FineGrained Layered Multicast

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Fine-Grained Layered Multicast

• John Byers
• Dept. of Computer Science, Boston University
• www.cs.bu.edu/byers
• Digital Fountain, Inc.
• www.digitalfountain.com
• Joint work with Michael Luby and Michael
  Mitzenmacher

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Multicast for Content Delivery
Sender
Receivers

• Pro one copy of packet per link -- saves
  bandwidth
• Cons challenges of reliability and congestion
  control, especially as session size scales

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Congestion Control Goals

• End-to-end No special router support
• Multi-rate Heterogeneous reception rates
  supported.
• Non-adaptive sender Sender behaves no
  differently whether one or a million receivers.
• Same outgoing packets independent of number of
  hosts
• Receiver-driven Each receiver autonomously
  adjusts reception rate
• Friendly to the network (bursts, buffer
  overflows) and fair to other flows (e.g. TCP)

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Base Solution Layered Multicast (initiated by
McCanne, Jacobson, Vetterli, SIGCOMM 1997)

• Basic Ideas
• Set of multicast groups for each session with
  geometrically increasing rates (1, 1, 2, 4, 8,
  16, ..).
• Receivers adjust reception rate by joining and
  leaving multicast groups in cumulative order.
• Challenges
• how to ensure TCP-friendliness?
• how to coordinate receivers behind a bottleneck?
• only works when content encoding tolerates
  rate-adaptation (layered video coding, FEC codes).

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One Instantiation RLC (Vicisano, Rizzo,
Crowcroft - Infocom 1998)
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RLC Protocol Basics

• Sender places increase signals in packets.
• Cumulative increase signals signal j applies to
  all layers up through j.
• Frequency of increase signals inversely
  proportional to layer rate.
• Receiver measures loss, observes increase
  signals, and adjusts reception rate accordingly
• Leave highest layer if loss.
• Join the next highest layer at an increase signal
  if no loss.

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Experience with RLC

• Coarse-grained approximation to additive
  increase.
• TCP-like in simulation.
• Early analysis/notions of TCP-friendliness.
• Adverse network impacts in practice
• Doubling causes abrupt rate increases.
• Large buffer overflows bursts of dropped
  packets.
• Also, IGMP leave latency can be substantial (not
  specific to the RLC scheme).
• Addressed in NGC 2000 companion paper.

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Fine-Grained Layered Multicast

• Receiver-driven, AIMD, multirate multicast
  congestion control

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What is Fine-Grained?

• So far...
• Cumulative subscription levels.
• Rate increases are multiplicative.
• Desired behavior more like TCP.
• Additive increase, multiplicative decrease.
• We give efficient non-cumulative layering scheme.
• What are the tradeoffs?
• We provide a framework in which to find out.
• Caveat Only applications which can take
  advantage of non-cumulative layering stand to
  benefit.

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Digital Fountain Approach (Byers, Luby,
Mitzenmacher, Rege SIGCOMM 98)
n
Source
Encoding Stream
Transmission
Received
n
Can recover file from any set of n encoding
packets.
Message
n
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Cumulative vs. Non-cumulative

• Standard cumulative layering
• Powers of two achievable.
• Example non-cumulative layering
• Any integral rate achievable by binary counting.
• But undesirable across other metrics

1, 1, 2, 4, 8, ...
1, 2, 4, 8, ...
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Four Metrics of a Layering Scheme

• Density
• Reception granularity
• Dilation
• Join/leave complexity

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Density

• Definition number of layers to support rates in
  normalized interval 1, R.
• Measures scalability of multicast group
  utilization.
• Example 1, 1, 2, 4, 8, scheme has logarithmic
  density in R.
• Schemes with polynomial density require use of an
  unscalable number of multicast groups.

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Reception Granularity

• Definition worst case ratio between receivers
  desired rate k and maximum achievable rate j lt k.
• Measures fine-grainedness.
• Example 1, 1, 2, 4, 8, scheme with cumulative
  layering has reception granularity of approx 2.
  A receiver who desires 15 can receive only 8.
• Example a 1, 2, 4, 8, scheme with
  non-cumulative layers has (optimal) reception
  granularity 1.

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Dilation (of a link)

• Definition ratio of total bandwidth demanded by
  all downstream receivers over maximum rate
  demanded by one downstream receiver.
• Measure of wasted bandwidth.

Cumulative Dilation 1
Non-Cumulative Dilation 16/9
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Join/Leave Complexity

• Definition worst-case number of join/leave
  operations to perform additive increase/multiplica
  tive decrease.
• Measures signalling overhead.
• Example Additive increase in non-cumulative
  1, 2, 4, 8, ... scheme can require
  joining/leaving log R layers.

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Comparison of Schemes
Density Granularity
Dilation AIMD Cumulative
log R 2 1
N/A
Non-Cum log R 1
near 2 log R
Fibonacci O(log R) 1
near 1.62 O(1)
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Fibonacci Layering Sequences

• B0 1, B1 2,
• Bj Bj-1 Bj-2 1 for j gt 1.
• Sequence Fib1 1, 2, 4, 7, 12, 20, 34,
• Increase by 1 Find smallest unsubscribed layer
  j. Join layer j, leave layers j-1 and j-2.

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Fibonacci Layering Sequences

• Multiplicative decrease Drop top layer.
• Approximate factor of two decrease
• What is approximate?
• Key fact Subscription sequences (as a bit
  string) do not have runs of zeroes longer than 2.
• Informal intuition Resulting density of
  subscription sequences bounds decrease factor.
• Decreases drop rate by a factor between 0.39 and
  0.62.
• Better precision can be obtained with more
  joins/leaves

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Improved Non-cumulative Fine-Grained Schemes

• Fibonacci scheme
• Wide range of variations possible

Density Granularity Dilation
Complexity O(log R) 1
near 1.62 O(1)
Exponential growth for Fibonacci numbers
Golden ratio
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Fibonacci Congestion Control Analysis

• Need average-case analysis over range of drop
  rates for TCP-fairness.
• Our scheme should behave fairly with TCP.
• One measure long term average rate.
• Use general TCP(a,b) analysis.
• Additive increase a, multiplicative decrease b.
• Derive equation for average throughput as
  function of a, b, and random loss rate p.
• See e.g., Yang Lam, ICNP 00 or Floyd,
  Handley, Padhye 00 manuscript.

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Fibonacci Congestion Control Analysis

• Multicast has no specific round time
• Choose aggressive parameter Q corresponding to
  target TCP round trip time.
• Increase by 1 every Q seconds.
• Use TCP(a,b) analysis to set parameters which are
  fair to an equally aggressive TCP.

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Equations The Bottom Line

• For a target TCP RTT R, base layer bandwidth B0
  and golden ratio g set
• to achieve TCP-friendly throughput, using

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Fibonacci vs. RLC

• Fibonacci layering has smoother behavior.

Fibonacci
RLC
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Fibonacci and TCP

• Similar sawtooth behavior

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Conclusions

• Fine-grained provides AIMD multirate congestion
  control using non-cumulative layers.
• Framework and metrics for layering schemes.
• Only applications which can take advantage of
  non-cumulative layering stand to benefit
• FEC-encoded content (Digital Fountain style) is
  one.
• Are there others?

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For more informationwww.cs.bu.edu/byerswww.di
gitalfountain.comThank you.