A fast retransmit which reduces the time a sender waits before retransmitting a lost segment is typically used to ensure transmission of data without incurring data loss. Many application protocols have been enhanced and developed on the basis of the fast retransmit. The multipath transmission control protocol guarantees quality of service and reduces data transmission time in modern computer networks. Communication lines used in such a network can experience different states such as failure, partial failure, and maintenance. Hence a computer network that employs a fast retransmit can be regarded as stochastic and is called a stochastic-flow computer network with a fast retransmit (SCNFR). This study evaluates system reliability of a SCNFR for transmitting demand d successfully through two separate minimal paths (2SQP) under the time constraint. An algorithm is proposed for finding all minimal capacity vectors (MCVs) that satisfy the demand and time constraint. Then, the system reliability is computed in terms of all MCVs easily.