### Abstract

We examine the stability of wireless networks whose users are distributed over a
compact space. Users arrive at spatially uniform locations with intensity \lambda and each
user has a random number of packets to transmit with mean ??\beta. In each time slot, an
admissible subset of users is selected uniformly at random to transmit one packet. A
subset of users is called admissible when their simultaneous activity obeys the prevailing
interference constraints. We consider a wide class of interference constraints, including
the SINR model and the protocol model. Denote by \mu?? the maximum number of users
in an admissible subset for the model under consideration. We will show that the
necessary condition $\lamba \beta <\mu$ is also su??fficient for random admissible-set scheduling to achieve stability. Thus random admissible-set scheduling achieves stability, if feasible to do so at all, for a broad class of interference scenarios. The proof relies on a description of the system as a measure-valued process and the identi??cation of a Lyapunov function.

Original language | English |
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Place of Publication | Eindhoven |

Publisher | Eurandom |

Number of pages | 20 |

Publication status | Published - 2011 |

### Publication series

Name | Report Eurandom |
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Volume | 2011003 |

ISSN (Print) | 1389-2355 |

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## Cite this

Bouman, N., Borst, S. C., & Leeuwaarden, van, J. S. H. (2011).

*Stability of random admissible-set scheduling in spatial wireless systems*. (Report Eurandom; Vol. 2011003). Eurandom.