Title : Progress in Computing of multi - rate Traffic Engineering Formulas

Short Description: Peaked and multi-rate traffic switching requires the evaluation of Gamma function related formulas for nonintegral states or capacities and appropriate inversions. The main problem implies the ratio enumeration of very large numbers which have to be computed stable and efficiently. Unfortunately traditional high level languages are not suited for symbolic expressions as arguments and numerical evaluations run under fixed number precisions far below the required ranges. This prevents preliminary algebraic simplifications and forces number-based integer recursions completed by basic interpolations or early multiple parameter series expansions. During the last decade the concept of high-precision approximate numbers within computer algebra systems (CASs) and high level language (HLL) systems became established. Under such conditions a unified approach of traffic engineering is obtainable. We will see that the incomplete Gamma function forms a key and unique component of past and forthcoming traffic engineering relations. Thus, exact analytical computations supported by a wide range of programming paradigms may be done as far as possible before numerical evaluations take place. Unfortunately the efficient handling of deep nesting, extended looping and large number arrays still call for HLLs. Therefore, three implementation alternatives of C/C access to symbolicnumerical computing are extracted and referred.