K-terminal reliability in ring networks

The authors present a new formula for computing K-terminal reliability in a communication network whose stations and links (vertices and edges) form a network graph G having a ring topology, where K-terminal reliability is the probability R/sub K/(G) that a subset of R specific terminal stations in G can communicate. This new formula is applied to three Fiber Distributed Data Interface (FDDI) ring-network topologies, and for each topology the authors derive closed-form polynomial expressions of R/sub K/(G) in terms of the failure probabilities of links, network ports, and station common units. The authors define the concept of the K-minimal Eulerian circuit and use combinations of these circuits to obtain K-graphs and their resulting dominations, thus extending the use of K-graphs to ring networks in which data messages, tokens, or other control frames traverse operative network links with an Eulerian tour. Distinct K-graphs having a nonzero sum of dominations are called noncanceled K-graphs and correspond exactly to terms in closed-form polynomial expressions of R/sub K/(G). The authors show that trees have only one K-graph and that counter-rotating dual rings and rings of trees have at most 2K+1 noncanceled R-graphs. These results contribute the first closed-form polynomial R-terminal reliability expressions for the ring-of-trees topology. The results are useful in evaluating dependability, reliability, availability, or survivability of token rings and similar networks. >

[1]  Charles B. Silio,et al.  A reliability comparison of single and double rings , 1990, Proceedings. IEEE INFOCOM '90: Ninth Annual Joint Conference of the IEEE Computer and Communications Societies@m_The Multiple Facets of Integration.

[2]  Michael O. Ball,et al.  Computational Complexity of Network Reliability Analysis: An Overview , 1986, IEEE Transactions on Reliability.

[3]  Floyd E. Ross,et al.  An overview of FDDI: the fiber distributed data interface , 1989, IEEE J. Sel. Areas Commun..

[4]  Charles B. Silio,et al.  A reliability analysis of failsoft FDDI networks , 1992, [1992] Proceedings 17th Conference on Local Computer Networks.

[5]  Jacob J. Wolf A distributed double-loop computer network (DDLCN) , 1981 .

[6]  Mark K. Chang,et al.  Network reliability and the factoring theorem , 1983, Networks.

[7]  Charles B. Silio,et al.  An Approximate Method for the Performance Analysis of PLAYTHROUGH Rings , 1992, IEEE Trans. Computers.

[8]  Michael O. Ball Computing Network Reliability , 1979, Oper. Res..

[9]  A. Satyanarayana,et al.  A Unified Formula for Analysis of Some Network Reliability Problems , 1982, IEEE Transactions on Reliability.

[10]  R. Kevin Wood Factoring Algorithms for Computing K-Terminal Network Reliability , 1986, IEEE Transactions on Reliability.

[11]  Marc D. Cohn A network architecture for advanced aircraft , 1989, [1989] Proceedings. 14th Conference on Local Computer Networks.