### Abstract

The multi-carrier proportional fair scheduling (MC-PFS) problem in a multi-user system has been shown to be NP-hard. Carrier by carrier proportional fair scheduling (CC-PFS) is commonly used instead to allocate resources in real-time. Considering the sub-optimal nature of CC-PFS and its popularity, this paper formulates the optimization beyond CC-PFS as a constrained maximum sum rate problem (with users' data rates scheduled by CC-PFS as the constraint) and tackles the problem in two ways. Firstly, the problem is shown to be equivalent to the well-studied generalized assignment problem (GAP) under the assumption of infinitely backlogged data. By considering traffic arrivals, the problem becomes a nonlinear integer programming problem which can be solved by outer approximation (OA) algorithms. Secondly, the problem is shown to be equivalent to a classical trading problem, and a low complexity heuristic algorithm that can be run in real-time is developed based on trading resource blocks (RBs). Using a system scheduling many video call users, we show that in about half of the time slots, the sum rate can be improved over CC-PFS while each user transmits at least as many bits as scheduled by CC-PFS. The heuristic algorithm captures about 30% of the throughput improvement found by OA. Finally, the reason for the improvements over CC-PFS is found to be traffic arrival.

Original language | English (US) |
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Title of host publication | 2011 34th IEEE Sarnoff Symposium, SARNOFF 2011 |

DOIs | |

State | Published - 2011 |

Event | 2011 34th IEEE Sarnoff Symposium, SARNOFF 2011 - Princeton, NJ, United States Duration: May 3 2011 → May 4 2011 |

### Other

Other | 2011 34th IEEE Sarnoff Symposium, SARNOFF 2011 |
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Country | United States |

City | Princeton, NJ |

Period | 5/3/11 → 5/4/11 |

### Fingerprint

### Keywords

- carrier by carrier
- CC-PFS
- GAP
- MC-PFS
- multi-carrier
- multi-user
- OFDMA
- proportional fair
- trading resource blocks
- traffic arrival

### ASJC Scopus subject areas

- Computer Networks and Communications
- Computer Science Applications

### Cite this

*2011 34th IEEE Sarnoff Symposium, SARNOFF 2011*[5876485] https://doi.org/10.1109/SARNOF.2011.5876485

**Optimizing beyond the carrier by carrier proportional fair scheduler.** / Han, Alexander X.; Lu, I-Tai.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*2011 34th IEEE Sarnoff Symposium, SARNOFF 2011.*, 5876485, 2011 34th IEEE Sarnoff Symposium, SARNOFF 2011, Princeton, NJ, United States, 5/3/11. https://doi.org/10.1109/SARNOF.2011.5876485

}

TY - GEN

T1 - Optimizing beyond the carrier by carrier proportional fair scheduler

AU - Han, Alexander X.

AU - Lu, I-Tai

PY - 2011

Y1 - 2011

N2 - The multi-carrier proportional fair scheduling (MC-PFS) problem in a multi-user system has been shown to be NP-hard. Carrier by carrier proportional fair scheduling (CC-PFS) is commonly used instead to allocate resources in real-time. Considering the sub-optimal nature of CC-PFS and its popularity, this paper formulates the optimization beyond CC-PFS as a constrained maximum sum rate problem (with users' data rates scheduled by CC-PFS as the constraint) and tackles the problem in two ways. Firstly, the problem is shown to be equivalent to the well-studied generalized assignment problem (GAP) under the assumption of infinitely backlogged data. By considering traffic arrivals, the problem becomes a nonlinear integer programming problem which can be solved by outer approximation (OA) algorithms. Secondly, the problem is shown to be equivalent to a classical trading problem, and a low complexity heuristic algorithm that can be run in real-time is developed based on trading resource blocks (RBs). Using a system scheduling many video call users, we show that in about half of the time slots, the sum rate can be improved over CC-PFS while each user transmits at least as many bits as scheduled by CC-PFS. The heuristic algorithm captures about 30% of the throughput improvement found by OA. Finally, the reason for the improvements over CC-PFS is found to be traffic arrival.

AB - The multi-carrier proportional fair scheduling (MC-PFS) problem in a multi-user system has been shown to be NP-hard. Carrier by carrier proportional fair scheduling (CC-PFS) is commonly used instead to allocate resources in real-time. Considering the sub-optimal nature of CC-PFS and its popularity, this paper formulates the optimization beyond CC-PFS as a constrained maximum sum rate problem (with users' data rates scheduled by CC-PFS as the constraint) and tackles the problem in two ways. Firstly, the problem is shown to be equivalent to the well-studied generalized assignment problem (GAP) under the assumption of infinitely backlogged data. By considering traffic arrivals, the problem becomes a nonlinear integer programming problem which can be solved by outer approximation (OA) algorithms. Secondly, the problem is shown to be equivalent to a classical trading problem, and a low complexity heuristic algorithm that can be run in real-time is developed based on trading resource blocks (RBs). Using a system scheduling many video call users, we show that in about half of the time slots, the sum rate can be improved over CC-PFS while each user transmits at least as many bits as scheduled by CC-PFS. The heuristic algorithm captures about 30% of the throughput improvement found by OA. Finally, the reason for the improvements over CC-PFS is found to be traffic arrival.

KW - carrier by carrier

KW - CC-PFS

KW - GAP

KW - MC-PFS

KW - multi-carrier

KW - multi-user

KW - OFDMA

KW - proportional fair

KW - trading resource blocks

KW - traffic arrival

UR - http://www.scopus.com/inward/record.url?scp=79959942219&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79959942219&partnerID=8YFLogxK

U2 - 10.1109/SARNOF.2011.5876485

DO - 10.1109/SARNOF.2011.5876485

M3 - Conference contribution

AN - SCOPUS:79959942219

SN - 9781612846811

BT - 2011 34th IEEE Sarnoff Symposium, SARNOFF 2011

ER -