# Topology Inference and Link Parameter Estimation Based on End-to-End Measurements +
## 4 Performance Evaluation
### Results and Discussion
As such, it reduces the computational and traffic overhead of the measurement process by decreasing the generated probing load and the consumption of valuable network resources (e.g., bandwidth, CPU, and memory). Assuming ideal conditions for the conventional tools (i.e., a priori known topology and unobstructed access to all intermediate nodes) and focusing only on link parameter estimation, we demonstrate the relation between measurement overhead and estimation accuracy for the NT-based approach and a representative conventional monitoring tool by selecting the general physical routing tree topology with 10 nodes and measuring the links' loss rates with the iperf tool using UDP probes (running an iperf server and client at the endpoints of the links). In particular, iperf was configured to send 1022, 1532, and 2042 probes at each link, resulting in 8176, 12,256, and 16,336 probes in total over the entire network. The achieved RMSE (the average of three measurements) was 0.5970, 0.4277, and 0.3335, respectively. As can be seen by comparing the respective results listed in Table 1, our approach can yield comparable estimation errors while utilizing a smaller number of probes, even in such a small-scale sample network. In order to demonstrate the impact of the reduction update scheme to the estimation accuracy, we consider the following generic formula:  
\[\ell(u,k)=\alpha\ell(i,k)+(1-\alpha)\ell(j,k),\text{ with }0\leq\alpha\leq 1, \ \forall k\in D,\ k\
eq u,i,j. \tag{16}\]  
Equation (16) can be employed during the reduction step of the clustering algorithm to compute the LCA depth of the newly created parent node \(u\) with every other node \(k\) as a convex combination of the LCA depths of that node with the two selected RNNs (i.e., nodes \(i\) and \(j\)). Since the coefficients of a convex combination must be non-negative and must sum to 1, in our case, \(\alpha\) takes a value within the range 0--1. We select one of the experimental scenarios (Bin. 32) and we plot the resulting RMSE in relation to the value  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Physical**} & \multicolumn{2}{c}{**Single**} & \multicolumn{3}{c}{**Complete**} & \multicolumn{3}{c}{**Average**} & \multicolumn{3}{c}{**Weighted**} \\ \multicolumn{2}{c}{**Routing Tree**} & \multicolumn{1}{c}{**2k**} & \multicolumn{1}{c}{**5k**} & \multicolumn{1}{c}{**10k**} & \multicolumn{1}{c}{**2k**} & \multicolumn{1}{c}{**5k**} & \multicolumn{1}{c}{**10k**} & \multicolumn{1}{c}{**2k**} & \multicolumn{1}{c}{**5k**} & \multicolumn{1}{c}{**10k**} & \multicolumn{1}{c}{**2k**} & \multicolumn{1}{c}{**5k**} & \multicolumn{1}{c}{**10k**} \\ \hline
**Type** & **\# Nds** & \multicolumn{6}{c}{**Root Mean Square Error for Loss Rate Estimation (\%)**} \\ \hline Bin. & 8 & 0.6369 & 0.4859 & 0.3879 & 0.5892 & 0.3714 & 0.4061 & 0.6124 & 0.4248 & 0.3961 & 0.6124 & 0.4248 & 0.3961 \\ Bin. & 16 & 1.1824 & 0.6066 & 0.4431 & 1.8491 & 0.7492 & 0.4333 & 1.2346 & 0.6496 & 0.3912 & 1.2189 & 0.6442 & 0.3902 \\ Bin. & 24 & 1.2486 & 0.4924 & 0.4086 & 1.2859 & 0.5643 & 0.4939 & 1.1297 & 0.4881 & 0.4152 & 1.1393 & 0.5087 & 0.3963 \\ Bin. & 32 & 1.5678 & 0.9790 & 0.7226 & 1.5692 & 0.9542 & 0.5588 & 1.1749 & 0.8423 & 0.4649 & 1.1980 & 0.8354 & 0.4399 \\ Gen. & 10 & 0.7798 & 0.3335 & 0.4609 & 0.7787 & 0.3172 & 0.6394 & 0.6826 & 0.3180 & 0.5238 & 0.6627 & 0.3177 & 0.5357 \\ Gen. & 20 & 1.1571 & 0.5012 & 0.3354 & 0.9676 & 0.6972 & 0.3640 & 0.9334 & 0.5398 & 0.3079 & 0.8770 & 0.5344 & 0.3173 \\ Gen. & 30 & 0.9128 & 0.5867 & 0.6108 & 0.8889 & 0.5476 & 0.4623 & 0.7308 & 0.5169 & 0.4707 & 0.7432 & 0.5157 & 0.4718 \\ Gen. & 40 & 1.2380 & 0.8134 & 0.6406 & 1.2977 & 0.8368 & 0.6924 & 1.0557 & 0.6950 & 0.5111 & 1.1451 & 0.6597 & 0.5120 \\ \hline
**Type** & **\# Nds** & \multicolumn{6}{c}{**Root Mean Square Error for Jitter Estimation (ms)**} \\ \hline Bin. & 8 & 2.2884 & 2.2625 & 1.8829 & 2.4840 & 2.3450 & 1.9747 & 2.3589 & 2.2891 & 1.9122 & 2.3589 & 2.2891 & 1.9122 \\ Bin.