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In a computer or communication network, the reliability and transfer-delay of communication are important measures of performance. This paper describes a method of evaluating the reliability of a network with delay. When network elements fail, delay is defined as the length of the shortest remaining path between two specified nodes. We find the occurrence probability of events that a central node can communicate with a group of terminal nodes so that a specified delay is not exceeded. The desired events are mutually exclusive and contain a tree. Our algorithm efficiently generates all the events by noting network topology. The paper includes the case of several central nodes.