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Mathematical Problems in Engineering
Volume 2015, Article ID 410172, 13 pages
http://dx.doi.org/10.1155/2015/410172
Research Article

A Probabilistic Spatial Distribution Model for Wire Faults in Parallel Network-on-Chip Links

Faculty of Engineering and Technology, Cyprus University of Technology, 3603 Limassol, Cyprus

Received 4 October 2014; Accepted 11 January 2015

Academic Editor: Jinhu Lü

Copyright © 2015 Arseniy Vitkovskiy et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.