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On the Placement of Web Server Replicas

Lili Qiu, Microsoft ResearchVenkata N. Padmanabhan, Microsoft Research

Geoffrey M. Voelker, UCSD

IEEE INFOCOM’2001, Anchorage, AK, April 2001

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Outline Overview Related work Our approach Simulation methodology & results Summary

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Motivation Growing interests in Web

server replicas Exponential growth in Web usage Content providers want to offer

better service at lower cost Solution: replication

Forms of Web server replicas Mirror sites Content Distribution Networks

(CDNs) CDN: a network of servers Examples: Akamai, Digital Island

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Clients Content Provider

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Placement of Web Server Replicas

Problem specification Among a set of N potential sites, pick K sites as

replicas to minimize users’ latency or bandwidth usage

Internet

ClientsContent

Providers

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Related Work Placement of Web proxies [LGI+99] Cache location [KRS00] Placement of Internet instrumentation

[JJJ+00]

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Our Approach Model Internet as a graph Parameterize the graph using measured inputs

# requests generated from each region Distance between different regions

Map the placement problem onto a graph optimization problem

Assumption: Each client uses a single replica that is closest to it

Solve graph optimization problem Using various approximation algorithms

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Minimum K-median Problem

Given a complete graph G=(V,E), d(j), c(i,j)

d(j): # requests c(i,j): distance between node

i and j Latency or hop counts or other metric to be

optimized Find a subset V’ V with |

V’| = K s.t. it minimizes

vV minwV’ d(v)c(v,w) NP-hard problem

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Placement Algorithms Tree based algorithm [LGG+99]

Assume the underlying topologies are trees, and model it as a dynamic programming problem

O(N3M2) for choosing M replicas among N potential places

Random Pick the best among several random

assignments Hot spot

Place replicas near the clients that generate the largest load

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Placement Algorithms (Cont.)

Greedy algorithm Calculate costs of assigning clients to replicas Select replica with lowest cost Adjust costs based upon assignment, repeat until

done

Super-Optimal algorithm Lagrangian relaxation + subgradient method

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Simulation Methodology Network topology

Randomly generated topologies Using GT-ITM Internet topology generator

Real Internet network topology AS level topology obtained using BGP routing data from

a set of seven geographically dispersed BGP peers Web Workload

Real server traces MSNBC, ClarkNet, NASA Kennedy Space Center

Performance Metric Relative performance: costpractical/costsuper-optimal

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Simulation Methodology (Cont.)

Simulate a network of N nodes (100 N 3000)

Cluster clients using network aware clustering [KW00]

IP addresses with the same address prefix belong to a cluster

A small number of popular clusters account for most requests

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.) 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

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.) Predicted workload (using moving window

average) Noisy topology information

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 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

Within a factor of 1.1 – 1.5 of the super-optimal Insensitive to noise

Stay within a factor of 2 of the super-optimal when the salted error is a factor of 4

The hot spot algorithm performs nearly as well Within a factor of 1.6 – 2 of the super-optimal

Obtaining input data Moving window average for load prediction Using BGP router data to obtain topology information

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Conclusion Recommend using the greedy

algorithm for deciding the placement of Web server replicas

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Acknowledgement Craig Labovitz Yin Zhang Ravi Kumar

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Comments on greedy algorithm performance Worst-case performance: unbounded Bad example

A full homogeneous binary tree with n=2i leaves and n caches

optimal cost = 0 greedy cost = (n-1)*d

However, the worst-case scenario seems unlikely to occur in real and random topologies

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ddd d

0 0

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Simulation Results inRandom 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 inReal Internet Topologies

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Obtaining Input Data Workload

The number of requests generated by popular client clusters

Stable Placement algorithm can use moving window average

for predicting load with negligible impact on performance

Network topology Propagation delay Hop count AS hop count Internet weather map

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Placement of Web Server Replicas

Goal Placing K replicas to

minimize users’ latency or bandwidth usage

Minimum K-median problem Select K servers to

minimize the sum of assignment costs

NP-hard problem

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