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A Guide to the Stochastic Network Calculus
"... Abstract—The aim of the stochastic network calculus is to comprehend statistical multiplexing and scheduling of nontrivial traffic sources in a framework for endtoend analysis of multinode networks. To date, several models, some of them with subtle yet important differences, have been explored t ..."
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Abstract—The aim of the stochastic network calculus is to comprehend statistical multiplexing and scheduling of nontrivial traffic sources in a framework for endtoend analysis of multinode networks. To date, several models, some of them with subtle yet important differences, have been explored to achieve these objectives. Capitalizing on previous works, this paper contributes an intuitive approach to the stochastic network calculus, where we seek to obtain its fundamental results in the possibly easiest way. For this purpose, we will now and then trade generality or precision for simplicity. In detail, the method that is assembled in this work uses moment generating functions, known from the theory of effective bandwidths, to characterize traffic arrivals and network service. Thereof, affine envelope functions with exponentially decaying overflow profile are derived to compute statistical endtoend backlog and delay bounds for networks. I.
Measurement and Prediction of Centrical/Peripheral Network Properties based on Regression Analysis A Parametric Foundation for Performance SelfManagement in WSNs
"... Abstract—Predicting performancerelated behavior of the underlying network structure becomes more and more indispensable in terms of the aspired application outcome quality. However, the reliable forecast of QoS metrics like packet transfer delay in wireless network systems is still a challenging ..."
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Abstract—Predicting performancerelated behavior of the underlying network structure becomes more and more indispensable in terms of the aspired application outcome quality. However, the reliable forecast of QoS metrics like packet transfer delay in wireless network systems is still a challenging task. Even though existing approaches are technically capable of determining such network properties under certain assumptions, they mostly abstract away from primal aspects that inherently have an essential impact on temporal network performance dynamics. Also, they usually require auxiliary resources to be implemented and deployed along with the actual network components. In the course of developing a lightweight measurementbased alternative for the selfinspection and prediction of volatile performance characteristics in environments of any kind, we selectively investigate the duration of message delivery and packet loss rate
TOWARDS A STATISTICAL NETWORK CALCULUS– DEALING WITH UNCERTAINTY IN ARRIVALS
"... Abstract. The stochastic network calculus (SNC) has become an attractive methodology to derive probabilistic performance bounds. So far the SNC is based on (tacitly assumed) exact probabilistic assumptions about the arrival processes. Yet, in practice, these are only true approximately–at best. In m ..."
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Abstract. The stochastic network calculus (SNC) has become an attractive methodology to derive probabilistic performance bounds. So far the SNC is based on (tacitly assumed) exact probabilistic assumptions about the arrival processes. Yet, in practice, these are only true approximately–at best. In many situations it is hard, if possible at all to make such assumptions a priori. A more practical approach would be to base the SNC operations on measurements of the arrival processes (preferably even online). In this report, we develop this idea and incorporate measurements into the framework of SNC taking the further uncertainty resulting from estimation errors into account. This is a crucial step towards a statistical network calculus (StatNC) eventually lending itself to a selfmodelling operation of networks with a minimum of a priori assumptions. In numerical experiments, we are able to substantiate the novel opportunities by StatNC. 1.
1Towards a Statistical Network Calculus– Dealing with Uncertainty in Arrivals
"... Abstract—The stochastic network calculus (SNC) has become an attractive methodology to derive probabilistic performance bounds. So far the SNC is based on (tacitly assumed) exact probabilistic assumptions about the arrival processes. Yet, in practice, these are only true approximately–at best. In ma ..."
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Abstract—The stochastic network calculus (SNC) has become an attractive methodology to derive probabilistic performance bounds. So far the SNC is based on (tacitly assumed) exact probabilistic assumptions about the arrival processes. Yet, in practice, these are only true approximately–at best. In many situations it is hard, if possible at all, to make such assumptions a priori. A more practical approach would be to base the SNC operations on measurements of the arrival processes (preferably even online). In this paper, we develop this idea and incorporate measurements into the framework of SNC taking the further uncertainty resulting from estimation errors into account. This is a crucial step towards a statistical network calculus (StatNC) eventually lending itself to a selfmodelling operation of networks with a minimum of a priori assumptions. In numerical experiments, we are able to substantiate the novel opportunities by StatNC.
Capacity–Delay–Error Boundaries: A Composable Model of Sources and Systems
"... Abstract—This paper develops a notion of capacity–delay–error (CDE) boundaries as a performance model of networked sources and systems. The goal is to provision effective capacities that sustain certain statistical delay guarantees with a small probability of error. We use a stochastic nonequilibr ..."
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Abstract—This paper develops a notion of capacity–delay–error (CDE) boundaries as a performance model of networked sources and systems. The goal is to provision effective capacities that sustain certain statistical delay guarantees with a small probability of error. We use a stochastic nonequilibrium approach that models the variability of traffic and service to formalize the influence of delay constraints on the effective capacity. Permitting unbounded delays, known ergodic capacity results from information theory are recovered in the limit. We prove that the model has the property of additivity, which enables composing CDE boundaries obtained for sources and systems as if in isolation. A method for construction of CDE boundaries is devised based on momentgenerating functions, which includes the large body of results from the theory of effective bandwidths. Solutions for essential sources, channels, and respective coders are derived, including Huffman coding, MPEG video, Rayleigh fading, and hybrid automatic repeat request. Results for tandem channels and for the composition of sources and channels are shown. Index Terms—Queueing analysis, information theory, channel models, time varying channels, quality of service. I.
1 A Stochastic Power Network Calculus for Integrating Renewable Energy Sources into the Power
"... Abstract—Renewable energy such as solar and wind generation will constitute an important part of the future grid. As the availability of renewable sources may not match the load, energy storage is essential for grid stability. In this paper we investigate the feasibility of integrating solar photovo ..."
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Abstract—Renewable energy such as solar and wind generation will constitute an important part of the future grid. As the availability of renewable sources may not match the load, energy storage is essential for grid stability. In this paper we investigate the feasibility of integrating solar photovoltaic (PV) panels and wind turbines into the grid by also accounting for energy storage. To deal with the fluctuation in both the power supply and demand, we extend and apply stochastic network calculus to analyze the power supply reliability with various renewable energy configurations. To illustrate the validity of the model, we conduct a case study for the integration of renewable energy sources into the power system of an island off the coast of Southern California. In particular, we asses the power supply reliability in terms of the average Fraction of Time that energy is NotServed (FTNS).
1 Stochastic Bandwidth Estimation in Networks with Random Service
"... Abstract — Numerous methods for available bandwidth estimation have been developed for wireline networks and their effectiveness is welldocumented. However, most methods fail to predict bandwidth availability reliably in a wireless setting. It is accepted that the increased variability of wireless ..."
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Abstract — Numerous methods for available bandwidth estimation have been developed for wireline networks and their effectiveness is welldocumented. However, most methods fail to predict bandwidth availability reliably in a wireless setting. It is accepted that the increased variability of wireless channel conditions makes bandwidth estimation more difficult, however, a (satisfactory) explanation why these methods are failing is missing. This paper seeks to provide insights into the problem of bandwidth estimation in wireless networks, or, more broadly, in networks with random service. We express bandwidth availability in terms of bounding functions with a defined violation probability. Exploiting properties of a stochastic minplus linear system theory, the task of bandwidth estimation is formulated as inferring an unknown bounding function from measurements of probing traffic. We present derivations showing that simply using the expected value of the available bandwidth in networks with random service leads to a systematic overestimation of the traffic departures. Furthermore, we show that in a multihop setting with random service at each node, available bandwidth estimates requires observations over (in principle infinitely) long time periods. We propose a new estimation method for random service which is based on iterative constant rate probes that take advantage of statistical methods. We show how our estimation method can be realized to achieve both good accuracy and confidence levels. We evaluate our method for wired single and multihop networks, as well as for wireless networks. I.