We propose a new type of Graph Rewriting Systems (GRS) that provide a theoretical foundation for using the reduction method which plays an important role on analyze network reliability. By introducing this GRS, several facts were obtained as follows: (1) We clarified the reduction methods of network reliability analysis in the theoretical framework of GRS. (2) In the framework of GRS, we clarified the significance of the completeness in the reduction methods. (3) A procedure of recognizing complete systems from only given rewriting rules was shown. Specially the procedure (3) is given by introducing a boundary graph (B-Graph). Finally an application of GRS to network reliability analysis is shown.

We propose a high-speed protection scheme for multiple-priority-class traffic transmission in WDM ring networks. This scheme achieves high-speed protection by quickly suspending transmission of low-priority traffic when a failure is detected. Each node suspends transmission of the low-priority traffic being sent over the backup path corresponding to the impaired primary path after receiving a failure notification and checking a table that includes the primary paths passing through the node, the backup paths corresponding to the primary paths, and low-priority traffic transmitted by the node. If a node detects a failure, it sends a single failure notification for each ring to the source node of the primary path, and the nodes on the route sequentially suspend low-priority traffic. Simulation shows that the proposed scheme reduces the failure-recovery time by up to 60% compared with the conventional scheme.

This paper reports the results of a new test on what types of failure cause falls in the stock prices of telecommunication service providers. This analysis of stock price is complementary to our previous one on market share. A clear result of our new test is that the type of failure causing falls in stock price is different from the type causing decline in market share. Specifically, the previous study identified frequent failures as causes of decline in market share, while the current study indicates large failures affecting many users as causes of falls in stock price. Together, these analyses give important information for reliability designs of telecommunications networks.

Although unavailability and failure frequency are important reliability measures for designing telecommunications networks, having two different reliability measures causes difficulties when their evaluation results contradict each other. To overcome this difficulty, for determining a single reliability measure is proposed. Market share, which is an important management index, was used and the effect of each reliability measure on this index was studied. If we the effect of one of the reliability measures is small enough to be ignored, then the other one is chosen as the single reliability measure. The procedure of the proposed statistical analysis method and test results suggesting that failure frequency is promising as a single reliability measure are discussed.