Graph Modeling for Network Level Photography English VersionUSING GRAPHICAL MODEL FOR NETWORK TOMOGRAPHYWeiping ZhuComputer Science ADFA University of New South Wales AustraliaEmail weipingcsadfadeucn

ve a deep understanding of the network performance, including loss ratio, delay, and throughput. However, obtaining such information is not always straightforward, especially for large and complex networks. Traditional statistical methods, such as regression analysis, may not be effective due to the high dimensionality and non-linearity of the network performance data.

In recent years, using network tomography, which infers network performance from end-to-end measurements, has become a popular approach. Network tomography has been applied in various fields, such as wireless networks, optical networks, and the Internet.

In this paper, we propose to use a graphical model to perform network tomography. Graphical models are a powerful tool for representing complex dependencies between variables. They provide a more efficient and accurate way to infer network performance than traditional statistical methods.

2. Graphical Model for Network Tomography

A graphical model is a probabilistic graphical representation of a set of random variables and their conditional dependencies. In the context of network tomography, we can use a graphical model to represent the network performance variables and their dependencies.

Figure 1 shows a simple graphical model for network tomography. The circles represent random variables, and the arrows represent their conditional dependencies. In this model, we assume that the loss ratio and delay on each link are independent random variables, and the end-to-end loss ratio and delay are dependent on the loss ratio and delay on each link.

To infer the network performance from end-to-end measurements, we need to use the Expectation-Maximization (EM) algorithm. The EM algorithm is an iterative algorithm that alternates between computing the expected values of the hidden variables and maximizing the likelihood function.

3. Simulation Results

We conducted simulations using the network simulator 2 (ns2) to evaluate the performance of the graphical model for network tomography. We compared the results obtained using the EM algorithm with the results obtained using the maximum likelihood estimator (MLE) previously proposed.

Figure 2 shows the comparison of the inferred loss ratio and delay on each link using the graphical model and the MLE. The results obtained using the EM algorithm are almost identical to the results obtained using the MLE, indicating that the graphical model is an accurate and efficient method for network tomography.

4. Conclusion

In this paper, we proposed to use a graphical model for network tomography. The graphical model provides a more efficient and accurate way to infer network performance than traditional statistical methods. Simulations conducted using ns2 showed that the results obtained using the graphical model and the EM algorithm are almost identical to the results obtained using the MLE. The graphical model is a promising approach for network tomography and can be applied in various fields, such as wireless networks and optical networks