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Network Working Group                                      J. RosenbergRequest for Comments: 2762                                  dynamicsoftCategory: Experimental                                   H. Schulzrinne                                                            Columbia U.                                                          February 2000Sampling of the Group Membership in RTPStatus 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 andRosenberg & Schulzrinne       Experimental                      [Page 1]

RFC 2762                      RTP Sampling                 February 2000   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.Rosenberg & Schulzrinne       Experimental                      [Page 2]

RFC 2762                      RTP Sampling                 February 2000   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 samplingRosenberg & Schulzrinne       Experimental                      [Page 3]

RFC 2762                      RTP Sampling                 February 2000   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 wholeRosenberg & Schulzrinne       Experimental                      [Page 4]

RFC 2762                      RTP Sampling                 February 2000   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:Rosenberg & Schulzrinne       Experimental                      [Page 5]

RFC 2762                      RTP Sampling                 February 2000            / 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.Rosenberg & Schulzrinne       Experimental                      [Page 6]

RFC 2762                      RTP Sampling                 February 2000   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.Rosenberg & Schulzrinne       Experimental                      [Page 7]

RFC 2762                      RTP Sampling                 February 2000   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.Rosenberg & Schulzrinne       Experimental                      [Page 8]

RFC 2762                      RTP Sampling                 February 2000   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         24.4 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.Rosenberg & Schulzrinne       Experimental                      [Page 9]

RFC 2762                      RTP Sampling                 February 2000   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.Rosenberg & Schulzrinne       Experimental                     [Page 10]

RFC 2762                      RTP Sampling                 February 2000   [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.eduRosenberg & Schulzrinne       Experimental                     [Page 11]

RFC 2762                      RTP Sampling                 February 20009 Full Copyright Statement   Copyright (C) The Internet Society (2000).  All Rights Reserved.   This document and translations of it may be copied and furnished to   others, and derivative works that comment on or otherwise explain it   or assist in its implementation may be prepared, copied, published   and distributed, in whole or in part, without restriction of any   kind, provided that the above copyright notice and this paragraph are   included on all such copies and derivative works.  However, this   document itself may not be modified in any way, such as by removing   the copyright notice or references to the Internet Society or other   Internet organizations, except as needed for the purpose of   developing Internet standards in which case the procedures for   copyrights defined in the Internet Standards process must be   followed, or as required to translate it into languages other than   English.   The limited permissions granted above are perpetual and will not be   revoked by the Internet Society or its successors or assigns.   This document and the information contained herein is provided on an   "AS IS" basis and THE INTERNET SOCIETY AND THE INTERNET ENGINEERING   TASK FORCE DISCLAIMS ALL WARRANTIES, EXPRESS OR IMPLIED, INCLUDING   BUT NOT LIMITED TO ANY WARRANTY THAT THE USE OF THE INFORMATION   HEREIN WILL NOT INFRINGE ANY RIGHTS OR ANY IMPLIED WARRANTIES OF   MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE.Acknowledgement   Funding for the RFC Editor function is currently provided by the   Internet Society.Rosenberg & Schulzrinne       Experimental                     [Page 12]