I have worked in the field of reliability for a good many years. I have presented both beginner and advanced reliability engineering courses. I have even read several books. 🙂 But, across all this, component redundancy has never been explained beyond simple serial and parallel configurations.
So, it was a shock to my system to be presented with a scenario that couldn’t be solved using a simple parallel system.
My previous work had challenged me only as far as:
- Active parallel
- Stand-by parallel
- M-out-of-n parallel
- Keystone-component parallel
But now I was being challenged by a network that was none of these.
Computer networks have been developed that follow more expansive topologies. For example:
Many papers have been published on the relative network reliability of these and several variants, but it was even more of a surprise when I could not find a solution to the specific scenario my client was using.
Figure 1: Double-ring topology using separate opposing-direction data feeds.
This topology defines that each node receives 2 independent data-feeds, and the system is considered to be functional if at least one data-feed is received by each node. Multiple breaks in the data-feed are allowed, provided that each node links to the computer feed by either the forward or reverse data-feeds. There is no cross-link between these data-feeds.
I have solved the network reliability for this topology and hope to present at a future reliability conference. However, as a challenge, I invite you to provide a mathematical solution based on:
- Each segment of the data feed, linking adjacent nodes, has a reliability R(t). All segments have equal reliability. There are N nodes, with N forward segments and N reverse segments.
- All nodes must receive data in order for the system to be considered functional. The reliability of each node is not part of the solution – their system contribution is a simple series calculation and would be easily added to the dual-ring topology solution.
- The reliability of the main computer data feed is also not part of the requested solution – as with the nodes, its contribution is a simple series calculation.
And if you identify an already published paper that solves the network reliability for this topology, based on R(t) for each segment, I would of course value a link.
I look forward to hearing from you. Please contact me at Les Warrington
I will also publish a follow-up article on Accendo with my solution in a few weeks.