| User experience and empirical reliability data from distributed computer networks using common carrier facilities for communication have shown some major weaknesses of the standard independent failure models in analyzing such systems. These observations point to a strong positive correlation of failures of different communication lines. Two models for dealing with communication line failure dependence are developed here. The (beta)-model assumes that the rate of failure of a communication line increases from (lamda) to (beta)(lamda) whenever one or more adjacent lines fail. This model is used to analyze special communication systems such as primary and secondary components (communication lines) with a switch, N terminals connected to a central CPU, etc. A system of two redundant components with general distribution on their time-to-repair (with restricted and unrestricted repair facilities) is analyzed by an extension of the (beta)-model.;A second model (the Q-(psi) model) is developed for dealing with source-sink communication unavailability of a distributed computer communication network using communication facilities such as the telephone plant facilities.;The model assumes that the unconditional line unavailability equals q and the conditional line unavailability, when one or more lines sharing one common node have failed, equals (psi) (GREATERTHEQ) q. Other conditional line unavailabilities, i.e., those conditioned on the status of lines at both ends of a communication line, or on the states of i lines sharing a common node, etc., are found. Modified cut-sets, which are mutually exclusive, are generated for the distributed computer communication network under consideration. The product rule for calculating joint probabilities is used on each modified cut and the resulting conditional probabilities are calculated using the q-(psi) model conditional probabilities as specified by the resulting topologies. This allows availabilities to be calculated for most of the communication networks likely to be encountered in practical systems. |
