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A fast retransmit, which reduces the sender’s waiting time before retransmitting a lost segment, is applied to guarantee data integrity with no data loss in transmission. Based on fast retransmit, many application protocols have been enhanced and evolved to ensure quality of service and reduce data transmission time. One of application protocols is the multipath transmission control protocol which is catholically applied in modern computer networks. Communication lines used in this kind of network have different states, namely, failure, partial failure, and maintenance. Therefore, a computer network with a fast retransmit can be classified as stochastic and is called a stochastic-flow computer network with a fast retransmit (SCNFR). This paper assesses the system reliability of SCNFR for the successful transmission of demand d through ${k}$ (${k} \,\, >1$) separate minimal paths (${k}$ SMiP) under the latency. An algorithm is proposed to find all minimal capacity vectors (MCVs) that satisfy the demand and latency. Then, the system reliability is computed based on all MCVs. We adopt two practical cases of the pan-European research and education network and the Taiwan academic network to explore the effectiveness of the algorithm. The results show that the system reliability can be classified as decision reference while the manager decides the better ${k}$ SMiP with higher system reliability. [ABSTRACT FROM AUTHOR]