### Abstract

In broadcast channels, network utility maximization formulates a scheduling problem in order to maximize a sum of given utility functions. It is known that the network utility maximization is achieved if a gradient method is used. In this paper, however, we show that the network utility maximization is achieved only if a gradient method is used. That proves the equivalence between a problem formulated by the network utility maximization and a problem with a gradient method. The gradient method simplifies the object function of a scheduling problem by modifying utility functions to a gradient form, so that it makes easy to deal with the problem. We apply the gradient method to a problem with utility functions given by generalized proportional fairness. It is revealed that using the gradient method for the generalized proportional fairness is equivalent to applying a binomial approximation. Simulation results are presented with various scheduling parameters.

Original language | English |
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Title of host publication | 2011 IEEE 73rd Vehicular Technology Conference, VTC2011-Spring - Proceedings |

DOIs | |

Publication status | Published - 2011 Aug 29 |

Event | 2011 IEEE 73rd Vehicular Technology Conference, VTC2011-Spring - Budapest, Hungary Duration: 2011 May 15 → 2011 May 18 |

### Other

Other | 2011 IEEE 73rd Vehicular Technology Conference, VTC2011-Spring |
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Country | Hungary |

City | Budapest |

Period | 11/5/15 → 11/5/18 |

### All Science Journal Classification (ASJC) codes

- Computer Science Applications
- Applied Mathematics
- Electrical and Electronic Engineering

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## Cite this

*2011 IEEE 73rd Vehicular Technology Conference, VTC2011-Spring - Proceedings*[5956391] https://doi.org/10.1109/VETECS.2011.5956391