1. CMPE 252A : Computer Networks
Chen Qian
UCSC Baskin Engineering
Lecture 20

2. New Challenges Large-scale distributed services and applications
Napster, Gnutella, End System Multicast, etc
Large number of configuration choices
K participants  O(K2) e2e paths to consider
Stanford
MIT
CMU
Berkeley
Stanford
MIT
CMU
Berkeley
Stanford
MIT
CMU
Berkeley

3. Role of Network Distance Prediction
On-demand network measurement can be highly accurate, but
Not scalable
Slow
Network distance
Round-trip propagation and transmission delay
Relatively stable
Network distance can be predicted accurately without on-demand measurement
Fast and scalable first-order performance optimization
Refine as needed

4. Applying Network Distance
Napster, Gnutella
Use directly in peer-selection
Quickly weed out 95% of likely bad choices
End System Multicast
Quickly build a good quality initial distribution tree
Refine with run-time measurements
Key: network distance prediction mechanism must be scalable, accurate, and fast

5. Global Network Positioning (GNP)
Model the Internet as a geometric space (e.g. 3-D Euclidean)
Characterize the position of any end host with coordinates
Use computed distances to predict actual distances
Reduce distances to coordinates
(x2,y2,z2) y
(x1,y1,z1) x z
(x4,y4,z4)
(x3,y3,z3)

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

7. A Solution
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.

8. Vivaldi
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.

9. Prediction Error Where Lij: the actual RTT between nodes i and j
xi: the coordinates assigned to node i
||xi-xj||: 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.

10. Centralized Algorithm
Tries to minimize the error of predicted RTT values by simulating the movements of nodes under spring forces.
100 N1 N2
A single spring at rest
150 N1 N2
longer spring 50 N1 N2
shorter spring

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

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

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

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

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

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

17. Adaptive Timestep
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.
optimal
optimal

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

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

20. Evaluation Methodology
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
More geographically diverse at that time

21. 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

22. 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.

23. Setup 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

24. Setup 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
A small proportion of nodes have large errors?

25. Timestep choice
(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.

26. Timestep choice 200 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.

27. Communication pattern
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.

28. Communication pattern
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.

29. Adapting to network changes
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.

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

31. 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).
100 ms N1 N3
Not always true in Internet
48 ms
48 ms N2

32. 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.

33. 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!

34. 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!

35. 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.

36. 2D+Height Performs better than 2D and 3D!
Does not look very promising because they take the median!

37. 2D+Height Nodes with large errors
Height plots results smaller max error and median error

38. Conclusion
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.