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

Arseniy Vitkovskiy, Paul Christodoulides, Vassos Soteriou Soteriou

Research output: Contribution to journalArticle

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 languageEnglish (US)
Article number410172
JournalMathematical Problems in Engineering
Volume2015
DOIs
StatePublished - Jan 1 2015

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Spatial Distribution
Spatial distribution
Necklace
Fault
Wire
Consecutive
Recovery
Chip multiprocessors
Combinatorial Problems
Parallel Processing
Analytical Model
Latency
Count
Connectivity
Chip
High Performance
Metals
Directly proportional
Partition
Model

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

Cite this

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

In: Mathematical Problems in Engineering, Vol. 2015, 410172, 01.01.2015.

Research output: Contribution to journalArticle

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