From the viewpoint of service level agreements,the transmission accuracy rate is one of critical performance indicators to assess internet quality for system managers and customers.Under the assumption that each arc’s capacity is deterministic,the quickest path problem is to find a path sending a specific of data such that the transmission time is minimized.However,in many real-life networks such as computer networks,each arc has stochastic capacity,lead time and accuracy rate.Such a network is named a multi-state computer network.Under both assured accuracy rate and time constraints,we extend the quickest path problem to compute the probability that d units of data can be sent through multiple minimal paths simultaneously.Such a probability named system reliability is a performance indicator to provide to managers for understanding the ability of system and improvement.An efficient algorithm is proposed to evaluate the system reliability in terms of the approach of minimal paths. From the viewpoint of service level agreements, the transmission accuracy rate is one of critical performance indicators to assess internet quality for system managers and customers. Under the assumption that each arc’s capacity is deterministic, the quickest path problem is to find a path to send a specific of data such that the the transmission time is minimized. Host to many networks such as computer networks, each arc has stochastic capacity, lead time and accuracy rate.Such a network is named a multi-state computer network .Under both both assured accuracy rate and time constraints, we extend the quickest path problem to weigher that d units of data can be sent through multiple minimal paths simultaneously.Such a probability named system reliability is a performance indicator to provide to managers for understanding the ability of system and improvement. An efficient algorithm is proposed to evaluate the system reliability in terms of the approach of minimal paths.