Numerous methods for available bandwidth estimation have been developed for wireline networks and their effectiveness is well-documented. 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 min-plus 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 multi-hop 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 multi-hop networks, as well as for wireless networks.

This paper develops a notion of capacity-delayerror-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 non-equilibrium 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, that enables composing capacity-delayerror-boundaries obtained for sources and systems as if in isolation. A method for construction of capacity-delay-errorboundaries is devised based on moment generating 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 ARQ. Results for tandem channels and for the composition of sources and channels are shown.

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Abstract-This paper develops an envelope-based approach to establish a link between information and queueing theory. Unlike classical, equilibrium information theory, information envelopes focus on the dynamics of sources and coders, using functions of time that bound the number of bits generated. In the limit the information envelopes converge to the average behavior and recover the entropy of a source, respectively, the average codeword length of a coder. In contrast, on short time scales and for sources with memory it is shown that large deviations from known equilibrium results occur with nonnegligible probability. These can cause significant network delays. Compared to well-known traffic models from queueing theory, information envelopes consider the functioning of information sources and coders, avoiding a priori assumptions, such as exponential traffic, or empirical, trace-based traffic models. Using results from the stochastic network calculus, the envelopes yield a characterization of the operating points of source coders by the triplet of capacity, delay, and error. In the limit, assuming an optimal coder the required capacity approaches the entropy with arbitrarily small probability of error if infinitely large delays are permitted. We derive a corresponding characterization of channels and prove that the model has the desirable property of additivity, that allows analyzing coders and channels separately.

We develop a stochastic foundation for bandwidth estimation of networks with random service, where bandwidth availability is expressed in terms of bounding functions with a defined violation probability. Exploiting properties of a stochastic max-plus algebra and system theory, the task of bandwidth estimation is formulated as inferring an unknown bounding function from measurements of probing traffic. We derive an estimation methodology that is based on iterative constant rate probes. Our solution provides evidence for the utility of packet trains for bandwidth estimation in the presence of variable cross traffic. Taking advantage of statistical methods, we show how our estimation method can be realized in practice, with adaptive train lengths of probe packets, probing rates, and replicated measurements required to achieve both high accuracy and confidence levels. We evaluate our method in a controlled testbed network, where we show the impact of cross traffic variability on the time-scales of service availability, and provide a comparison with existing bandwidth estimation tools.

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