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In the multi-status network, data could be transmitted via different path. The network and its elements such as links and nodes are usually regarded with two statuses. However, in the real-life cases, due to the communication traffic jam and physical errors from network devices, it is a multi-state network. In order to discuss the reliability examination of such cases, this paper introduces an innovative algorithm to evaluate the reliability with continuous time intervals as constraints. Each source transmit a data sequence via a minimal path, where two paths have the same link.