In previous work, the authors presented a 3D hexagonal wireless direct-interconnect network for a massively parallel computer, with a focus on analysing processor utilisation. In this study, we consider the characteristics of such an architecture in terms of link utilisation and power consumption. We have applied a store-and-forward packet-switching algorithm to both our proposed architecture and a traditional wired 5D direct network (the same as IBM's Blue Gene). Simulations show that for small and medium-size networks the link utility of the proposed architecture is comparable with (and in some cases even better than) traditional 5D networks. This work demonstrates that there is a potential for wireless processing array concepts to address High-Performance Computing (HPC) challenges whilst alleviating some significant physical construction drawbacks of traditional systems.