  In this paper we propose a generalized R redundancy cycle technique that
provides optical networks almost fault-tolerant communications. More
importantly, when applied using only single cycles rather than the standard
paired cycles, the generalized R redundancy technique is shown to almost halve
the necessary light-trail resources in the network while maintaining the
fault-tolerance and dependability expected from cycle-based routing. For
efficiency and distributed control, it is common in distributed systems and
algorithms to group nodes into intersecting sets referred to as quorum sets.
Optimal communication quorum sets forming optical cycles based on light-trails
have been shown to flexibly and efficiently route both point-to-point and
multipoint-to-multipoint traffic requests. Commonly cycle routing techniques
will use pairs of cycles to achieve both routing and fault-tolerance, which
uses substantial resources and creates the potential for underutilization.
Instead, we intentionally utilize R redundancy within the quorum cycles for
fault-tolerance such that every point-to-point communication pairs occur in at
least R cycles. The result is a set of R = 3 redundant cycles with 93.23-99.34%
fault coverage even with two simultaneous faults all while using 38.85-42.39%
fewer resources.
