Graphical-algebraic analysis of ring network reliability

We combine graph theoretic and algebraic approaches to produce a new tool for computing terminal-pair reliability of ring networks. Terminal-pair reliability is defined as the probability that two stations of interest in the network can communicate.; We solve a significant open problem by using this new tool to derive closed-form reliability expressions for multi-level dual homing ring networks in which the roots of a dual homing tree may be either adjacent or non-adjacent. We further illustrate the utility of this new tool by obtaining closed-form reliability expressions of an extended ring LAN where two ring networks are joined by a bridge. A component ring in an extended ring LAN can be a dual counter-rotating ring, a ring of trees or a dual homing ring. We also use this tool to obtain closed-form conditional reliability expressions for a dual counter-rotating ring, given that a station or a primary link has already failed.; Prior analyses of ring networks with both self-heal and station bypass switches place no limits on the number of consecutive station failures; however, in fiber optic ring networks there are power loss constraints that limit the number of consecutively bypassed station failures. We extend the results of prior work on dual counter-rotating ring networks by incorporating optical power loss limitations and obtain closed-form terminal-pair reliability expressions for this case.; The results presented here constitute a new approach to network reliability analysis and significantly 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. The contributions of this research are a new technique and a set of tools that can be used by network designers in performing terminal-pair reliability analyses of ring network structures.