Abstract
We consider a route in a rectilinear grid communications network and compute the ratio of the additional capacity per tandem node required to make the route immune to a single tandem node failure (which causes all arcs incident to the node to fail), divided by the additional capacity per arc required to make the route immune to a single arc failure. For any route satisfying a mild assumption, we prove the ratio is between 1 and 4/3. For random routes, we show that the expected value of the ratio is 10/9 for routes using 2 arcs, 202/189 for routes using 3 arcs, and has the limit (as the number of arcs increases to infinity) of 7/6. The theoretical results are in close agreement with empirical results, using a network design algorithm, for large data communications networks.
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Rosenberg, E. Capacity Requirements for Node and Arc Survivable Networks. Telecommunication Systems 20, 107–131 (2002). https://doi.org/10.1023/A:1015493417623
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DOI: https://doi.org/10.1023/A:1015493417623