Stochastic networks and the extreme value distribution

This paper extends the extreme value theory to the problem of approximating the probability distribution of the duration of the longest path in stochastic networks and its parameters. It is demonstrated that the distribution function of the longest path can be more adequately represented by an extreme value distribution rather than by the normal distribution in most cases of interest. In particular, extreme value theory is used to derive estimates for the mean and the variance of the distribution. These estimates are compared with the simulated mean and variance as well as with estimates obtained by other estimating procedures. The new estimates are shown to be closer to the simulated mean and variance. Conditions that help determine which theory, normal or extreme value, is more applicable for a certain network are also provided.