p-cycle network design with hop limits and circumference limits

p-cycles offer an approach to protection of optical transport networks which is as fast as a ring-based network but with mesh-like capacity efficiency. One misconception about p-cycle designs seems to be that they involve long protection paths, even though it is trivial to limit the circumference of cycles admitted to the design problem. In addition, through straddling span considerations the average protection path on a p-cycle is actually shorter than in a corresponding ring. Nonetheless there are some open questions regarding path and cycle circumference limit effects with p-cycles. One question is whether p-cycle networks exhibit a "threshold hop-limit" effect corresponding to that well-known aspect of span-restorable mesh networks. (Beyond the threshold hop-limit there are negligible savings in capacity.) To study this question we extend the existing p-cycle network design theory to include the capability of direct restriction of protection path lengths, rather than indirect restriction through circumference limits. A second, quite practical question is to ask how well simple limitation of cycle circumferences serves as a surrogate for a more involved design method of directly asserting a hop (or distance) limit on the maximum length of protection paths. The answers to the questions and the methods developed to address them both enhance our ability to design p-cycle networks in which optically transparent length may affect transmission quality, or where the length of protection paths may affect cost if regeneration is required en route of a protection path. The main findings are that p-cycles do exhibit threshold hop-limiting effects (at about two or three hops above those in corresponding mesh networks) and that cycle limiting is a simple and effective surrogate for direct limitation on path lengths in p-cycle design problems.