### Abstract

High-performance chip multiprocessors contain numerous parallel-processing cores where a fabric devised as a network-on-chip (NoC) efficiently handles their escalating intertile communication demands. Unfortunately, prolonged operational stresses cause accelerated physically induced wearout leading to permanent metal wire faults in links. Where only a subset of wires may malfunction, enduring healthy wires are leveraged to sustain connectivity when a partially faulty link recovery mechanism is utilized, where its data recovery latency overhead is proportional to the number of consecutive faulty wires. With NoC link failure models being ultimately important, albeit being absent from existing literature, the construction of a mathematical model towards the understanding of the distribution of wire faults in parallel on-chip links is very critical. This paper steps in such a direction, where the objective is to find the probability of having a "fault segment" consisting of a certain number of consecutive "faulty" wires in a parallel NoC link. First, it is shown how the given problem can be reduced to an equivalent combinatorial problem through partitions and necklaces. Then the proposed algorithm counts certain classes of necklaces by making a separation between periodic and aperiodic cases. Finally, the resulting analytical model is tested successfully against a far more costly brute-force algorithm.

Original language | English (US) |
---|---|

Article number | 410172 |

Journal | Mathematical Problems in Engineering |

Volume | 2015 |

DOIs | |

State | Published - Jan 1 2015 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Engineering(all)

### Cite this

*Mathematical Problems in Engineering*,

*2015*, [410172]. https://doi.org/10.1155/2015/410172

**A probabilistic spatial distribution model for wire faults in parallel network-on-chip links.** / Vitkovskiy, Arseniy; Christodoulides, Paul; Soteriou, Vassos Soteriou.

Research output: Contribution to journal › Article

*Mathematical Problems in Engineering*, vol. 2015, 410172. https://doi.org/10.1155/2015/410172

}

TY - JOUR

T1 - A probabilistic spatial distribution model for wire faults in parallel network-on-chip links

AU - Vitkovskiy, Arseniy

AU - Christodoulides, Paul

AU - Soteriou, Vassos Soteriou

PY - 2015/1/1

Y1 - 2015/1/1

N2 - High-performance chip multiprocessors contain numerous parallel-processing cores where a fabric devised as a network-on-chip (NoC) efficiently handles their escalating intertile communication demands. Unfortunately, prolonged operational stresses cause accelerated physically induced wearout leading to permanent metal wire faults in links. Where only a subset of wires may malfunction, enduring healthy wires are leveraged to sustain connectivity when a partially faulty link recovery mechanism is utilized, where its data recovery latency overhead is proportional to the number of consecutive faulty wires. With NoC link failure models being ultimately important, albeit being absent from existing literature, the construction of a mathematical model towards the understanding of the distribution of wire faults in parallel on-chip links is very critical. This paper steps in such a direction, where the objective is to find the probability of having a "fault segment" consisting of a certain number of consecutive "faulty" wires in a parallel NoC link. First, it is shown how the given problem can be reduced to an equivalent combinatorial problem through partitions and necklaces. Then the proposed algorithm counts certain classes of necklaces by making a separation between periodic and aperiodic cases. Finally, the resulting analytical model is tested successfully against a far more costly brute-force algorithm.

AB - High-performance chip multiprocessors contain numerous parallel-processing cores where a fabric devised as a network-on-chip (NoC) efficiently handles their escalating intertile communication demands. Unfortunately, prolonged operational stresses cause accelerated physically induced wearout leading to permanent metal wire faults in links. Where only a subset of wires may malfunction, enduring healthy wires are leveraged to sustain connectivity when a partially faulty link recovery mechanism is utilized, where its data recovery latency overhead is proportional to the number of consecutive faulty wires. With NoC link failure models being ultimately important, albeit being absent from existing literature, the construction of a mathematical model towards the understanding of the distribution of wire faults in parallel on-chip links is very critical. This paper steps in such a direction, where the objective is to find the probability of having a "fault segment" consisting of a certain number of consecutive "faulty" wires in a parallel NoC link. First, it is shown how the given problem can be reduced to an equivalent combinatorial problem through partitions and necklaces. Then the proposed algorithm counts certain classes of necklaces by making a separation between periodic and aperiodic cases. Finally, the resulting analytical model is tested successfully against a far more costly brute-force algorithm.

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U2 - 10.1155/2015/410172

DO - 10.1155/2015/410172

M3 - Article

VL - 2015

JO - Mathematical Problems in Engineering

JF - Mathematical Problems in Engineering

SN - 1024-123X

M1 - 410172

ER -