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Network Tomography Based on k-cast End-to-End Experiments



Project Title: Network Tomography Based on k-cast End-to-End Experiments

PI Involved: George Michailidis, Associate Professor, Statistics, University of Michigan

Collaborator: Vijay N. Nair, Professor, Statistics, University of Michigan

Students: Bowei Xi, Ph.D. (2004), Statistics, University of Michigan
Earl Lawrence, Ph.D. (2005), Statistics, University of Michigan

Project Description

Broadly, our goal is to assess network link characteristics in order to develop methods for quality assurance against network failure and security from malicious attack. We focus on estimating link loss rates and delay distributions using end-to-end measurements made across several links. We do this by transmitting end-to-end probe packets from a sender node to collections of receiver nodes. For example, in the simple network shown here, we might send a number of probe packets from the sender <0> to each set in the collection of receiver pairs <4,5>, <5,6>, and <6,7>. Based on the measured end-to-end losses and delays of these packet probes, we can reconstruct the loss rates and delay distributions for each individual link in the network. Along these lines we have pursued several goals. We have established a necessary and sufficient identifiability condition for the collection of experiments. We have also developed fast estimation algorithms with a goal of real-time monitoring for intrusion and anomaly detection. There are several current and future directions we are pursuing. We have begun work on estimating and/or characterizing continuous distributions using moment estimating equations and quasi-likelihood techniques. Additionally, we have started to consider the situation in which the link characteristics vary with time. These improvements further enhance our ability to make accurate assessments of the network and thereby improve our ability to monitor it.
Figure 1: Three-layer binary tree network.
Figure 2: Theoretical and estmimated delay distributions for Link 6 in the example described above. The actual delays were drawn from an exponential distribution. The algorithm discretizes the delays and computes the MLE under no parametric assumptions.
Figure 3: Simulation results for least square loss estimation techniques. Numerous data sets were generated for a four-layer binary tree. Here are boxplots of the results for ordinary least squares, generalized least squares, and iteratively reweighted least squares applied to each data set. The results for Link 1 are shown.
Figure 4: Online monitoring example. This movie demonstrates a four-layer binary tree with degradation along one end-to-end path. The transmission rate of Link 3 drops at time t=60s. Click above to watch the movie.

References

1. R. Caceres, N.G. Duffield, J. Horowitx, and D. Towsley , "Multicast-Based Inference of Network Internal Loss Characteristics," IEEE Transactions on Information Theory, 1999
2. Y.C. Hung and G. Michailidis (2006), "Improving Quality of Service for Switched Processing Systems," to appear in Proceedings of 11th Intl. Workshop on Computer-Aided Modeling, Analysis and Design of Communication Links and Networks CAMAD'06, Trento, Italy, June 2006
3. E. Lawrence (Michailidis advisor), "Flexicast Delay Active Tomography," PhD Thesis, Dept. of Statistics, July 2005
4. E. Lawrence, G. Michailidis, and V.N. Nair, "Inference of Network Delay Distributions Using the EM Algorithm," Technical Report, University of Michigan, 2003
5. E. Lawrence, G. Michailidis, V.N Nair, "Local Area Network Analysis Using End-to-End Delay Tomography" Performance Evaluation Review 33, pp. 39-45, 2005.
6. E. Lawrence, G. Michailidis, and V.N Nair (2005), "Flexicast delay tomography," to appear in the Journal of the Royal Statistical Society-B
7. E. Lawrence, G. Michailidis, V.N Nair, and B. Xi (2005), "Network Tomography: A Review and Recent Developments," to appear in Institute of Mathematical Statistics Volume in honor of Peter Bickel, Fan and Koul (eds)
8. E. Lawrence, G. Michailidis, and V.N. Nair (2006), "Statistical Inverse Problems in Active Network Tomography," to appear in Institute of Mathematical Statistics Volume in memory of Yehuda Vardi, Zhang and Liu (eds)
9. F. Lo Presti, N.G. Duffield, J. Horowitx, and D. Towsley, "Multicast-Based Inference of Network-Internal Delay Distributions," ACM/IEEE Transactions on Networking, 2002
10. G. Michailidis, V.N. Nair, and B. Xi, "Fast Least-Squares Based Algorithms for Estimating and Monitoring Network Losses With Active Network Tomography", (Submitted), 2003
11. G. Michailidis and N. Bambos (2005), "On the Singular Behavior of a Queueing System with Random Connectivity," Proceedings of the 44th IEEE Conference on Decision and Control (CDC), Seville, Spain (2005)
12. D.A. Rolls, G. Michailidis, and F. Hernandez-Campos (2005), Queueing analysis of network traffic: methodology and visualization tools
Computer Networks , 48, 447-473, 2006.
13. K.M. Wasserman, G. Michailidis, and N. Bambos (2006), Optimal processor allocation to differentiated job flows
Performance Evaluation (2006), 63, 1-14.
14. B. Xi, G. Michailidis, V.N. Nair, Estimating Network Loss Rates Using Active Tomography, to appear in Journal of the American Stat Association
15. P. Xu, G. Michailidis, M. Devetsikiotis (2006), Profit-oriented resource allocation using online scheduling in flexible heterogeneous networks, Telecommunication Systems (2006), 31, 289-303, 2006.