On multicast trees: structure and size estimation

This work presents a thorough investigation of the structure of multicast trees cut from the Internet and power-law topologies. Based on both generated topologies and real Internet data, we characterize the structure of such trees and show that they obey the rank-degree power law; that most high degree tree nodes are concentrated in a low diameter neighborhood; and that the sub-tree size also obeys a power law.Our most surprising empirical finding suggests that there is a linear ratio between the number of high degree network nodes, namely nodes whose tree degree is higher than some constant, and the number of leaf nodes in the multicast tree (clients). We also derive this ratio analytically. Based on this finding, we develop the Fast Algorithm, that estimates the number of clients, and show that it converges faster than one round trip delay from the root to a randomly selected client.

[1]  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.

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

[3]  Ramesh Govindan,et al.  Heuristics for Internet map discovery , 2000, Proceedings IEEE INFOCOM 2000. Conference on Computer Communications. Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (Cat. No.00CH37064).

[4]  Eitan Altman,et al.  Optimal on-line estimation of the size of a dynamic multicast group , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[5]  Donald F. Towsley,et al.  Multicast session membership size estimation , 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]  Henning Schulzrinne,et al.  RTP: A Transport Protocol for Real-Time Applications , 1996, RFC.

[7]  Jean-Jacques Pansiot,et al.  On routes and multicast trees in the Internet , 1998, CCRV.

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

[9]  Ibrahim Matta,et al.  On the origin of power laws in Internet topologies , 2000, CCRV.

[10]  Bill Cheswick,et al.  Mapping the Internet , 1999, Computer.

[11]  Abhishek Ghose,et al.  On characterizing affinity and its impact on network performance , 2003, MoMeTools '03.

[12]  Marvin A. Sirbu,et al.  Pricing Multicast Communication: A Cost-Based Approach , 2001, Telecommun. Syst..

[13]  Michalis Faloutsos,et al.  On power-law relationships of the Internet topology , 1999, SIGCOMM '99.

[14]  Ian Wakeman,et al.  Scalable feedback control for multicast video distribution in the Internet , 1994, SIGCOMM 1994.

[15]  Kevin C. Almeroth,et al.  Modeling the branching characteristics and efficiency gains in global multicast trees , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

[16]  Hongsuda Tangmunarunkit,et al.  Scaling of multicast trees: comments on the Chuang-Sirbu scaling law , 1999, SIGCOMM '99.

[17]  Albert,et al.  Topology of evolving networks: local events and universality , 2000, Physical review letters.

[18]  Walter Willinger,et al.  The origin of power laws in Internet topologies revisited , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[19]  P. Krishnan,et al.  The cache location problem , 2000, TNET.

[20]  Donald Ervin Knuth,et al.  The Art of Computer Programming , 1968 .

[21]  Randy H. Katz,et al.  Characterizing the Internet hierarchy from multiple vantage points , 2002, Proceedings.Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies.

[22]  Brad Cain,et al.  Source-Specific Multicast for IP , 2006, RFC.

[23]  Kenneth L. Calvert,et al.  Modeling Internet topology , 1997, IEEE Commun. Mag..

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

[25]  Cohen,et al.  Resilience of the internet to random breakdowns , 2000, Physical review letters.

[26]  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.