Mean and variance of a call arrival process with exponentially distributed holding times are defined by the mean and variance, respectively, of the number of occupied trunks in a virtual infinite trunk group to which the arriving calls are virtually directed, where the holding times in the virtual infinite trunk group have the same distribution, but are independent of already sampled holding times, i.e., at each (virtual) arrival the holding times are newly sampled (freed stream). The peakedness of the call arrival process is the ratio of variance and mean.
The above concept of mean and peakedness for a call arrival process is independent of the character of the call arrival process, e.g. overflow or carried stream from another link, and should be used in particular in larger networks. However, calculating the peakedness is quite difficult both theoretically and numerically. For these reasons up to now this concept of peakedness is not used in network analysis algorithms, cf. André Girard: Routing and Dimensioning in Circuit-Switched Networks, Addison-Wesley, 1990 (p. 110).
Using the above concept in this project fast and numerically stable algorithms for the means and peakednesses of the overflow and carried streams of a link have been developed for up to two call arrival processes which are characterized by their means and peakednesses. The algorithms have been generalized to the case of trunk reservation which is often used for stabilizing networks. They are recursive and of complexity O(C), where C denotes the capacity of the link. As these algorithms are very fast (some milliseconds) they can be used for network analysis algorithms basing on a fitting of the first two moments and a unified handling of all streams, thus opening a new method in network analysis.
