This study focuses on TCP retransmission, firstly evaluates network reliability of a SCNR for transmitting data d successfully through multiple minimal paths (MPs) within a time threshold T. Furthermore, a backup policy is predetermined to indicate the main and backup MPs to improve network reliability (referred to as backup reliability). A computer network that employs a TCP retransmission can be regarded as stochastic and is called a stochastic computer network with a retransmission (SCNR), because communication lines used by such a network can experience different states such as failure, partial failure, and maintenance. An algorithm is proposed for generating all lower boundary points (LBPs) that can satisfy a time threshold. Then, the network reliability is computed in terms of all LBPs for (d, T) using the recursive sum of disjoint products algorithm. Thus, the backup reliability can be easily computed by the proposed procedure.