Multicast Pull Scheduling

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Multicast Pull Scheduling

• Kirk Pruhs

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The Big Problem
Movie Distribution
Olympics
Database Replication via Internet
Software Download
Harry Potter Book Download
Pay-Per-View Movies
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The Standard Centralized Unicast Pull Approach is
Not Scalable

• Creates unnecessary network congestion
• Overloads the server

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One Possible Solution Multicast
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Response Times for the 3 Different Multicast
Distribution Methods
Unicast Pull
Multicast Pull
Average response time
Multicast Push
High load
Low load
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Appropriate Distribution Method Depends on
Popularity of Data
Multicast Push
Unicast Pull
Multicast Pull
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Another Application (RODS) Realtime Outbreak
Detection System

• Developed at Pitt
• Deployed in Utah for
• Winter Olympics
• Now collects information
• on 70 of doctors visits
• in Utah
• Since the anthrax attacks,
• RODS has received lots of
• funding

http//www.health.pitt.edu/rods/
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Project Goals

• Build a prototype data dissemination system that
  uses all three basic data dissemination methods
  appropriately
• Supported by an NSF grant from ANIR program
• Joint work with Panos Chysanthis and Vincenzo
  Liberatore
• Study the interesting data management problems
  that arise in such a system
• Supported by an NSF grant from CCR program

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Middleware Architecture and Data Management Issues
Application Layer
Server Side
Client Side
Document Selection
Unicast Pull Scheduling
Multicast Push Scheduling
Multicast Pull Scheduling
Indexing
Caching
Multicast Transport Layer, e.g. Java Reliable
Multicast
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Rest of the Talk Multicast Pull Scheduling
From www.direcpc.com
From Newsweek magazine
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Simple Example Instance of Multicast Pull
Scheduling
Input
Schedule
Average response time (9 18 3 2 )/4
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Standard Worst-case Algorithm Analysis Technique

• Competitive ratio of algorithm A is
• maxI A(I)/Opt(I)
• A(I) is the average response time on input I
  using algorithm A
• Opt(I) is the average response time for the
  optimal schedule
• For example, a 2-competitive algorithm A
  guarantees that it will produce a schedule with
  average response time at most twice of the
  optimal average response time

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Warm-up ProblemUnit Sized Documents

• Obvious Algorithm?
• Most Requests First (MRF) Broadcast the document
  with the most requests
• Surprisingly, MRF has unbounded competitive ratio
  (proof next slide)
• Moral Multicast pull scheduling is trickier than
  it might first appear

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Most Requests First (MRF) is not
anO(1)-competitive algorithm
Input
Average response time n
MRF
Optimal
Average response time 1
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There is no O(1)-competitive Online Server
Scheduling Algorithm for Multicast Pull
Input
Average response time n
Online schedule
Average response time 1
Optimal schedule
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Resource Augmentation Analysis

• Compare the limited (e.g. online) algorithm with
  more resources (e.g. a faster processor or more
  processors) to the optimal algorithm with less
  resources
• Online algorithm A is s-speed c-competitive if
• maxI As(I)/Opt1(I) lt c
• Subscript denotes processor speed
• Example A 2-speed 3-competitive algorithm
  equipped with a speed 2 processor guarantees an
  average response time at most 3 times the optimal
  average response time for a 1 speed processor

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Classic Server QoS Curves

• Online is not
• O(1)-competitive
• Online is O(1)-speed
• O(1)-competitive

Online
Optimal
Average response time
High load
Low load
Fast processor
Slow Processor
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Old Chinese Saying

• Three blind shoemakers are better than one
  politician

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Most Requests First (MRF) is not
anO(1)-competitive algorithm
O(1)-speed
Input
Average response time n
MRF
Optimal
Average response time 1
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The Power of the Adversary in Multicast Pull
Scheduling

• Recall general lower bound instance
• Intuition The adversary forces the online
  algorithm to labor on sequential work

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Definition of Parallel and Sequential Work
Rate work is completed
Rate work is completed
low
low
high
high
Processing power devoted to the work
Processing power devoted to the work
Parallel work
Sequential work
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Another Application Where Sequential Work Arises
Scheduling Jobs on a Multi-Processor
Parallel work
Sequential work
Input
One Possible Optimal Schedule
P1
P2
Average response time ( 6 3 8)/3
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The Main Result to Date (with Jeff Edmonds)

• A method to construct a multicast pull scheduling
  algorithm B from a nonclairvoyant unicast
  scheduling algorithm A.
• If algorithm A is an s-speed c-competitive
  algorithm when jobs have parallel and sequential
  components, then B is a (2 e )s-speed
  c-competitive
• Formalizes the surprising insight that the
  difficulty of multicast pull scheduling the
  difficulty of unicast scheduling of jobs with
  parallel and sequential components

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Constructing the Multicast Pull Algorithm B from
the Unicast Algorithm A
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Equipoise Algorithm for Unicast Scheduling of
Jobs with Parallel and Sequential Components

• Equipoise (Round Robin) transmits each file at
  the same rate.
• Edmonds (1999) showed that the algorithm
  Equipoise is a (2 e )-speed O(1
  1/e)-competitive algorithm

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The BEquipoise Multicast Pull Algorithm

• BEquipoise broadcasts each document at a rate
  proportional to the number of requests to that
  document
• The algorithm BEquipoise is a (4e)-speed O(1
  1/e)-competitive algorithm
• BEquipoise will work reasonably well if the
  server load lt ¼
• Bequipoise is not an 2-speed O(1)-competitive
  algorithm

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Possible O(1)-competitive (1e)-speed Algorithms ?

• Unit sized files Longest Wait First (LWF) Send
  out the document where the sum of the ages of the
  outstanding requests is maximized
• Arbitrary sized files Longest Total Stretch
  First (LTSF) Send out the document where the sum
  of the ages of the outstanding requests, divided
  by the file size, is maximized
• Appear to be the current experimental champions
  (Acharya and Muthukrishnan)

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Future Directions

• Are LWF and LTSF (1 e)-speed O(1
  1/e)-competitive algorithms for multicast pull
  scheduling?
• If not, is an (1 e)-speed O(1
  1/e)-competitive algorithm possible?
• One possibility is to find an (1 e)-speed O(1
  1/e)-competitive algorithm for unicast scheduling
  of jobs with arbitrary speed-up curves, and to
  remove the factor of two in the speed in our
  reduction.
• Is there an O(1)-competitive polynomial-time
  offline algorithm for multicast pull scheduling?
• The problems are known to be NP-hard (Erlebach
  and Hall)
• Open for both the case of unit sized files and
  arbitrary sized files

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Every talk has to have a Dilbert cartoon.