Adaptive Multicast Tree Construction for Elastic Data Streams

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Adaptive Multicast Tree Construction for Elastic
Data Streams

• Ying Zhu, Ken Q. Pu
• University of Ontario Institute of Technology
  (UOIT), Canada
• IEEE Global Communications Conference (GLOBECOM
  2008)
• ying.zhu_at_uoit.ca, ken.pu_at_uoit.ca

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Overlay Multicast

• Multicast in overlay peer-to-peer networks
• Fast deployable and flexible
• Applications to P2P file sharing, multimedia
  streaming, content distribution,
• Approach construction of multicast tree or trees
  in the overlay network
• Some challenges
• Limited available bandwidth in bottleneck links
• Node dynamics and variations in transmission
  rates
• Cross-traffic interference among competing
  multicast sessions

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Multicasting of Elastic Data

• Multimedia data stream can be downsampled
• Using packet drop policies to change from a
  higher transmission rate to a lower transmission
  rate
• Examples of such elastic data
• voice data
• video streams
• sensor readings
• stock quotes
• Downsampling provides potential for better
  utilization of underlying network resources
• Easily implementable on overlay nodes which have
  capabilities of data replication and manipulation

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Construction of Multicast Trees for Elastic Data

• Problem
• Multiple multicast sessions
• Each multicast session consists of a source node
  and a set of receiver nodes
• A multicast tree is constructed for each
  multicast session
• Every receiver in a given session can express a
  quality-of-service requirement on its received
  data stream through a utility function
• Goal is to maximize receivers utilities while
  minimizing network load

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Node Capabilities

• A fundamental advantage of overlay multicast is
  the assumption that each node has the following
  capabilities
• Each node maintains the list of multicast
  sessions for each of its outgoing links
• Each node performs bandwidth allocation of its
  outgoing links for their respective multicast
  sessions
• Each node performs replication and downsampling
  (if necessary) of data before multicasting to its
  children

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Receiver Utility Function

• Different receivers may have differing
  requirements or preferences in receiving the same
  multicast data
• We propose to use a utility function Uv to map
  receiving rate to a measure of preference for
  receiver v
• Examples

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Receiver Utility Function

• Different receivers may have differing purposes
  hence requirements in receiving the same
  multicast data
• We propose to use a utility function Uv to map
  receiving rate to a measure of preference for
  receiver v
• Examples

This receiver prefers rates up to 5 but gives no
more preference for higher rates
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Receiver Utility Function

• Different receivers may have differing purposes
  hence requirements in receiving the same
  multicast data
• We propose to use a utility function Uv to map
  receiving rate to a measure of preference for
  receiver v
• Examples

This receiver requires at least rate of 2 but no
preference for higher rates
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Receiver Utility Function

• Different receivers may have differing purposes
  hence requirements in receiving the same
  multicast data
• We propose to use a utility function Uv to map
  receiving rate to a measure of preference for
  receiver v
• Examples

This receiver always prefers higher rates
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Receiver Utility Function

• Different receivers may have differing purposes
  hence requirements in receiving the same
  multicast data
• We propose to use a utility function Uv to map
  receiving rate to a measure of preference for
  receiver v
• Examples

NOTE Utility functions are always monotonic.
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Multicast Trees Construction

• Given A set of multicast sessions and for each
  session, a source and a set of receivers
• Objectives
• Construct a multicast tree for every session
• For each link, the sum of flows from all the
  trees does not exceed the capacity of the link
• Receivers utilities are maximized
• A trees utility is the sum of all its
  receivers utilities
• A receiver vs utility, Uv(r), maps its rate r
  in the tree to a preference measure
• r is simply the capacity of the lowest-capacity
  link in the path from source to v in the tree
• Network load is mnimized
• Network load is the sum of all the flows from
  all the multicast trees

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Path Construction by Lexicographical Ordering

• Given a path p from s to t
• utility of p, U(p) is the utility of t
• load of p, L(p), is the sum of flows on links in
  p
• Goal Find a path from source s to target t that
  maximizes U while minimizing L
• Multi-objective optimization by lexicographical
  ordering
• if U(p1) gt U(p2), p1 is better than p2
• if U(p1) U(p2) and L(p1) lt L(p2), p1 is better
  than p2
• otherwise, p2 is better than p1
• Optimal path can be computed by Dijkstras
  algorithm by using the above ordering instead of
  distance comparison

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Problem with Lexicographical Ordering

• Because we order by U first, the utility is
  weighted much more than the load in finding the
  optimal path
• Example
• Path p1 (a,d) is clearly better than path p2
  (a,b,c,d)? it has a slightly lower rate but much
  lower network load
• But p1 will be selected over p2 by
  lexicographical ordering
• Need more control over the tradeoff between U and
  L

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Path Optimizing by Scoring Function

• We propose to use a scoring function f(u,l)
  maps u and l to a single score
• We define a simple separable scoring function
• f(u,l) u e-al, for some constant a gt 0
• Separable means f(u,l) is in the form g(u)
  h(l)
• By varying a, we can control preference between
  utility maximizing and load minimizing
• Proposition If a path p is optimal according to
  a separable scoring function f, then any prefix
  subpath of p is optimal w.r.t. f.

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Optimal-Path Algorithm

• Proposition Dijkstras algorithm can be used to
  find an optimal path w.r.t. any separable scoring
  function.
• The Optimal-Path algorithm is a slight variation
  of Dijkstras shortest path algorithm
• Paths are compared using scoring function on the
  flows instead of distances
• A maximum in-flow to the source is added

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Single Session Multicast Tree

• Optimal tree construction is NP-complete
• We propose an iterative heuristic algorithm using
  Optimal-Path algorithm
• Initially tree contains only the source.
• For each receiver r, find an optimal path in the
  network from any node already in the tree to r.
• Add this path to the tree.
• To avoid introducing cycles, if r is already in
  the tree (from an earlier iteration), then detach
  r and its subtree, and do 2) and 3).

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Multiple Session Multicast Trees

• Path construction requires more information than
  for single-session case
• Need to manage allocation of bandwidth of single
  link to multiple sessions
• Each P2P downstream link maintains these
  information
• total bandwidth of link
• bandwidth allocation to each session for this
  link
• available unused bandwidth for this link
• The P2P management layer manages bandwidth used
  by multiple sessions and performs fair bandwidth
  allocation if total requested rate exceeds
  physical capacity

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Multiple Session Multicast Construction

• Construction of multiple session trees uses
• Information of per-session available bandwidth
  (fairly allocated and maintained by upstream node
  of each P2P link)
• An iterative algorithm that does incremental
  adjustment by continually re-building multicast
  trees for the sessions
• Except for the first iteration, it uses a slight
  variation of the single session multicast tree
  algorithm by starting with an existing tree
  instead of an empty tree

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Simulation Results (1)

• Set up
• Random networks were generated using network
  generator Brite.
• 3 types of networks generated, with various
  network sizes and numbers of multicast receivers.
• Each network has 15 multicast sessions.

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Simulation Results (2)

• The iterative algorithm converges within 50
  iterations, for all three network sizes.

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Simulation Results (3)

• Network size 250
• receivers 50
• During runtime, a network failure is introduced
  by randomly removing links in the network.
• Iterative algorithm recovers quickly from the
  failure.
• It is adaptive to network dynamics.
• The lower throughput is due to sparser network
  links, hence more sharing of physical capacity by
  multiple sessions.

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Future Work