Computer Science – Networking and Internet Architecture
Scientific paper
2011-10-23
Computer Science
Networking and Internet Architecture
13 pages
Scientific paper
Network calculus is an elegant theory which uses envelopes to determine the worst-case performance bounds in a network. Statistical network calculus is the probabilistic version of network calculus, which strives to retain the simplicity of envelope approach from network calculus and use the arguments of statistical multiplexing to determine probabilistic performance bounds in a network. One of the key results of deterministic network calculus is that the end-to-end performance measures determined using a network service envelope is bounded by $ {\cal O} (H) $, where $H$ is the number of nodes traversed by a flow. There have been many attempts to achieve a similar linear scaling of probabilistic performance bounds in statistical network calculus but with limited success. The main contribution of this paper is to establish an end-to-end stochastic network calculus with the notion of effective bandwidth and effective capacity from large deviations theory which provides end-to-end delay and backlog bounds that grows linearly in the number of nodes ($H$) traversed by the arrival traffic, under relatively general assumptions.
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