### Abstract

Congestion control algorithms used in the Internet are difficult to analyze or simulate on a large scale, i.e., when there are large numbers of nodes, links, and sources in a network. The reasons for this include the complexity of the actual implementation of the algorithm and the randomness introduced in the packet arrival and service processes due to many factors such as arrivals and departures of sources and uncontrollable short flows in the network. To make the analysis or simulation tractable, often deterministic fluid approximations of these algorithms are used. These approximations are in the form of either deterministic delay differential equations, or more generally, deterministic functional-differential equations (FDEs). In this paper, we ignore the complexity introduced by the window-based implementation of such algorithms and focus on the randomness in the network. We justify the use of deterministic models for proportionally-fair congestion controllers under a limiting regime where the number of flows in a network is large.

Original language | English (US) |
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Pages (from-to) | 1050-1072 |

Number of pages | 23 |

Journal | IEEE Transactions on Information Theory |

Volume | 50 |

Issue number | 6 |

DOIs | |

State | Published - Jun 1 2004 |

### Keywords

- Delay-differential equations
- Fluid model
- Internet congestion control
- Many-flows asymptotics
- Proportional fairness

### ASJC Scopus subject areas

- Information Systems
- Computer Science Applications
- Library and Information Sciences

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## Cite this

*IEEE Transactions on Information Theory*,

*50*(6), 1050-1072. https://doi.org/10.1109/TIT.2004.828063