CMPE 252A : Computer Networks Chen Qian Computer Engineering UCSC Baskin Engineering Lecture 13 Some slides from Eugene Ng

Survey paper due 11/21 At the beginning of class, hardcopy or softcopy via email to both me and TAs.

Global Network Positioning: A New Approach to Network Distance Prediction Tze Sing Eugene Ng

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

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

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

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)

Landmark Operations y x (x2,y2) (x1,y1) (x3,y3) L1 L2 L3 L1 L2 L3 Small number of distributed hosts called Landmarks measure inter-Landmark distances Internet Compute Landmark coordinates by minimizing the overall discrepancy between measured distances and computed distances Cast as a generic multi-dimensional global minimization problem

Landmark Operations Landmark coordinates are disseminated to ordinary end hosts A frame of reference e.g. (2-D, (L1,x1,y1), (L2,x2,y2), (L3,x3,y3)) T. S. Eugene Ng eugeneng@cs.cmu.edu Carnegie Mellon University

Ordinary Host Operations (x2,y2) L2 (x1,y1) (x4,y4) L1 L1 L3 x L2 Internet L3 (x3,y3) Each ordinary host measures its distances to the Landmarks, Landmarks just reflect pings Ordinary host computes its own coordinates relative to the Landmarks by minimizing the overall discrepancy between measured distances and computed distances Cast as a generic multi-dimensional global minimization problem

GNP Advantages High scalability and high speed Enable new applications End host centric architecture, eliminates server bottleneck Coordinates reduce O(K2) communication overhead to O(K*D) Coordinates easily exchanged, predictions are locally and quickly computable by end hosts Enable new applications Structured nature of coordinates can be exploited Simple deployment Landmarks are simple, non-intrusive (compatible with firewalls)

Evaluation Methodology 19 Probes we control 12 in North America, 5 in East Asia, 2 in Europe Select IP addresses called Targets we do not control Probes measure Inter-Probe distances Probe-to-Target distances Each distance is the minimum RTT of 220 pings

Evaluation Methodology (Cont’d) Choose a subset of well-distributed Probes to be Landmarks, and use the rest for evaluation T T P2 (x1,y1) P1 T T P3 (x2, y2) P4 T T

Computing Coordinates Multi-dimensional global minimization problem Will discuss the objective function later Simplex Downhill algorithm [Nelder & Mead ’65] Simple and robust, few iterations required f(x) x

Data Sets Global Set 19 Probes 869 Targets uniformly chosen from the IP address space biased towards always-on and globally connected nodes 44 Countries 467 in USA, 127 in Europe, 84 in East Asia, 39 in Canada, …, 1 in Fiji, 65 unknown Abilene Set 10 Probes are on Abilene 127 Targets that are Abilene connected web servers

Performance Metrics Directional relative error Symmetrically measure over and under predictions Relative error = abs(Directional relative error) Rank accuracy % of correct prediction when choosing some number of shortest paths

GNP vs IDMaps (Global)

GNP vs IDMaps (Global)

Basic Questions How to measure model error? How to select Landmarks? How does prediction accuracy change with the number of Landmarks? What is geometric model to use? How can we further improve GNP?

Measuring Model Error is measured distance is computed distance is an error measuring function

Error Function Squared error May not be good because one unit of error for short distances carry the same weight as one unit of error for long distances

More Error Functions Normalized error Logarithmic transformation

Comparing Error Functions 6 Landmarks 15 Landmarks Squared Error 1.03 0.74 Normalized Error 0.5 Logarithmic Transformation 0.75 0.51

Selecting N Landmarks Intuition: Landmarks should be well separated Method 1: Clustering start with 19 clusters, one probe per cluster iteratively merge the two closest clusters until there are N clusters choose the center of each cluster as the Landmarks Method 2: Find “N-Medians” choose the combination of N Probes that minimizes the total distance from each not chosen Probe to its nearest chosen Probe Method 3: Maximum separation choose the combination of N Probes that maximizes the total inter-Probe distances

K-Fold Validation Want more than just one set of N Landmarks to reduce noise Select N+1 Landmarks based on a criterion Eliminate one Landmark to get N Landmarks i.e., N+1 different sets of N Landmarks that are close to the selection criterion

Comparing Landmark Selection Criteria (6 Landmarks) Clustering N-Medians Max sep. GNP 0.74 0.78 1.04 IDMaps 1.39 1.43 5.57

Comparing Landmark Selection Criteria (9 Landmarks) Clustering N-Medians Max sep. GNP 0.68 0.7 0.83 IDMaps 1.16 1.09 1.74 T. S. Eugene Ng eugeneng@cs.cmu.edu Carnegie Mellon University

Number of Landmarks/Tracers T. S. Eugene Ng eugeneng@cs.cmu.edu Carnegie Mellon University

What Geometric Model to Use? Spherical surface, cylindrical surface No better than 2-D Euclidean space Euclidean space of varying dimensions

Euclidean Dimensionality

Why Additional Dimensions Help? ISP A B C D 1 5 2-dimensional model A,B C,D A B C D 3-dimensional model 1 5 A A B C D A 0 1 5 5 B 1 0 5 5 C 5 5 0 1 D 5 5 1 0

Reducing Measurement Overhead Hypothesis: End hosts do not need to measure distances to all Landmarks to compute accurate coordinates P1 P3 P2 P5 T P6 (x, y) P4

Triangular Inequality Violations T. S. Eugene Ng eugeneng@cs.cmu.edu Carnegie Mellon University

Removing Triangular Inequality Violations Remove Target (t) from data if t in {a, b, c} (a,c)/((a,b)+(b,c)) > threshold Try two thresholds 2.0; 647 of 869 Targets remain 1.5; 392 of 869 Targets remain Note: at 1.1, only 19 of 869 Targets remain!!!

Removing Triangular Inequality Violations T. S. Eugene Ng eugeneng@cs.cmu.edu Carnegie Mellon University

Removing Triangular Inequality Violations T. S. Eugene Ng eugeneng@cs.cmu.edu Carnegie Mellon University

Removing Triangular Inequality Violations T. S. Eugene Ng eugeneng@cs.cmu.edu Carnegie Mellon University

Why Not Use Geographical Distance? T. S. Eugene Ng eugeneng@cs.cmu.edu Carnegie Mellon University

Summary Network distance prediction is key to performance optimization in large-scale distributed systems GNP is scalable End hosts carry out computations O(K*D) communication overhead due to coordinates GNP is fast Distance predictions are fast local computations GNP is accurate Discover relative positions of end hosts T. S. Eugene Ng eugeneng@cs.cmu.edu Carnegie Mellon University

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

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.

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.

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.

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

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

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

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

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

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

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

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

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.

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

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

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

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.

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

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?

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.

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.

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.

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.

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.

Accuracy: Vivaldi vs. GNP How about communication cost?

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

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.

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!

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!

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.

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

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

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.