2-local superderivations on a superalgebra Mn(C) by Fosner A., Fosner M.

By Fosner A., Fosner M.

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Using a network calculus tool to propagate these results on the complete network, the approach derives analytically upper bounds on delays. However, these bounds are extremely pessimistic as observed when these are cross-checked with experimental upper bounds obtained by simulation for a set of scenarios. The ratio of the end-to-end delay obtained by simulation and the one calculated with the network calculus is mostly between 5% and 40%. Moreover, all VL paths with a ratio of atleast 70% have a length of 1 (they cross a single switch).

4 gives results for the 95th and 99th percentiles, respectively, for µ = 1, 5, 100. , 30. As expected, the results are identical. 2. Exponential components with different rate parameters In the case where the rate parameters of the exponential components are not necessarily the same, the end-to-end distribution is a hypoexponential distribution. In general, if we have n independently distributed exponential random variables Xi, then the ∑ , is hypoexponentially distributed. We random variable, note that the PDF and CDF formulas of the hypoexponential distribution are not readily available in the literature.

Hence, the percentiles can be calculated as: µ + erfc−1(P), where erfc is the complimentary error function of the Gaussian distribution. A heuristic formula is subsequently developed along the same lines, but this time the weighing factor instead of being erfc is chosen such that the formula would be exact if the individual delays were exponentially distributed. The third approach is based upon the dominant pole associated with each M/G/1 node. If the moment generating function of the delay in one node can be written as: Dn(s) = Hn(s)/(s − pn), where s − pn is the dominant pole, the endto-end distribution is a weighted sum of the Cumulative Density Function (CDF) of Erlang variables.

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