The high energy consumption of electronic data processors, together with physical challenges limiting their further improvement, has triggered intensive interest in alternative computation paradigms. Here we focus on network-based biocomputation (NBC), a massively parallel approach where computational problems are encoded in planar networks implemented with nanoscale channels. These networks are explored by biological agents, such as biological molecular motor systems and bacteria, benefitting from their energy efficiency and availability in large numbers. We analyse and define the fundamental requirements that need to be fulfilled to scale up NBC computers to become a viable technology that can solve large NP-complete problem instances faster or with less energy consumption than electronic computers. Our work can serve as a guide for further efforts to contribute to elements of future NBC devices, and as the theoretical basis for a detailed NBC roadmap.