatively different than in a fault-free system. © 2010 IEEE.
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