Analysis of Steiner subtrees of Random Trees for Traceroute Algorithms

We consider in this paper the problem of discovering, via a traceroute algorithm, the topology of a network, whose graph is spanned by an infinite branching process. A subset of nodes is selected according to some criterion. As a measure of efficiency of the algorithm, the Steiner distance of the selected nodes, i.e. the size of the spanning sub-tree of these nodes, is investigated. For the selection of nodes, two criteria are considered: A node is randomly selected with a probability, which is either independent of the depth of the node (uniform model) or else in the depth biased model, is exponentially decaying with respect to its depth. The limiting behavior the size of the discovered subtree is investigated for both models

Adaptive algorithms for identifying large flows in IP traffic

We propose in this paper an on-line algorithm based on Bloom filters for identifying large flows in IP traffic (a.k.a. elephants). Because of the large number of small flows, hash tables of these algorithms have to be regularly refreshed. Recognizing that the periodic erasure scheme usually used in the technical literature turns out to be quite inefficient when using real traffic traces over a long period of time, we introduce a simple adaptive scheme that closely follows the variations of traffic. When tested against real traffic traces, the proposed on-line algorithm performs well in the sense that the detection ratio of long flows by the algorithm over a long time period is quite high. Beyond the identification of elephants, this same class of algorithms is applied to the closely related problem of detection of anomalies in IP traffic, e.g., SYN flood due for instance to attacks. An algorithm for detecting SYN and volume flood anomalies in Internet traffic is designed. Experiments show that an anomaly is detected in less than one minute and the targeted destinations are identified at the same time

A Stochastic Model for Topology Discovery of Tree Networks

A model describing the discovery by means of traceroute of the topology an Internet access network with a tree structure is proposed in this paper. This model allows us to assess the efficiency of traceroute procedures to determine the complete set of routers of the network. Under some stochastic assumptions, explicit analytical expressions are obtained for the mean number of routers discovered when a subset of the stations is used in the traceroute procedure. Several tree architectures are then discussed when the total number of routers gets large, and asymptotic expansions are derived. The results are compared with real data obtained from measurements

Mesures de la topologie et du trafic Internet

PARIS-BIUSJ-Thèses (751052125) / SudocPARIS-BIUSJ-Mathématiques rech (751052111) / SudocSudocFranceF