An Algebraic Approach to Practical and Scalable Overlay Network

Monitoring

Yan Chen, David Bindel, Hanhee Song, Randy H. Katz

Presented by Mahesh Balakrishnan

Motivation

Overlay networks Monitoring of end-to-end paths The need for a separate Monitoring Service Metrics: Latency... Loss Rate? The Goal: A Scalable Overlay Loss Rate

Monitoring Service

Existing Work…

Latency-only Schemes Clustering:

– Nodes are clustered together, and cluster representative is monitored

– Claim: Inaccurate for congestion detection Co-ordinates:

– Cannot give congestion information

Existing Work.

Network Tomography: Determining internal network properties from black-box measurements

Shavitt, et al. Algebraic approach Ozmutlu, et al. Selecting minimal set of paths to

cover all links

General Metric Systems: RON

Core Idea

Assumptions:– Access to link composition of paths– Ability to measure path (but not link) characteristics

From the possible n2 end-to-end paths, select a basis set of k paths (k << n2) to monitor.

The characteristics of all paths can be inferred from this basis set.

Centralized algorithm: all nodes send measurements to central node.

The Math

Eq 1: Represent paths as

vectors:

A

D

C

B

l1

l2

3p1

)1)(1(1 211 llp

011

v

)1log()1log()1log(

011

)1log()1log()1log(

3

2

1

211

lllllp

AD

BD

AC

System of Linear Equations

srG }1|0{

1 sRx…

=

Path Matrix Link Rates Path Rates

1 rRb

Example Network

111100011

G

A

D

C

B

l1

l2

3p1

AB

AC

BC

bGx k = Number of essential paths 1 < k <= sG is rank deficient: k < s

More Math

k = # of essential paths = rank (G) k <= s Usually G is rank-

deficient: k < s Select k linearly

independent paths to monitor:

bxG G

One-time QR Decomposition: O(rk2) time… O(n4)!

Inferring other paths: O(k2)

=…k

s

Assessment Criteria

Accuracy Scalability: How does k grow w.r.t n?

Other concerns:– centralized solution– compute time under churn– storage load

Effect of Topology on k growth

Star Topology, Strict Hierarchy: s = O(n), => k = O(n)

Clique: Each path (end host pair) contains a unique link, hence k = O(n2)

Hierarchy is good, Dense Connectivity is bad Conjecture: k = O(nlogn) for the internet What if only a small % of end nodes are on

overlay?

Linear Regression Tests

Synthetic Hierarchical Real

Handling Change

Path Addition: O(k2) Path Removal: O(k2) [Naïve : O(rk2) Node Addition: O(nk2) Node Removal: O(nk2)

– Cannot use path removal algorithm directly; path will be replaced using another path involving node

– Remove all paths, then look for replacements Cubic in n: Churn in large systems?

Routing Changes

End-to-end internet paths are generally stable

Traceroute Topology checked on a daily basis, in

presence of drastic loss rate changes If path has changed at certain links, other

paths with that link are checked as well

Load Balancing/Topology Measurement Errors

Paths in G are randomly reordered before basis set is selected

Untraceable paths/segments are modeled as single links; they always get selected in basis

Router aliases – one physical link presented as several virtual links – all virtual links get similar loss rates

Evaluation: Simulation

Three synthetic BRITE topologies: Barabasi-Albert, Waxman, hierarchical

One ‘real’ router topology (Mercator) Methodology:

– Loss Distribution: Good = 0-1%, Bad = 5-10%– Loss Model: Bernoulli, Gilbert

Simulate loss for selected paths, infer for other paths

Accuracy: Synthetic Topology

All Configurations under 0.008, 1.18

Accuracy: Real Topology

Accuracy

Real Topology

Synthetic Hierarchical Topology

Running Time

3 seconds for 100 nodes, 21 minutes for 500!

Load Balancing

Effect of Churn/Routing Change

Path Addition: 125 msec Path Removal: 445 msec Node Addition: 1.18 sec Node Removal: 16.9 sec What about n >> 60?

Node Deletion

Node Addition

Network Link Removal

PlanetLab Experiments

51 hosts, each from different organization Each node sends a UDP packet to every

other host in each trial 300 trials of 300 msec each Receiver counts packets for loss rate Traceroute used for topology measurement

PlanetLab Results

Cumulative coverage/FP Cumulative error (Worst Run)

Average Abs. Error = 0.0027, Average Error Factor 1.1

Effect of traffic on loss rates

Sensitivity Analysis done at night, on empty networks

Threshold at 12.8 Mbps

Why do this?

Conclusion

Algebraic Method for inferring loss rates of all paths from a basis set

Quite Accurate Reasonable load imposed on each node But is it really scalable? Centralized solution, cubic dependence on n

for handling node addition/removal