@MISC{Jiang08stochasticnetwork, author = {Yuming Jiang}, title = {Stochastic Network Calculus}, year = {2008} }

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Abstract

A basic calculus is presented for stochastic service guaran-tee analysis in communication networks. Central to the cal-culus are two definitions, maximum-(virtual)-backlog-centric (m.b.c) stochastic arrival curve and stochastic service curve, which respectively generalize arrival curve and service curve in the deterministic network calculus framework. With m.b.c stochastic arrival curve and stochastic service curve, vari-ous basic results are derived under the (min, +) algebra for the general case analysis, which are crucial to the develop-ment of stochastic network calculus. These results include (i) superposition of flows, (ii) concatenation of servers, (iii) output characterization, (iv) per-flow service under aggre-gation, and (v) stochastic backlog and delay guarantees. In addition, to perform independent case analysis, stochastic strict server is defined, which uses an ideal service process and an impairment process to characterize a server. The concept of stochastic strict server not only allows us to im-prove the basic results (i) – (v) under the independent case, but also provides a convenient way to find the stochastic ser-vice curve of a serve. Moreover, an approach is introduced to find the m.b.c stochastic arrival curve of a flow and the stochastic service curve of a server.