Multicast session membership size estimation

We derive estimators and bounds that drive probabilistic polling algorithms for the estimation of the session size, n, of any potentially large scale multicast session. We base our analysis upon a mapping of polling mechanisms to the problem of estimating the parameter n of the binomial (n,p) distribution. From the binomial model, we derive an interval estimator for n, and we characterize the tradeoff between the estimator's quality and its overhead in a manner readily matched to application requirements. We derive other estimators and bounds that enable applications to treat as a tunable parameter the confidence that they will not exceed their overhead limits. We also suggest revised estimators and other improvements for the mechanisms proposed by Bolot, Turletti and Wakeman (1994), and Nonnenmacher and Biersack (see Proceedings of IEEE INFOCOM '98, Los Alamitos, California, IEEE Computer Society Press, 1998).

[1]  H. J. Larson,et al.  Introduction to the Theory of Statistics , 1973 .

[2]  ZHANGLi-xia,et al.  A reliable multicast framework for light-weight sessions and application level framing , 1995 .

[3]  G. Casella,et al.  Statistical Inference , 2003, Encyclopedia of Social Network Analysis and Mining.

[4]  Don Towsley,et al.  Real-Time Reliable Multicast Using Proactive Forward Error Correction TITLE2: , 1998 .

[5]  Donald F. Towsley,et al.  Measurement and modelling of the temporal dependence in packet loss , 1999, IEEE INFOCOM '99. Conference on Computer Communications. Proceedings. Eighteenth Annual Joint Conference of the IEEE Computer and Communications Societies. The Future is Now (Cat. No.99CH36320).

[6]  I. Olkin,et al.  A Comparison of n Estimators for the Binomial Distribution , 1981 .

[7]  Joerg Nonnenmacher,et al.  Reliable multicast transport to large groups , 1998 .

[8]  Saul Blumenthal,et al.  Estimating the Binomial Parameter n , 1981 .

[9]  J. Wolfowitz,et al.  Introduction to the Theory of Statistics. , 1951 .

[10]  Don Towsley,et al.  Packet loss correlation in the MBone multicast network , 1996, Proceedings of GLOBECOM'96. 1996 IEEE Global Telecommunications Conference.

[11]  Henning Schulzrinne,et al.  RTP: A Transport Protocol for Real-Time Applications , 1996, RFC.

[12]  Martin Fox,et al.  Estimation of the Parameter n in the Binomial Distribution , 1968 .

[13]  Ernst W. Biersack,et al.  Optimal multicast feedback , 1998, Proceedings. IEEE INFOCOM '98, the Conference on Computer Communications. Seventeenth Annual Joint Conference of the IEEE Computer and Communications Societies. Gateway to the 21st Century (Cat. No.98.

[14]  R. F.,et al.  Mathematical Statistics , 1944, Nature.

[15]  Henning Schulzrinne,et al.  Timer reconsideration for enhanced RTP scalability , 1998, Proceedings. IEEE INFOCOM '98, the Conference on Computer Communications. Seventeenth Annual Joint Conference of the IEEE Computer and Communications Societies. Gateway to the 21st Century (Cat. No.98.

[16]  Ian Wakeman,et al.  Scalable Feedback Control for Multicast Video Distribution in the Internet , 1994, SIGCOMM.

[17]  M. Handley.  An Examination of MBone Performance , 1997 .

[18]  Ernst W. Biersack,et al.  Scalable feedback for large groups , 1999, TNET.