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• A stochastic-flow computing network is constructed. • Any transmission unit is allowed to search flow vectors. • An approach of flow vector generation for non-integer demands is established. • An algorithm is constructed for network reliability with non-integer demands. • Two examples are provided to show the effectiveness of the proposed algorithm. A multi-state computing network (MSCN) consists of multi-state edges such that the performance levels of the MSCN might differ. Network reliability is concerned with the probability that the predetermined demand from multiple sources can be successfully transmitted through the network. One of the major methods for efficiently calculating network reliability is to generate all minimal capacity vectors (MCVs), which represents the minimal capacity required for each edge. Every MCV is transformed from the flow vectors satisfying predetermined demands based on the minimal paths (MPs). In general, the amount flows were set as integers for flow vector generation in previous studies. In fact, the amount of data might be the non-integer type (such as 2.4Gbps) in the practical data transmission. An algorithm with a new approach for flow vector generation is developed to efficiently deal with demand as the non-integer type with any transmission unit such that the search spaces of the flows are stable. The experimental results of numerical examples and a practical case show that the proposed algorithm is more effective and efficient than the approaches in the literature. [ABSTRACT FROM AUTHOR]