%0 Journal Article %1 vardi1996network %A Vardi, Y. %D 1996 %I Taylor & Francis, Ltd. on behalf of the American Statistical Association %J Journal of the American Statistical Association %K communications network_tomography original statistics unknown_network %N 433 %P pp. 365-377 %T Network Tomography: Estimating Source-Destination Traffic Intensities from Link Data %U http://www.jstor.org/stable/2291416 %V 91 %X The problem of estimating the node-to-node traffic intensity from repeated measurements of traffic on the links of a network is formulated and discussed under Poisson assumptions and two types of traffic-routing regimens: deterministic (a fixed known path between each directed pair of nodes) and Markovian (a random path between each directed pair of nodes, determined according to a known Markov chain fixed for that pair). Maximum likelihood estimation and related approximations are discussed, and computational difficulties are pointed out. A detailed methodology is presented for estimates based on the method of moments. The estimates are derived algorithmically, taking advantage of the fact that the first and second moment equations give rise to a linear inverse problem with positivity restrictions that can be approached by an EM algorithm, resulting in a particularly simple solution to a hard problem. A small simulation study is carried out.

@article{vardi1996network, abstract = {The problem of estimating the node-to-node traffic intensity from repeated measurements of traffic on the links of a network is formulated and discussed under Poisson assumptions and two types of traffic-routing regimens: deterministic (a fixed known path between each directed pair of nodes) and Markovian (a random path between each directed pair of nodes, determined according to a known Markov chain fixed for that pair). Maximum likelihood estimation and related approximations are discussed, and computational difficulties are pointed out. A detailed methodology is presented for estimates based on the method of moments. The estimates are derived algorithmically, taking advantage of the fact that the first and second moment equations give rise to a linear inverse problem with positivity restrictions that can be approached by an EM algorithm, resulting in a particularly simple solution to a hard problem. A small simulation study is carried out.}, added-at = {2015-05-08T07:02:56.000+0200}, author = {Vardi, Y.}, biburl = {https://www.bibsonomy.org/bibtex/2ba510c27cbb869266a5d31d7ea126ff0/peter.ralph}, description = {[from Lawrence et al:] "The term network tomography, introduced by Vardi (1996), has been used in the literature to characterize two broad classes of inverse problems. The first is pas- sive tomography where aggregate data are collected at the router level. The goal is to disaggregate these to obtain finer-level information. The most common ap- plication, which was the original problem studied in Vardi (1996), is estimation of the origin-destination traffic matrix of a network."}, interhash = {6c0e2a360dc884fd32117b1ad8c254f7}, intrahash = {ba510c27cbb869266a5d31d7ea126ff0}, issn = {01621459}, journal = {Journal of the American Statistical Association}, jstor_articletype = {research-article}, jstor_formatteddate = {Mar., 1996}, keywords = {communications network_tomography original statistics unknown_network}, language = {English}, number = 433, pages = {pp. 365-377}, publisher = {Taylor & Francis, Ltd. on behalf of the American Statistical Association}, timestamp = {2015-05-08T07:02:56.000+0200}, title = {Network Tomography: Estimating Source-Destination Traffic Intensities from Link Data}, url = {http://www.jstor.org/stable/2291416}, volume = 91, year = 1996 }