Ring-network with a constrained number of consecutively-bypassed stations

A new technique combines prior graph theoretic and algebraic techniques for obtaining closed-form terminal-pair reliability expressions of ring topology networks. The applicability of this technique is illustrated by obtaining closed-form terminal-pair reliability expressions for dual counter-rotating ring networks that use both self-heal and station-bypass switches in which all components can fail. These expressions appreciably extend the utility of prior work on ring-network reliability by incorporating network configuration limitations caused by optical power loss constraints. The number of consecutively bypassed station failures in an optical fiber ring topology network such as those exemplified by FDDI rings or synchronous optical network (SONET) rings is limited by the optical power loss constraints. The combined graph theoretic and algebraic technique permits the incorporation of known results on the reliability of consecutive k-out-of-n:F systems so that closed-form terminal-pair reliability expressions can be derived. The results are a new approach to network-reliability analysis and appreciably extend known theory to new situations not previously analyzed. In particular, the combined graphical-algebraic analysis tool developed here allows ring-network designers to analyze the reliability of ring-network structures thought previously to be too difficult to analyze with closed-form expressions and to be amenable only to reliability approximation by simulation. We use this technique in our derivation of closed-form expressions for terminal-pair reliability in dual counter-rotating ring networks