Poisson distribution, i.e.: where d is the number of call departures in time T and is the mean number of call departures in time T. The intervals, T, between call arrivals and departures are intervals between independent, identically distributed random events. It can be shown that these intervals have a negative exponential distribution, i.e.: where h is the mean holding time (MHT). The heavy-tail distribution A distribution is said to have a heavy tail if One simple example of a heavy-tailed distribution is the Pareto distribution. Modelling self-similar traffic Since (unlike traditional telephony traffic) packetised traffic exhibits self-similar or fractal characteristics, conventional traffic models do not apply to networks which carry self-similar traffic. With the convergence of voice and data, the future multi-service network will be based on packetised traffic, and models which accurately reflect the nature of self-similar traffic will be required to develop, design and dimension future multi-service networks. Previous analytic work done in Internet studies adopted assumptions such as exponentially-distributed packet inter-arrivals, and conclusions reached under such assumptions may be misleading or incorrect in the presence of heavy-tailed distributions. Deriving mathematical models which accurately represent long-range dependent traffic is a fertile area of research. Self-similar stochastic processes modeled by Tweedie distributions Leland et al have provided a mathematical formalism to describe self-similar stochastic processes. For the sequence of numbers with mean , deviations , variance , and autocorrelation function with lag k, if the autocorrelation of this sequence has the long range behavior as k and where L(k) is a slowly varying function at large values of k, this sequence is called a self-similar process. The method of expanding bins can be used to analyze self-similar processes. Consider a set of equal-sized non-overlapping bins that divides the original sequence of N elements into groups of m equal-sized segments (N/m is integer) so that new reproductive sequences, based on the mean values, can be defined: . The variance determined from this sequence will scale as the bin size changes such that if and only if the autocorrelation has the limiting form . One can also construct a set of corresponding additive sequences , based on the expanding bins, . Provided the autocorrelation function exhibits the same behavior, the additive sequences will obey the relationship Since and are constants this relationship constitutes a variance-to-mean power law (Taylor's law), with p=2-d. Tweedie distributions are a special case of exponential dispersion