Theoretical underpinnings for the efficiency of restorable networks using preconfigured cycles ("p-cycles")

Previous work on restorable networks has shown experimentally that one can support 100% restoration with an optimized set of closed cycles of spare capacity while requiring little or no increase in spare capacity relative to a span-restorable mesh network. This is important and unexpected because it implies that future restoration schemes could be as capacity efficient as a mesh network, while being as fast as ring-based networks because there is no real-time work at any nodes other than the two failure nodes. This paper complements the prior work by giving a greater theoretical basis and insight to support the prior results. We are able to show in a bounding-type of argument that the proposed protection cycles ("p-cycles") have as high a restoration efficiency as it is possible to expect for any type of preconfigured pattern, and are categorically superior to preconfigured linear segments or trees. We are also able to show that the capacity efficiency of a fully preconfigured p-cycle network has the same well-known lower bound as that of a span restorable mesh network which is cross-connected on-demand. These results provide a theoretical underpinning for the efficiency of p-cycles and confirmation of the experimental observations.