Network Working Group J. Rosenberg
Request for Comments: 2762 dynamicsoft
Category: Experimental H. Schulzrinne
Columbia U.
February 2000
Sampling of the Group Membership in RTP
Status of this Memo
This memo defines an Experimental Protocol for the Internet
community. It does not specify an Internet standard of any kind.
Discussion and suggestions for improvement are requested.
Distribution of this memo is unlimited.
Copyright Notice
Copyright (C) The Internet Society (2000). All Rights Reserved.
Abstract
In large multicast groups, the size of the group membership table
maintained by RTP (Real Time Transport Protocol) participants may
become unwieldy, particularly for embedded devices with limited
memory and processing power. This document discusses mechanisms for
sampling of this group membership table in order to reduce the memory
requirements. Several mechanisms are proposed, and the performance of
each is considered.
1 Introduction
RTP, the Real Time Transport Protocol [1], mandates that RTCP packets
be transmitted from each participant with a period roughly
proportional to the group size. The group size is obtained by storing
a table, containing an entry for each unique SSRC seen in RTP and
RTCP packets. As members leave or time out, entries are deleted, and
as new members join, entries are added. The table is thus highly
dynamic.
For large multicast sessions, such as an mbone broadcast or IP-based
TV distribution, group sizes can be extremely large, on the order of
hundreds of thousands to millions of participants. In these
environments, RTCP may not always be used, and thus the group
membership table isn't needed. However, it is highly desirable for
RTP to scale well for groups with one member to groups with one
million members, without human intervention to "turn off" RTCP when
it's no longer appropriate. This means that the same tools and
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systems can be used for both small conferences and TV broadcasts in a
smooth, scalable fashion.
Previous work [2] has identified three major scalability problems
with RTP. These are:
1. Congestion due to floods of RTCP packets in highly dynamic groups;
2. Large delays between receipt of RTCP packets from a single user;
3. Large size of the group membership table.
The reconsideration algorithm [2] helps to alleviate the first of
these. This document addresses the third, that of large group size
tables.
Storage of an SSRC table with one million members, for example,
requires at least four megabytes. As a result, embedded devices with
small memory capacity may have difficulty under these conditions. To
solve this problem, SSRC sampling has been proposed. SSRC sampling
uses statistical sampling to obtain a stochastic estimate of the
group membership. There are many issues that arise when this is done.
This document reviews these issues and discusses the mechanisms which
can be applied by implementors. In particular, it focuses on three
methods for adapting the sampling probability as the group membership
varies. It is important to note that the IETF has been notified of
intellectual property rights claimed in regard to some or all of the
specification contained in this document, and in particular to one of
the three mechanisms: the binning algorithm described below. For more
information consult the online list of claimed rights. The two other
approaches presented are inferior to the binning algorithm, but are
included as they are believed to be unencumbered by IPR.
2 Basic Operation
The basic idea behind SSRC sampling is simple. Each participant
maintains a key K of 32 bits, and a mask M of 32 bits. Assume that m
of the bits in the mask are 1, and the remainder are zero. When an
RTCP packet arrives with some SSRC S, rather than placing it in the
table, it is first sampled. The sampling is performed by ANDing the
key and the mask, and also ANDing the SSRC and the mask. The
resulting values are compared. If equal, the SSRC is stored in the
table. If not equal, the SSRC is rejected, and the packet is treated
as if it has never been received.
The key can be anything, but is usually derived from the SSRC of the
user who is performing the sampling.
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This sampling process can be described mathematically as:
D = (K*M == S*M)
Where the * operator denotes AND and the == operator denotes a test
for equality. D represents the sampling decision.
According to the RTP specification, the SSRC's used by session
participants are chosen randomly. If the distribution is also
uniform, it is easy to see that the above filtering will cause 1 out
of 2**m SSRC's to be placed in the table, where m is the number of
bits in the mask, M, which are one. Thus, the sampling probability p
is 2**-m.
Then, to obtain an actual group size estimate, L, the number of
entries in the table N is multiplied by 2**m:
L = N * 2**m
Care must be taken when choosing which bits to set to 1 in the mask.
Although the RTP specification mandates randomly chosen SSRC, there
are many known implementations which do not conform to this. In
particular, the ITU H.323 [3] series of recommendations allows the
central control element, the gatekeeper, to assign the least
significant 8 bits of the SSRC, while the most significant are
randomly chosen by RTP participants.
The safest way to handle this problem is to first hash the SSRC using
a cryptographically secure hash, such as MD5 [4], and then choose 32
of the bits in the result as the SSRC used in the above computation.
This provides much better randomness, and doesn't require detailed
knowledge about how various implementations actually set the SSRC.
2.1 Performance
The estimate is more accurate as the value of m decreases, less
accurate as it increases. This can be demonstrated analytically. If
the actual group size is G, the ratio of the standard deviation to
mean of the estimate L (coefficient of variation) is:
sqrt((2**m - 1)/G)
This equation can be used as a guide for selecting the thresholds for
when to change the sampling factor, as discussed below. For example,
if the target is a 1% standard deviation to mean, the sampling
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probability p=2**-m should be no smaller than .5 when there are ten
thousand group members. More generally, to achieve a desired standard
deviation to mean ratio of T, the sampling probability should be no
less than:
p > 1 / (1 + G*(T**2))
3 Increasing the Sampling Probability
The above simple sampling procedure would work fine if the group size
was static. However, it is not. A participant joining an RTP session
will initially see just one participant (themselves). As packets are
received, the group size as seen by that participant will increase.
To handle this, the sampling probability must be made dynamic, and
will need to increase and decrease as group sizes vary.
The procedure for increasing the sampling probability is easy. A
participant starts with a mask with m=0. Under these conditions,
every received SSRC will be stored in the table, so there is
effectively no sampling. At some point, the value of m is increased
by one. This implies that approximately half of the SSRC already in
the table will no longer match the key under the masking operation.
In order to maintain a correct estimate, these SSRC must be discarded
from the table. New SSRC are only added if they match the key under
the new mask.
The decision about when to increase the number of bits in the mask is
also simple. Let's say an RTP participant has a memory with enough
capacity to store C entries in the table. The best estimate of the
group is obtained by the largest sampling probability. This also
means that the best estimate is obtained the fuller the table is. A
reasonable approach is therefore to increase the number of bits in
the mask just as the table fills to C. This will generally cause its
contents to be reduced by half on average. Once the table fills
again, the number of bits in the mask is further increased.
4 Reducing the Sampling Probability
If the group size begins to decrease, it may be necessary to reduce
the number of one bits in the mask. Not doing so will result in
extremely poor estimates of the group size. Unfortunately, reducing
the number of bits in the mask is more difficult than increasing
them.
When the number of bits in the mask increases, the user compensates
by removing those SSRC which no longer match. When the number of bits
decreases, the user should theoretically add back those users whose
SSRC now match. However, these SSRC are not known, since the whole
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point of sampling was to not have to remember them. Therefore, if the
number of bits in the mask is just reduced without any changes in the
membership table, the group estimate will instantly drop by exactly
half.
To compensate for this, some kind of algorithm is needed. Two
approaches are presented here: a corrective-factor solution, and a
binning solution. The binning solution is simpler to understand and
performs better. However, we include a discussion of the corrective-
factor solution for completeness and comparison, and also because it
is believed to be unencumbered by IPR.
4.1 Corrective Factors
The idea with the corrective factors is to take one of two
approaches. In the first, a corrective factor is added to the group
size estimate, and in the second, the group size estimate is
multiplied by a corrective factor. In both cases, the purpose is to
compensate for the change in sample mask. The corrective factors
should decay as the "fudged" members are eventually learned about and
actually placed in the membership list.
The additive factor starts at the difference between the group size
estimate before and after the number of bits in the mask is reduced,
and decays to 0 (this is not always half the group size estimate, as
the corrective factors can be compounded, see below). The
multiplicative corrective factor starts at 2, and gradually decays to
one. Both factors decay over a time of cL(ts-), where c is the
average RTCP packet size divided by the RTCP bandwidth for receivers,
and L(ts-) is the group size estimate just before the change in the
number of bits in the mask at time ts. The reason for this constant
is as follows. In the case where the actual group membership has not
changed, those members which were forgotten will still be sending
RTCP packets. The amount of time it will take to hear an RTCP packet
from each of them is the average RTCP interval, which is cL(ts-).
Therefore, by cL(ts-) seconds after the change in the mask, those
users who were fudged by the corrective factor should have sent a
packet and thus appear in the table. We chose to decay both functions
linearly. This is because the rate of arrival of RTCP packets is
linear.
What happens if the number of bits in the mask is reduced once again
before the previous corrective factor has expired? In that case, we
compound the factors by using yet another one. Let fi() represent the
ith additive correction function, and gi() the ith multiplicative
correction function. If ts is the time when the number of bits in the
mask is reduced, we can describe the additive correction factor as:
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/ 0 , t < ts
| ts + cL(ts-) - t
fi(t) = |( L(ts-) - L(ts+)) ---------------- , ts < t < ts+cL(ts-)
| cL(ts-)
| 0 , t > ts + cL(ts-)
\
and the multiplicative factor as:
/ 1 , t < ts
|
| ts + 2cL(ts-) - t
gi(t) | ----------------- , ts < t < ts + cL(ts-)
| cL(ts-)
|
\ 1 , t > ts + cL(ts-)
Note that in these equations, L(t) denotes the group size estimate
obtained including the corrective factors except for the new factor.
ts- is the time right before the reduction in the number of bits, and
ts+ the time after. As a result, L(ts-) represents the group size
estimate before the reduction, and L(ts+) the estimate right after,
but not including the new factor.
Finally, the actual group size estimate L(t) is given by:
-----
\
L(t) = / fi(t) + N*(2**m)
-----
i
for the additive factor, and:
------
| |
| |
L(t)= | | N*(2**m)*gi(t)
for the multiplicative factor.
Simulations showed that both algorithms performed equally well, but
both tended to seriously underestimate the group size when the group
membership was rapidly declining [5]. This is demonstrated in the
performance data below.
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As an example, consider computation of the additive factor. The group
size is 1000, c is 1 second, and m is two. With a mask of this size,
a participant will, on average, observe 250 (N = 250) users. At t=0,
the user decides to reduce the number of bits in the mask to 1. As a
result, L(0-) is 1000, and L(0+) is 500. The additive factor
therefore starts at 500, and decays to zero at time ts + cL(ts-) =
1000. At time 500, lets assume N has increased to 375 (this will, on
average, be the case if the actual group size has not changed). At
time 500, the additive factor is 250. This is added to 2**m times N,
which is 750, resulting in a group size estimate of 1000. Now, the
user decides to reduce the number of bits in the mask again, so that
m=0. Another additive factor is computed. This factor starts at
L(ts-) (which is 1000), minus L(ts+). L(ts+) is computed without the
new factor; it is the first additive factor at this time (250) plus
2**m (1) times N (375). This is 625. As a result, the new additive
factor starts at 1000 - 625 (375), and decays to 0 in 1000 seconds.
4.2 Binning Algorithm
In order to more correctly estimate the group size even when it is
rapidly decreasing, a binning algorithm can be used. The algorithm
works as follows. There are 32 bins, same as the number of bits in
the sample mask. When an RTCP packet from a new user arrives whose
SSRC matches the key under the masking operation, it is placed in the
mth bin (where m is the number of ones in the mask) otherwise it is
discarded.
When the number of bits in the mask is to be increased, those members
in the bin who still match after the new mask are moved into the next
higher bin. Those who don't match are discarded. When the number of
bits in the mask is to be decreased, nothing is done. Users in the
various bins stay where they are. However, when an RTCP packet for a
user shows up, and the user is in a bin with a higher value than the
current number of bits in the mask, it is moved into the bin
corresponding to the current number of bits in the mask. Finally, the
group size estimate L(t) is obtained by:
31
----
\
L(t) = / B(i) * 2**i
----
i=0
Where B(i) are the number of users in the ith bin.
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The algorithm works by basically keeping the old estimate when the
number of bits in the mask drops. As users arrive, they are gradually
moved into the lower bin, reducing the amount that the higher bin
contributes to the total estimate. However, the old estimate is still
updated in the sense that users which timeout are removed from the
higher bin, and users who send BYE packets are also removed from the
higher bin. This allows the older estimate to still adapt, while
gradually phasing it out. It is this adaptation which makes it
perform much better than the corrective algorithms. The algorithm is
also extremely simple.
4.3 Comparison
The algorithms are all compared via simulation in Table 1. In the
simulation, 10,001 users join a group at t=0. At t=10,000, 5000 of
them leave. At t=20,000, another 5000 leave. All implement an SSRC
sampling algorithm, unconditional forward reconsideration and BYE
reconsideration. The table depicts the group size estimate from time
20,000 to time 25,000 as seen by the single user present throughout
the entire session. In the simulation, a memory size of 1000 SSRC was
assumed. The performance without sampling, and with sampling with the
additive, multiplicative, and bin-based correction are depicted.
As the table shows, the bin based algorithm performs particularly
well at capturing the group size estimate towards the tail end of the
simulation.
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Time No Sampling Binned Additive Multiplicative
---- ----------- ------ -------- --------------
20000 5001 5024 5024 5024
20250 4379 4352 4352 4352
20500 3881 3888 3900 3853
20750 3420 3456 3508 3272
21000 3018 2992 3100 2701
21250 2677 2592 2724 2225
21500 2322 2272 2389 1783
21750 2034 2096 2125 1414
22000 1756 1760 1795 1007
22250 1476 1472 1459 582
22500 1243 1232 1135 230
22750 1047 1040 807 80
23000 856 864 468 59
23250 683 704 106 44
23500 535 512 32 32
23750 401 369 24 24
24000 290 257 17 17
24250 198 177 13 13
24500 119 129 11 11
24750 59 65 8 8
25000 18 1 2 2
4.4 Sender Sampling
Care must be taken in handling senders when using SSRC sampling.
Since the number of senders is generally small, and they contribute
significantly to the computation of the RTCP interval, sampling
should not be applied to them. However, they must be kept in a
separate table, and not be "counted" as part of the general group
membership. If they are counted as part of the general group
membership, and are not sampled, the group size estimate will be
inflated to overemphasize the senders.
This is easily demonstrated analytically. Let Ns be the number of
senders, and Nr be the number of receivers. The membership table will
contain all Ns senders and (1/2)**m of the receivers. The total group
size estimate in the current memo is obtained by 2**m times the
number of entries in the table. Therefore, the group size estimate
becomes:
L(t) = (2**m) Ns + Nr
which exponentially weights the senders.
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This is easily compensated for in the binning algorithm. A sender is
always placed in the 0th bin. When a sender becomes a receiver, it is
moved into the bin corresponding to the current value of m, if its
SSRC matches the key under the masked comparison operation.
5 Security Considerations
The use of SSRC sampling does not appear to introduce any additional
security considerations beyond those described in [1]. In fact, SSRC
sampling, as described above, can help somewhat in reducing the
effect of certain attacks.
RTP, when used without authentication of RTCP packets, is susceptible
to a spoofing attack. Attackers can inject many RTCP packets into the
group, each with a different SSRC. This will cause RTP participants
to believe the group membership is much higher than it actually is.
The result is that each participant will end up transmitting RTCP
packets very infrequently, if ever. When SSRC sampling is used, the
problem can be amplified if a participant is not applying a hash to
the SSRC before matching them against their key. This is because an
attacker can send many packets, each with different SSRC, that match
the key. This would cause the group size to inflate exponentially.
However, with a random hash applied, an attacker cannot guess those
SSRC which will match against the key. In fact, an attacker will have
to send 2**m different SSRC before finding one that matches, on
average. Of course, the effect of a match causes an increase of group
membership by 2**m. But, the use of sampling means that an attacker
will have to send many packets before an effect can be observed.
6 Acknowledgements
The authors wish to thank Bill Fenner and Vern Paxson for their
comments.
7 Bibliography
[1] Schulzrinne, H., Casner, S., Frederick, R. and V. Jacobson, "RTP:
a transport protocol for real-time applications", RFC 1889,
January 1996.
[2] J. Rosenberg and H. Schulzrinne, "Timer reconsideration for
enhanced RTP scalability", IEEE Infocom, (San Francisco,
California), March/April 1998.
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[3] International Telecommunication Union, "Visual telephone systems
and equipment for local area networks which provide a non-
guaranteed quality of service," Recommendation H.323,
Telecommunication Standardization Sector of ITU, Geneva,
Switzerland, May 1996.
[4] Rivest, R., "The MD5 message-digest algorithm", RFC 1321, April
1992.
[5] Rosenberg, J., "Protocols and Algorithms for Supporting
Distributed Internet Telephony," PhD Thesis, Columbia University,
Dec. 1999. Work in Progress.
8 Authors' Addresses
Jonathan Rosenberg
dynamicsoft
200 Executive Drive
West Orange, NJ 07052
USA
EMail: jdrosen@dynamicsoft.com
Henning Schulzrinne
Columbia University
M/S 0401
1214 Amsterdam Ave.
New York, NY 10027-7003
USA
EMail: schulzrinne@cs.columbia.edu
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