1. Modeling the Branching Characteristics and Efficiency Gains in Global Multicast Trees
Robert C. Chalmers and Kevin C. Almeroth
UC Santa Barbara, Computer Science
Infocom 2001
my name
title
work done in conjunction with my advisor

2. web site - http://www.nmsl.cs.ucsb.edu/mwalk/
Goals
goal: to characterize multicast efficiency
efficiency in relation to duplicate unicast streams
goal: to accurately model tree topologies
do inter-domain trees share common properties?
requirement: a clear understanding of the shape of multicast trees
apparent from title - two goals (name them)
when talking about efficiency,
focused on bandwidth efficiency in relation to unicast
mcast is more efficient since packet duplication occurs when paths diverge
when looking at tree topologies,
mainly interested in finding common properties that accurately describe the majority of inter-domain multicast trees
to satisfy either goal we must have a clear understanding of shape
and its impact on measures such as efficiency
focus on where branching occurs within the tree
=> to get a better feeling for how shape impact efficiency, we’ll take a closer look at a few key factors of shape
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3. web site - http://www.nmsl.cs.ucsb.edu/mwalk/
Key Factors of Shape
height
increase in shared links
breadth
near bottom - sharing
near top - duplication
number of receivers
more likely to share
name the factors
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4. web site - http://www.nmsl.cs.ucsb.edu/mwalk/
Key Factors of Shape
height
increase in shared links
breadth
near bottom - sharing
near top - duplication
number of receivers
more likely to share
height is important when looking at efficiency
taller trees are more efficient
since more links are shared
for unicast - higher number of duplicate packets over those links
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5. web site - http://www.nmsl.cs.ucsb.edu/mwalk/
Key Factors of Shape
height
increase in shared links
breadth
near bottom - sharing
near top - duplication
number of receivers
more likely to share
where breadth occurs in the tree is important
late branching improves the efficiency of tall trees since more receivers are taking advantage of the shared links
early branching reduces efficiency since it involves packet duplication
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6. web site - http://www.nmsl.cs.ucsb.edu/mwalk/
Key Factors of Shape
height
increase in shared links
breadth
near bottom - sharing
near top - duplication
number of receivers
more likely to share
the total number of receivers is a key factor
as more receivers join they are more likely to share existing portions of the tree
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7. web site - http://www.nmsl.cs.ucsb.edu/mwalk/
Key Factors of Shape
height
increase in shared links
breadth
near bottom - sharing
near top - duplication
number of receivers
more likely to share
The bottom line is
where does branching occur within the tree
and what is its affect on sharing
=> so how do we go about measuring efficiency?
branching
where does it occur
how does it affect sharing
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8. web site - http://www.nmsl.cs.ucsb.edu/mwalk/
Measuring Efficiency
compare total mcast and ucast hops
 = 1 - Lm / Lu
% gain using mcast
Lm = 18, Lu = 38
 = / 38 = .52
52% reduction in links traversed
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in previous work we introduced a simple metric
compares total number of multicast hops to the total number of unicast hops in a distribution tree
read formula
delta represents the percentage gain in bandwidth utilization achieved by using multicast rather than unicast
in other words, what percentage of duplicate packets are removed from the network
take this tree for example
there are 18 links in the tree, therefore L_m = 18
but if you count the number of hops consumed by duplicate unicast packets (shown in red next to each link) you find L_u = 38
calculating delta tells us that in this case multicast provides a 52% reduction in the number of links traversed
=> but measuring efficiency only goes so far, could we possibly estimate the efficiency of a tree if we new some properties of the tree.
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9. Estimating Efficiency
expands on work to price mcast (Chuang-98)
Lm / Lu = Nk
k  for a range of generated networks
assuming Lu = Lu / N
 = 1 - N
where  = k - 1  = -0.2
expanding on work done by Chuang and Sirbu to price multicast, we have developed an estimate for multicast efficiency which is a function of the number of group receivers.
they presented a power-law (read formula)
where L_m = total number of multicast hops
L_u (bar) = average number of hops between any two nodes in the net
N = total number of receivers
k = economies of scale factor
for a number of generated topologies they found k be approximately 0.8
now, if we make a simplifying assumption that L_u (bar) = the average distance between the source and each receiver
we derive an estimate for delta (read formula)
where N is the number of receivers
and epsilon is the efficiency factor which should be approx -0.2
=> so, this provides us with a power-law characterization of mcast efficiency which depends only on the number of receivers
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10. Estimating Efficiency (cont’d)
20-40 receivers  60-70% improved efficiency
80% savings for 150 users, 90% for 1,000
the characterization is interesting
it tells us how efficient a inter-domain multicast trees of varying sizes should be
we see that within a small number of receivers, mcast out-performs ucast by a wide margin.
on this graph we see a plot for three values of epsilon
the value of -0.2 as derived from Chuang and Sirbu
and values and which is the range we observed for real multicast groups
but, jumping ahead just a little
=> how could we be sure that this estimate was representative of real multicast groups
C and S used mainly generated network topologies and randomly distributed receiver distributions
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11. web site - http://www.nmsl.cs.ucsb.edu/mwalk/
Efficiency Analysis
we collected RTCP and mtrace data for a number of multicast sessions
reconstructed the sessions off-line to measure efficiency
as well as collect topology info such as degree distributions
we already knew that the characterization held for generated tress
the idea was to validate the efficiency characterization for real groups
and then loosen both temporal and spatial constraints to ensure that the characterization held throughout the space between
=> first step was to determine whether receiver duration had an effect on multicast efficiency
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12. web site - http://www.nmsl.cs.ucsb.edu/mwalk/
Receiver Duration
1-minute timeout
early clustering
20-minute timeout
infinite timeout
starting with a small 1-minute timeout while maintaining the original inter-arrival times for each receiver we calculated the metric and plotted it against the estimate
as we see, the data fits quite well
an interesting effect can be seen between 5-10 receivers
where efficiency is higher than expected
due to receiver clustering
a number of receivers join the group from a single sub-net
then we extended the timeout to 5, 20 minutes and eventually to the length of the session
receivers still joined according to the original data, but once in the group they did not leave
data fits quite well
duration does not effect efficiency
=> next step was to randomize the original arrival times
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13. web site - http://www.nmsl.cs.ucsb.edu/mwalk/
Inter-Arrival Times
random receiver activity
by ignoring duration and randomizing inter-arrival times, we ignore the time domain entirely
the data fits the estimate very well
an interesting effect of randomization is a reduction in the magnitude of the efficiency factor from 0.34 to 0.30
due to smoothing over of temporal clustering which normally improves efficiency
=> next step, stretch the spatial domain
|| drops from 0.34 to 0.30
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14. Receiver Distribution
synthesized group distribution
To randomize receiver distribution we generated a synthesized dataset with almost 2000 receivers
random IPs were chosen and traces were made through the Internet using a local source
faithfully represented the inter-domain multicast topology
data fits extremely well
this means that it doesn’t matter which source/receivers you choose, efficiency is similar
|| still lower than for real groups
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15. web site - http://www.nmsl.cs.ucsb.edu/mwalk/
Efficiency and Shape
do consistent efficiencies imply similar shapes?
global mcast trees share common properties
long paths from source to backbone
branching in backbone only occurs at a limited number of peering points
long paths from backbone to receiver
the range of tree shapes are constrained by the underlying network connectivity
efficiencies may be similar, but does that imply the shapes of all these trees are similar
intuitively speaking they should be
for inter-domain multicast trees, most receivers are necessarily in other domains than the source
so, for the source to reach the receivers it must traverse its own domain, the backbone then the domains of each receiver
this should result in tall trees with most branching occurring at a limited number of peering points within the backbone
in general, we’ve found that the range of possible tree shapes are constrained by the underlying network connectivity
=> so, in a way we’ve come full circle. It’s now a question of branching and where the network will allow it to occur within the tree.
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16. Out-degree Frequencies
most nodes have a very low out-degree
result is chains of relay nodes (Pansiot-98)
degree frequencies in Internet routers follow a skewed distribution (Faloutsos-99)
so, if we talk about branching, then we are really looking at out-degree
what we see is that the majority of nodes (almost 80%) of a multicast tree have only a single out-going link
this results in long chains of relay nodes which simply forward the packet along a single path
generally trees are more likely to be tall than wide
similarly, routers in the Internet have been shown to have a skewed degree distribution
again, the underlying network dictates where branching can occur
=> so, our intuition tells us that the majority of the branching should occur at a few well-defined places in the back-bone and at the leaf routers connecting directly to receivers
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17. Average Degree average degree grows with N
and this is indeed what we witness
in general, the total average degree throughout the tree grows with the number of receivers, N
but, if we separate internal links from those directly connecting receivers
we see that the rise in average degree is mainly due to receivers clustering around leaf routers
the body of the tree stays fairly consistent and has an average degree very near 1.5
the backbone has a limited number of candidate links that can be grafted into the tree
as the number of receivers grow, those links become saturated
new growth occurs mainly at leaf routers
which is good for multicast efficiency
internal degree tapers off near 1.5
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18. web site - http://www.nmsl.cs.ucsb.edu/mwalk/
Conclusions
accurately characterized mcast efficiency
over a range of receiver dynamics and distributions
useful in effort to deploy multicast
identified common properties of mcast trees
useful to improve tree generation techniques
shape is constrained by network connectivity
for more information
achieved our two goals
accurately characterized multicast efficiency
identified common properties of inter-domain multicast trees
we’ve shown that our efficiency estimate performs well over a wide range of receiver dynamics and distributions
this should be very useful in the push to deploy multicast as a predictor of future efficiency gains
we’ve identified a number of properties that could be used to improve tree generation techniques
and have validated the use of randomly placed sources and receivers throughout a realistic network topology
most importantly, we have shown that the shape of real multicast trees are constrained by the underlying network topology
if you are interested in more info, please visit our website
any questions
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19. Addendum

20. web site - http://www.nmsl.cs.ucsb.edu/mwalk/
Unicast vs. Multicast
ratio of ucast to mcast path lengths for 1198 receivers in the SYNTH-1 dataset
majority of mcast paths are times the ucast path length
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