Transcript PPT

Meridian: A Lightweight Framework for Network Positioning
without Virtual Coordinates
Bernard Wong, Aleksandrs Slivkins and Emin Gün Sirer
Cornell University
http://www.cs.cornell.edu/~bwong/meridian
What is Meridian?
Status
Central Leader Selection
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Meridian is a lightweight framework for performing node selection based on a
set of network positioning constraints
Based on a small number of query-directed measurements
Meridian is organized as a loosely structured overlay
– Gossip-based membership tracking
– Each node keeps O(logN) state
The goal of the overlay is to have each node know enough local information to
authoritatively answer geographic queries for its region of the network
Queries regarding distant nodes are handed off to a neighbor in that region.
– Essentially, the idea is for each node-to-node query hand-off to “zoom in” to the
solution space
– Each hop exponentially reduces the distance to a target within the solution space
Meridian solves frequently encountered network positioning problems without
computing network coordinates
– No embedding error
– Low complexity
– Scalable without CAN
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Find closest node
– Web server, game server, etc.
Construct efficient overlays
– Find the most central node to a set of nodes to act as the set’s hub node
– Hub nodes get promoted higher in the tree hierarchy
Satisfying Service Level Agreements
– Find a node that meets multiple latency constraints
– Build clusters with a maximum inter-node latency
Discover good one-hop indirect routes
– Find lowest latency one-hop overlay route when direct route fails
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The protocol works as follows:
1. Client sends a “closest node
discovery to target T” request to a
Meridian node A
2. Node A determines its latency d to T
3. Node A probes its ring members
between d/2 and 3d/2 to determine
their distances to the target
4. The request is forwarded to the
closest node thus discovered that is
at least β times closer to the target
than A
5. Process continues until no node that
is β times closer can be found
Minimizes average distance to a set of
targets instead of one target
Protocol similar to closest node
discovery, but uses davg instead of d
For this example, node A is the best
leader out of nodes A to H, where nodes
A to H are also the targets
D
C
E
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Evaluation
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Closest Node Discovery
Motivating problems
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We have proven in a theoretical analysis that
– Meridian’s multi-hop search terminates in O(logN) hops
– Error will remain constant given each node has O(logN) ring members
The results hold for Internet latencies that can be modeled as growth
constrained or low doubling dimension metrics
– Both metrics are more general than a low dimension Euclidean metric
Full implementation and deployment of three applications using the Meridian
framework
1. Closest node discovery
• Finds the closest (lowest latency) node to a given target
2. Central leader selection
• Select the most centrally located node to a given target set
3. Multiple constraints system
• Discovers a node within latency bounds of multiple targets
We have evaluated these applications through both simulation parameterized
by a large-scale network measurement study, and a deployment on PlanetLab.
For our measurement study, we collected node-to-node round-trip latency
measurements for 2500 nodes and 6.25 million node pairs on the Internet using
the King measurement technique.
Closet Node Discovery
Light bars show the median error for discovering the
closest node. Darker bars show the inherent embedding
error with coordinate systems. Meridian's median closest
node discovery error is an order of magnitude lower than
schemes based on embeddings.
Central Leader Selection
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Client node
Target node T
Initial node A
Closest node B
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With larger group sizes, the central leader selection
algorithm is able to find a centrally situated node more
frequently. Meridian is significantly more accurate than
Vivaldi for all tested configurations.
Ring member of A
Ring member of B
Forwarding of query
Latency probe
Multiple Constraint System
The percentage of successful multi-constraint queries is
above 90% when the number of nodes that can satisfy the
constraints is 0.5% or more.
Multi-resolution Rings
The multi-resolution rings are a set of concentric, non-overlapping rings with
exponentially increasing radii
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A neighbor is placed in the appropriate ring of
a node depending on the peer’s latency to it
Exponentially increasing ring radii provides
authoritative local information
A ring membership management scheme is
used to further improve the diversity of nodes
within each ring
– The set of neighbors that form the largest
hypervolume k-polytope in a non-exported
local coordinate space is selected
– For k = 3, three nodes from each ring that
form the largest triangle are chosen
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Multiple Constraint System
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r=α
r=αs2
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Discover a node in the solution space that
satisfies the given constraints
Distance to the solution space s is calculated
as the sum of the square distance away from
meeting each constraint
– In this example, αa, αb , and αc are the latency
constraints to targets A, B, and C
respectively
Protocol similar to closest node discovery,
but uses s instead of d
αa
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αb
Summary
B
A
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αc
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Meridian can solve frequently encountered network positioning problems
Meridian is accurate, resilient to network dynamics, simple and lightweight
– Avoids many of the pitfalls of virtual coordinates
It remains to be seen whether Meridian can be applied to other network
positioning problems