In this paper, we revisit the estimation of the size distribution of packet flows in Internet traffic through an inversion approach for several packet sampling schemes which are based on probabilistic sampling (PS). We first study the statistical properties of the previously introduced inversion estimator in its general form and make connections to the singular value decomposition. This motivates the use of a regularization technique in the estimation of the flow size distribution. More specifically, a penalized weighted least square approach is proposed. We compare theoretically the penalized estimator under simplified assumptions against the (non-penalized) inversion approach in order to explain differences in their statistical behaviors. A data study with two real traces shows that the proposed penalized estimator outperforms the inversion estimator for all sampling schemes, corroborating the theoretical analysis. This work reveals that the simplest sampling schemes based on PS, that do not work with small sampling probabilities under the inversion approach, can be used with the penalized approach. Furthermore, the penalized approach allows considering smaller packet sampling rates for all the other sampling schemes.

Due to complexity and intractability reasons, most of the analytical studies on the reliability of communication paths in mobile ad hoc networks are based on the assumption of link independence. In this paper, an analytical framework is developed to characterize the random behavior of a multihop path and derive path metrics to characterize the reliability of paths. This is achieved through the modeling of a multihop path as a PDMP (piecewise deterministic Markov process). Two path based metrics are obtained as expectations of functionals of the process: the mean path duration and the path persistence. We show that these metrics are the unique solution of a set of integro-differential equations and provide a recursive scheme for their computation. Finally, numerical results illustrate the computation of the metrics; these results are compared with independent link approximation results.