### Abstract

Original language | English |
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Title of host publication | 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 |

Place of Publication | Piscataway, NJ |

Publisher | IEEE Institute of Electrical and Electronic Engineers |

Number of pages | 5 |

DOIs | |

Publication status | Published - 2007 |

MoE publication type | A4 Article in a conference publication |

Event | 5th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks and Workshops - Limasso, Cyprus Duration: 16 Apr 2007 → 20 Apr 2007 |

### Conference

Conference | 5th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks and Workshops |
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Country | Cyprus |

City | Limasso |

Period | 16/04/07 → 20/04/07 |

### Fingerprint

### Keywords

- peer to peer networks
- file distribution

### Cite this

*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

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*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

TY - GEN

T1 - Toward modeling of a single file broadcasting in a closed network

AU - Reittu, Hannu

AU - Norros, Ilkka

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

KW - peer to peer networks

KW - file distribution

U2 - 10.1109/WIOPT.2007.4480079

DO - 10.1109/WIOPT.2007.4480079

M3 - Conference article in proceedings

BT - 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

PB - IEEE Institute of Electrical and Electronic Engineers

CY - Piscataway, NJ

ER -