Transcript Document 7137238

On the Placement of Web
Server Replicas
Lili Qiu, Microsoft Research
Venkata N. Padmanabhan, Microsoft Research
Geoffrey M. Voelker, UCSD
IEEE INFOCOM’2001, Anchorage, AK, April 2001
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Outline
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Overview
Related work
Our approach
Simulation methodology & results
Summary
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Motivation
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Growing interests in Web
server replicas
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replica
replica
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Internet
replica
replica
replica
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Forms of Web server replicas
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Clients
Content
Providers
Exponential growth in Web usage
Content providers want to offer
better service at lower cost
Solution: replication
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Mirror sites
Content Distribution Networks
(CDNs)
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CDN: a network of servers
Examples: Akamai, Digital Island
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Placement of Web Server Replicas
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Problem specification
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Among a set of N potential sites, pick K sites as replicas
to minimize users’ latency or bandwidth usage
Internet
Clients
Content
Providers
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Related Work
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Placement of Web proxies [LGI+99]
Cache location [KRS00]
Placement of Internet instrumentation
[JJJ+00]
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Our Approach
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Model Internet as a graph
Parameterize the graph using measured inputs
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# requests generated from each region
Distance between different regions
Map the placement problem onto a graph
optimization problem
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Assumption:
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Each client uses a single replica that is closest to it
Solve graph optimization problem
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Using various approximation algorithms
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Minimum K-median Problem
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Given a complete graph
G=(V,E), d(j), c(i,j)
d(j): # requests
c(i,j): distance between node
i and j
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Latency
or hop counts
or other metric to be
optimized
Find a subset V’ V with
|V’| = K s.t. it minimizes
vV minwV’ d(v)c(v,w)
NP-hard problem
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Placement Algorithms
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Tree based algorithm [LGG+99]
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Random
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Assume the underlying topologies are trees, and
model it as a dynamic programming problem
O(N3M2) for choosing M replicas among N potential
places
Pick the best among several random assignments
Hot spot
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Place replicas near the clients that generate the
largest load
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Placement Algorithms (Cont.)
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Greedy algorithm
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Calculate costs of assigning clients to replicas
Select replica with lowest cost
Adjust costs based upon assignment, repeat until
done
Super-Optimal algorithm
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Lagrangian relaxation + subgradient method
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Simulation Methodology
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Network topology
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Randomly generated topologies
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Real Internet network topology
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AS level topology obtained using BGP routing data
from a set of seven geographically dispersed BGP
peers
Web Workload
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Real server traces
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Using GT-ITM Internet topology generator
MSNBC, ClarkNet, NASA Kennedy Space Center
Performance Metric
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Relative performance: costpractical/costsuper-optimal
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Simulation Methodology
(Cont.)
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Simulate a network of N
nodes (100  N  3000)
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Cluster clients using network
aware clustering [KW00]
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IP addresses with the same
address prefix belong to a
cluster
A small number of popular
clusters account for most
requests
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Top 10, 100, 1000, 3000
clusters account for about
24%, 45%, 78%, and 94% of
the requests respectively
Pick the top N clusters
Map them to different nodes
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Simulation Methodology
(Cont.)
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Random trees
Random graphs
AS-level topologies
Sensitivity to the error in the input
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Random Tree Topologies
Tree-based algorithm performs well as expected.
Greedy algorithm performs equally as well.
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Random Graph Topologies
The greedy and hot-spot algorithms
out-perform the tree-based algorithm.
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Large Random Graph Topologies
The greedy performs the best,
and the hot-spot performs nearly as well.
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AS-level Internet Topologies
The greedy performs the best,
and the hot-spot performs nearly as well.
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Effects of Imperfect Knowledge
about Input Data
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Predicted workload (using moving window average)
Perfect topology information
Within 5% degradation when using predicted workload
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Effects of Imperfect Knowledge
about Input Data (Cont.)
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Predicted workload (using moving window average)
Noisy topology information
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Perturb the distance between two nodes i and j by up to a
factor of 2
Within 15% degradation when using
predicted workload and noisy topology information
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Summary
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One of the first experimental studies on placement of
Web server replicas
Knowledge about client workload and topology is needed
for provisioning replicas
The greedy algorithm performs very well
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Within a factor of 1.1 – 1.5 of the super-optimal
Insensitive to noise
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The hot spot algorithm performs nearly as well
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Stay within a factor of 2 of the super-optimal when the
salted error is a factor of 4
Within a factor of 1.6 – 2 of the super-optimal
Obtaining input data
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Moving window average for load prediction
Using BGP router data to obtain topology information
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Conclusion
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Recommend using the greedy
algorithm for deciding the placement
of Web server replicas
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Acknowledgement
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Craig Labovitz
Yin Zhang
Ravi Kumar
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Comments on greedy
algorithm performance
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Worst-case performance: unbounded
Bad example
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A full homogeneous binary tree with n=2i leaves
and n caches
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optimal cost = 0
0
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greedy cost = (n-1)*d
d
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d
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d
However, the worst-case scenario seems
unlikely to occur in real and random
topologies
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Simulation Results in
Random Tree Topologies
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Random Tree Topologies
Tree-based algorithm performs well as expected.
Greedy algorithm performs equally as well.
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Random Graph Topologies
The greedy and hot-spot algorithms
out-perform the tree-based algorithm.
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Large Random Graph Topologies
The greedy performs the best,
and the hot-spot performs nearly as well.
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AS-level Internet Topologies
The greedy performs the best,
and the hot-spot performs nearly as well.
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Simulation Results in
Real Internet Topologies
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Obtaining Input Data
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Workload
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The number of requests generated by popular
client clusters
Stable
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Placement algorithm can use moving window average
for predicting load with negligible impact on
performance
Network topology
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Propagation delay
Hop count
AS hop count
Internet weather map
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Placement of Web Server Replicas
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Goal
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replica
replica
Internet
replica
replica
replica
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Minimum K-median
problem
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Clients
Placing K replicas to
minimize users’ latency
or bandwidth usage
Content
Providers
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Select K servers to
minimize the sum of
assignment costs
NP-hard problem
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