1 Vivaldi: A Decentralized Network Coordinate System Frank Dabek, Russ Cox, Frans Kaashoek, Robert Morris Presented by: Chen Qian

2 Probe-then-connect is an intuitive scheme to find a close server or host. However it is not practical to first probe all servers to find the closest one, in some cases. P2P systems such as KaZaA, BitTorrent have a large number of replica servers. DNS is an example of systems in which each piece of data is small. Motivation

3 Synthetic coordinate systems allow Internet hosts to predict the RTTs to any other hosts. The distance between the coordinates of two hosts should be an accurate predictor of the RTT. These systems can be constructed by each host only communicating with a small set of other hosts. A Solution

4 Global Network Positioning (GNP) is the first coordinate system. It is a landmark-based approach. There are several nodes in the network are landmarks, whose coordinates are given. A normal node uses its distances to three (or more) landmarks to estimate its coordinates. GNP

5 Vivaldi is a simple, adaptive, de- centralized algorithm for computing network coordinates. No low-dimensional coordinate space would predict RTTS exactly. Internet latencies violate the triangle inequality. Vivaldi introduces the notion height that improves the prediction accuracy. Vivaldi

6 Where L ij: the actual RTT between nodes i and j x i: the coordinates assigned to node i ||x i -x j ||: the distance between the coordinates of i and j Minimizing the squared-error function is equivalent to minimizing the energy in a physical mass-spring network. Prediction Error

7 Tries to minimize the error of predicted RTT values by simulating the movements of nodes under spring forces. Centralized Algorithm N1N2 100 N1N2 150 N1N2 50 A single spring at rest longer spring shorter spring

8 By Hook’s Law: Force vector Fij can be viewed as an error vector, which has a direction Algorithm Scalar quantity: the displacement of the spring from rest Unit vector which gives the direction of the force on i.

9 N1N2 Local minimum But the global minimum is not guaranteed. The system may come to rest in a local minimum. N3 N5N4 local minimum

10 Local minimum But the global minimum is not guaranteed. The system may come to rest in a local minimum. N1 N2 N3 N5 N4 lower error

11 Calculate sum of forces on node i Move a step in the direction of the sum of forces Centralized Algorithm

12 Continuously contact sample nodes For each sample node Calculate force (error change) of this sample Move a step in the direction of the error Simple Distributed Version

13 Identical to the individual forces calculated in the loop of the centralized algorithm Coordinates update

14 The main difficulty in implementing Vivaldi is ensuring that it converges to coordinates that predict RTT well. If the timestep is too small, convergence is slow. If the timestep is too large, convergence may fail. Adaptive Timestep optimal

15 The system should obtain both fast convergence and avoidance of oscillation. Simple adaptive timestep Adaptive timestep to deal with large errors Adaptive Timestep If the remote node has a large error, it should be given less weight than a remote node with small error.

16 Algorithm with adaptive timestep Compute error confidence Update local error Adjust time step

17 Latency data Matrix of inter-host Internet RTTs Compute coordinates from a subset of these RTTs Check accuracy of algorithm by comparing simulated results to full RTT matrix 4 Data sets (2 Measured, 2 Synthetic) 192 nodes Planet Lab network, all pair-ping gives fully populated matrix 1740 Internet DNS servers Collect full matrix using the King method Continuously measure pairs over a week and take the median value Evaluation Methodology More geographically diverse at that time

18 King’s method First DNS query is for a name in the domain of A. It returns the latency to A. Second query is for a name in the domain of B, but is sent initially to A. The difference between two queries is the latency between A and B

19 King’s method Take the median value, because King can report a RTT higher or lower than the true value if there is congestion. About 10% of the original nodes were removed from the data High load or queuing at name server A adds a delay that is significantly larger than the network latency. The initial query (to A) and recursive query (via A to B) will require roughly the same amount of time and the estimated latency between them will be near zero.

20 Simulation test setup Input RTT matrix Send a packet one a second Simulator delays each transmission by ½ RTT time Use measured RTT of the packets to update coordinates Limitation of the simulator: RTTs do not vary over time; cannot model queuing delay or changes in routing Setup

21 Error definitions Error of Link Absolute difference between predicted RTT and measured RTT. Error of Node Median of link errors involving this node Error of System Median of all node errors Setup A small proportion of nodes have large errors?

22 (a)Constant timestep: too small and too large values all cause large errors. (b)Adaptive timestep: c=0.25 yields both quick error reduction and low oscillation. Timestep choice

new nodes join a stable 200-node network Constant timestep, new nodes may confuse the old nodes. The system need to be re-converged. Timestep with weighted errors allows new nodes to find their places quickly. Timestep choice

24 Sampling only nearby nodes gives good local coordinates but poor global coordinates. The second case allow nodes to contact distant nodes as well, improving the accuracy of the coordinates. Communication pattern

25 Put 4 close neighbors and 4 far-away neighbors. Each node chooses one of the far neighbors with probability p. p =.5 quick convergence p <.5 convergence slows. But similar accurate coordinates are eventually chosen. Communication pattern

26 Ability to adapt to changes in the network (tested with “Transit-Stub”) At time 100 one of the transit stub links is made 10 time larger; after 20 s the system has re-converged. At time 300 the link goes back to its normal size and the system quickly re-converged to original error. Adapting to network changes

27 Accuracy: Vivaldi vs. GNP How about communication cost?

28 Model Selection Almost any coordinate space satisfies the triangle inequality (the distance between A and C should be less than or equal to the distance along the path A-B-C). N1 N2 N3 100 ms 48 ms Not always true in Internet

29 Triangle inequality The best indirect path usually has lower RTT than the direct path. But luckily only 5% pairs have a significant shorter indirect path.

30 Euclidean Spaces If geographic distance were the only factor in latency, a 2- D model would be sufficient. However, the fit is not perfect. Adding more dimensions, the accuracy of the fit improves slightly 3D is okay!

31 Spherical coordinates Does a spherical distance function provide a more accurate model, as the distances are drawn from paths along the surface of the Earth? No!

32 2D+Height The Euclidean portion models a high-speed Internet core with latencies proportional to geographic distance. The height models the time it takes packets to travel the access link from the node to the core. The cause of the access link latency may be queuing delay, low bandwidth, etc. A packet sent from one node to another must travel the source node’s height, then travel in the Euclidean space, then travel the destination node’s height.

33 2D+Height Performs better than 2D and 3D! Does not look very promising because they take the median!

34 2D+Height Nodes with large errors Height plots results smaller max error and median error

35 Presents a simple, adaptive, decentralized algorithm for computing synthetic coordinates, which help Internet hosts to estimate latencies Requires no fixed infrastructure. All nodes run the same algorithm. Converges quickly by adaptive timestep. Maintains accuracy even as a large number of new hosts join the network that are uncertain of their coordinates. Conclusion

36 Thanks! Q&A