Playback delay in p2p streaming systems with random packet forwarding

1
Playback delay in p2p streaming systems with
random packet forwarding

• Viktoria Fodor and Ilias Chatzidrossos
• Laboratory for Communication Networks
• School of Electrical Engineering
• KTH, Royal Institute of Technology

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P2P Multimedia Streaming

• Peer-to-peer system
• peers contribute with transmission bandwidth and
  processing power
• system transmission capacity scales as the number
  of peers increases
• Peer-to-peer live streaming
• newly generated content has to be propagated to
  all peers with low delay
• Different from offline content distribution
• strict delay requirements

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Context of this work

• We propose streaming algorithms for mesh based
  streaming systems
• Build an analytic framework for performance
  evaluation
• Verify the validity of our model
• Derive playback delay playout continuity
  charactersitics

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Mesh based overlays (I)

• Peers are organized in a mesh (grid)
• There is minimal overhead in maintaining the
  overlay
• Each peer has a set of neighboring peers that it
  communicates and exchanges data with
• Each data chunk in a mesh overlay goes down a
  spanning tree to reach all peers. That tree is
  different for every packet

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Mesh based overlays (II)

• Different forwarding schemes
• Push a peer decides which data to send to which
  neighbor
• Pull a peer explicitly asks for specific data
  from a neighbor
• Hybrid mixture of the above schemes

How do peers know whether some of their neighbors
have a specific packet or not?
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Buffer contents and buffer maps

• All peers have a buffer to absorb variations in
  packet delivery times
• Any of the packets that a peer has in its buffer
  could be potentially sent to some of its
  neighbors
• Data exchange between neighbors is based on
  information that they have on each others buffer
  contents
• A buffer map is a compact representation of a
  peers buffer, suitable for sending to other peers

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Push scheduling algorithms

• Random scheduling
• Peer constructs the list of neighbors that are
  missing at least one packet that itself has
• Chooses randomly one of them to forward to.
• Chooses randomly one missing packet to send
• Priority Scheduling
• Peer selection same as in the previous case.
• Once the neighbor is chosen, the oldest missing
  packet is sent

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System description

• No playback lag among peers
• At any point in time peers have the same limits
  for their buffers
• Time is slotted
• Length of a time-slot equal to a packet duration
  time
• All transmissions occur within a time-slot
• Synchronous and Asynchronous schemes
• Static Overlay
• Streaming server
• Upload capacity m streaming rate
• N peers
• Upload capacity streaming rate
• Download capacity unconstrained

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Data propagation

• At time-slot i, root node forwards packet i to m
  randomly chosen peers
• Each peer forwards one packet to one of its
  neighbors at each time-slot based on the
  algorithm used
• Buffer map exchanges among neighboring peers
  occur at every time-slot
• Forwarding decision based on perfect knowledge
• After B time-slots, peers start playing out the
  content they have received
• Buffer size Playback delay

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Model skeleton

• Transmission trees are different for each packet
• The path that a packet follows depends on the
  local decisions at the peers
• Peers having a large amount of neighbors generate
  per packet distribution trees that are very
  different
• The position of the peers in the distribution
  trees is statistically the same

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Model parameters

• Number of peers N
• Root capacity m
• Number of neighbors of a peer d
• Buffer size of peers B
• Buffer contents of peer a at time i

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Mathematical model (I)

• Denote by Pij the probability that an arbitrary
  peer is in possession of packet j by the end of
  time-slot i
• Probability that a packet j will be successfully
  played out
• A peer is in possession of a packet at the end of
  a time slot i, if it already had that packet at
  time-slot i-1 or if it did not have it but
  received it by some neighbor during slot i.

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Mathematical model (II)

• We consider an arbitrary peer r that does not
  have packet j and a neighbor thereof, s, that has
  it
• We define the events
• And we get that

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Model validation

• For small values of d, the dispersion of the
  measured probabilities around the mean is big
  whereas as d increases this dispersion becomes
  smaller and smaller

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Playout probability and number of neighbors

• Discrepancy between model and simulations for
  small values of d
• For d gt 8, the model gives a very good match with
  the simulations, verifying our assumption of
  statistical independence
• For d gt 10, the playout probability seems to be
  insensitive to the increase of d

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Playout probability and delay
Random Scheduling
Minimum delay for optimal tree
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Playout probability and delay
Priority scheduling
Minimum delay for optimal tree
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Scalability

• Increase of the minimum playback delay is
  logarithmic in N for both forwarding schedules

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Conclusions

• We have proposed a general model to study the
  playback delay in p2p streaming networks
• We have proved the validity of the model via
  simulations
• The random forwarding proves to be efficient in
  delivering data to a large amount of peers at a
  relatively low delay
• Priority scheduling performs poorly even at high
  playback delays and thus should not be used

20
Playback delay in p2p streaming systems with
random packet forwarding

• Viktoria Fodor and Ilias Chatzidrossos
• Laboratory for Communication Networks
• School of Electrical Engineering
• KTH, Royal Institute of Technology