An Analytical Study of Low Delay Multitreebased Overlay Multicast

1
An Analytical Study of Low Delay
Multi-tree-based Overlay Multicast

• György Dán and Viktória Fodor
• School of Electrical Engineering
• KTH, Royal Institute of Technology
• Stockholm, Sweden

Peer-to-Peer Streaming and IP-TV Workshop
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Motivation

• Live peer-to-peer streaming
• Many proposed systems
• Push-based vs. Pull-based
• Tree-based vs. mesh-based vs. unstructured
• Multi-hop data delivery
• Failures node departures, packet losses
• Delivery time hard to predict
• Playback delay and playout buffer dimensioning

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Does playback delay matter?

• Designers goalControl the playback delay
  (minimize?)
• Our goalIdentify sources of delay

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A packets eye view of the overlay

• Four components of delay DdDpDtr,oDprDtr,i
  (a pkt size, Cin input bandwidth, Cout output
  bandwidth)

• Tree properties depend on
• Tree-basedOverlay maintenance
• UnstructuredScheduling algorithm

• A spanning tree of the overlay traversed by a
  packet

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One-hop propagation model

• Possession-propagation-reception

1
Layer l-1
Dd
1
Layer l
6
One-hop propagation model
Possession probability

• Possession-propagation-reception

Per-hop delay
Layer l-1
Dd
Reception probability
Layer l
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Multi-hop propagation model

• Without FEC
• Apply the one hop model to every layer
• Result is the convolution of the per-hop delays

• With FEC
• Apply the one hop model to every layer
• Calculate the result iteratively

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Multi-hop propagation model

• Probability of reception by time h in layer l for
  packet j
• Probability of possession by time h in layer l
  for packet j
• Source node initial condition
• Numerical solution
• Converges
• Scalable

• A control theoretic interpretation Dynamical
  system with
• Input signal
• Output signals

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Multi-hop propagation model

• Probability of possession with playback delay b
  (playout deadline of packet j hjb(j-1)a/B)
• Probability of possession for arbitrary node and
  packet
• Inputs of the model
• Initial condition
• Nl number of nodes in layer l
• Fd(h) node-to-node delay distribution

- Source playout strategy - Overlay structure -
Scheduling, structure
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Application Multi-tree overlay

• Source and N nodes
• Source capacity gt mB
• t trees, each node forwards in d trees
• Retransmissions and FEC(n,k) for error control
• Packets sent at round-robin from the source

Tree 2
Tree 3
Tree 1
P3
P2
P1
R3
R2
8
2
5
3
9
6
1
8
7
2
5
4
1
7
6
4
3
9

• Initial condition

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Overlay structure

• Number of nodes per layer (Nl)
• Calculated recursively based on
• Node output capacity distribution
• Prioritization scheme
• Capacity allocation scheme
• Prioritization schemes
• Contribution based
• Contributors prioritized over non-contributors
  (NP)
• Priority proportional to potential contribution
  (P)
• Capacity allocation schemes
• In case of excess capacity
• Proportional contribution (MM)
• Non-proportional contribution (FU)

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Node-to-node Delay

• Input link
• Dtr,iWina/Cin
• Win waiting time of a packet in a G/D/1 queue
• Output link
• Dtr,o Wout uIdat/(?rB), where I?1, ?r/d
  d.r.v
• Wout waiting time as seen by an arriving batch
  of ?r/d packets in a GIX/D/1 queue
• Retransmissions
• Loss detection, etc
• Arrival processes
• What is a realistic model?

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Model validation

• Discrete event driven simulator
• Steady state
• Media server on a 10Mbps-20Mbps link (m50)
• Low bitrate media, B112kbps
• Nodes buffer 15s worth of packets
• Input and output capacity constraints
• Propagation delays
• Random network topology GT-ITM
• Node churn for randomness
• Results shown for packet losses

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Deterministic arrival process
N104,p0.1

• Inf.cap.Cin Cout 10 Mbps
• Inf.incap.Cin 10 MbpsCout128 kbps
• Fin.cap.Cin Cout 128kbps
• Number of trees influences the delay is there
  an optimal number?
• Dpr plays a minor role but increasing importance

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Poisson arrival process
N104,p0.1

• Inf.cap.CinCout10Mbps
• Inf.incap.Cin10MbpsCout128kbps
• Fin.cap.CinCout128kbps
• Queuing delay significant
• Decrease utilization

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Simulation
N104,p0.1

• Inf.incap.Cin10 MbpsCout128 kbps
• Fin.cap.CinCout128 kbps
• Similar to deterministic arrival process

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FEC and retransmissions

• Dynamically adjust playback delay
• FEC cannot achieve ?(b)1
• But FEC can help to keep the playback delay low
• Scalability?

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Capacity allocation and prioritization
N104
FUP

• Capacity allocation
• MM proportional
• FU non-proportional
• Prioritization
• NP contributor/non-contributor
• P proportional to contribution

MMP

• Prioritization and uneven capacity allocation
  best increases the average output capacity of
  the contributing nodes
• Inhomogeneous upload capacity can help to achieve
  better performance

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Conclusion

• Main factors that determine the delay
• Average upload capacity of contributing nodes
• Waiting times in queues at the nodes
• The ways to decrease the end-to-end delay are
• decreasing the number of layers (by
  prioritization), FU allocation, and by increasing
  m as much as possible no fairness...
• using an adequate number of trees (though using a
  few trees only might imperil the stability of the
  overlay for given n, k, p)
• dynamically adjusting the FEC redundancy
• using a bitrate not too close to ECout

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Open questions

• Application to pull-based systems
• Modeling tree structure and delay distributions
• Scalability in terms of delay
• Optimal chunk size and out-degree
• Easy to control in multi-tree-based overlays (?)
• How to control in a pull based overlay?

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An Analytical Study of Low Delay
Multi-tree-based Overlay Multicast

• György Dán and Viktória Fodor
• School of Electrical Engineering
• KTH, Royal Institute of Technology
• Stockholm, Sweden

Peer-to-Peer Streaming and IP-TV Workshop