Abstract

We analyse the queue Q L at a multiplexer with L sources which may display long-range dependence. This includes, for example, sources modelled by fractional Brownian Motion (fBM). The workload processes W due to each source are assumed to have large deviation properties of the form P [W t =a(t) ? x] ß e \Gammav(t)K(x) for appropriate scaling functions a and v, and ratefunction K. Under very general conditions, lim L!1 L \Gamma1 log P [Q L ? Lb] = \GammaI (b) provided the offered load is held constant, where the shape function I is expressed in terms of the cumulant generating functions of the input traffic. For power-law scalings v(t) = t v , a(t) = t a (such as occur in fBM) we analyse the asymptotics of the shape function: lim b!1 b \Gammau=a i I(b) \Gamma ffi b v=a j = u for some exponent u and constant depending on the sources. This demonstrates the economies of scale available through the multiplexing of a large number of such sources, by comparison with ...

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