On the Placement of Web Server Replicas

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On the Placement of Web Server Replicas

• Lili Qiu, Microsoft Research
• Venkata N. Padmanabhan, Microsoft Research
• Geoffrey M. Voelker, UCSD
• IEEE INFOCOM2001, 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

Internet
replica
replica
replica
replica
replica
Content Providers
Clients
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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
Content Providers
Clients
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Related Work

• Placement of Web proxies LGI99
• Cache location KRS00
• Placement of Internet instrumentation JJJ00

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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
• ?v?V minw?V d(v)c(v,w)
• NP-hard problem

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Placement Algorithms

• Tree based algorithm LGG99
• 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-opti
  mal

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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 n2i 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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0
0
d
d
d
d
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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

Internet
replica
replica
replica
replica
replica
Content Providers
Clients