Toward modeling of a single file broadcasting in a closed network

Hannu Reittu, Ilkka Norros

    Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingsScientificpeer-review

    2 Citations (Scopus)

    Abstract

    One fundamental question in modern communication is how to broadcast a file in an Internet overlay of peers with limited bandwidth. One prominent solution, already realised practically, is 'chunk casting'. The big file is divided into a large number of small chunks, each of which are broadcasted. Because of their small size, a peer can quickly upload such a chunk and their populations start to grow very rapidly in a large system. This makes also plausible that the pattern of the very first chunk replications can have big effect on the relative sizes of the chunk populations later on. On the other hand, the chunk replication process quickly takes a form of deterministic process, well described by some differential equations. The role of the short initial phase is to create initial conditions for the deterministic phase. We furnish an approax to proceed this passage. Due to randomness in the initial phase of evolution, the initial conditions for the differential equations are random. To And their distributions, the initial phase have to be solved. We give a simple example when this can be done. Assuming just two chunks and random encounters, the initial evolution can be coupled with Po lya urn model with well known distribution. Then the corresponding differential equations can be numerically solved and results compared with simulations of the true discrete model. Results seem to match reasonably well already for systems of few hundred nodes. A similar scheme is discussed also for arbitrary number of chunks.
    Original languageEnglish
    Title of host publicationProceedings of the 5th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks, WiOpt 2007. Limassol, Cyprus, 16 - 20 April 2007
    Place of PublicationPiscataway, NJ
    PublisherIEEE Institute of Electrical and Electronic Engineers
    Number of pages5
    DOIs
    Publication statusPublished - 2007
    MoE publication typeA4 Article in a conference publication
    Event5th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks and Workshops - Limasso, Cyprus
    Duration: 16 Apr 200720 Apr 2007

    Conference

    Conference5th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks and Workshops
    CountryCyprus
    CityLimasso
    Period16/04/0720/04/07

    Fingerprint

    broadcasting
    files
    differential equations
    encounters
    communication
    bandwidth
    simulation

    Keywords

    • peer to peer networks
    • file distribution

    Cite this

    Reittu, H., & Norros, I. (2007). Toward modeling of a single file broadcasting in a closed network. In Proceedings of the 5th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks, WiOpt 2007. Limassol, Cyprus, 16 - 20 April 2007 Piscataway, NJ: IEEE Institute of Electrical and Electronic Engineers . https://doi.org/10.1109/WIOPT.2007.4480079
    Reittu, Hannu ; Norros, Ilkka. / Toward modeling of a single file broadcasting in a closed network. Proceedings of the 5th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks, WiOpt 2007. Limassol, Cyprus, 16 - 20 April 2007. Piscataway, NJ : IEEE Institute of Electrical and Electronic Engineers , 2007.
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    abstract = "One fundamental question in modern communication is how to broadcast a file in an Internet overlay of peers with limited bandwidth. One prominent solution, already realised practically, is 'chunk casting'. The big file is divided into a large number of small chunks, each of which are broadcasted. Because of their small size, a peer can quickly upload such a chunk and their populations start to grow very rapidly in a large system. This makes also plausible that the pattern of the very first chunk replications can have big effect on the relative sizes of the chunk populations later on. On the other hand, the chunk replication process quickly takes a form of deterministic process, well described by some differential equations. The role of the short initial phase is to create initial conditions for the deterministic phase. We furnish an approax to proceed this passage. Due to randomness in the initial phase of evolution, the initial conditions for the differential equations are random. To And their distributions, the initial phase have to be solved. We give a simple example when this can be done. Assuming just two chunks and random encounters, the initial evolution can be coupled with Po lya urn model with well known distribution. Then the corresponding differential equations can be numerically solved and results compared with simulations of the true discrete model. Results seem to match reasonably well already for systems of few hundred nodes. A similar scheme is discussed also for arbitrary number of chunks.",
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    Reittu, H & Norros, I 2007, Toward modeling of a single file broadcasting in a closed network. in Proceedings of the 5th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks, WiOpt 2007. Limassol, Cyprus, 16 - 20 April 2007. IEEE Institute of Electrical and Electronic Engineers , Piscataway, NJ, 5th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks and Workshops, Limasso, Cyprus, 16/04/07. https://doi.org/10.1109/WIOPT.2007.4480079

    Toward modeling of a single file broadcasting in a closed network. / Reittu, Hannu; Norros, Ilkka.

    Proceedings of the 5th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks, WiOpt 2007. Limassol, Cyprus, 16 - 20 April 2007. Piscataway, NJ : IEEE Institute of Electrical and Electronic Engineers , 2007.

    Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingsScientificpeer-review

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    PB - IEEE Institute of Electrical and Electronic Engineers

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    ER -

    Reittu H, Norros I. Toward modeling of a single file broadcasting in a closed network. In Proceedings of the 5th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks, WiOpt 2007. Limassol, Cyprus, 16 - 20 April 2007. Piscataway, NJ: IEEE Institute of Electrical and Electronic Engineers . 2007 https://doi.org/10.1109/WIOPT.2007.4480079