### Abstract

We consider the problem of scheduling the transmissions of multiple data users (flows) sharing the same wireless channel (server). The unique feature of this problem is the fact that the capacity (service rate) of the channel vades randomly with time and asynchronously for different users. We study a scheduling policy called the exponential scheduling role, which was introduced in an earlier paper. Given a system with N users, and any set of positive numbers {a_{n}}, n = 1, 2,..., N, we show that in a heavy-traffic limit, under a nonrestrictive 'complete resource pooling' condition, this algorithm has the property that, for each time t, it (asymptotically) minimizes max_{n} a _{n}q̃_{n} (t), where q̃_{n} (t) is the queue length of user n in the heavy-traffic regime.

Original language | English (US) |
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Pages (from-to) | 1021-1045 |

Number of pages | 25 |

Journal | Advances in Applied Probability |

Volume | 36 |

Issue number | 4 |

DOIs | |

State | Published - Dec 1 2004 |

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### Keywords

- Complete resource pooling
- Exponential rule
- Heavy-traffic limit
- Optimality
- Quality of service
- Queueing network
- Scheduling
- State space collapse
- Wireless network
- Workload

### ASJC Scopus subject areas

- Statistics and Probability
- Applied Mathematics

### Cite this

*Advances in Applied Probability*,

*36*(4), 1021-1045. https://doi.org/10.1239/aap/1103662957