It has been hypothesised that a global neuronal workspace underlies the brain's capacity to process information consciously. This paper describes a significant variation on a previously reported computer simulation of such a global neuronal workspace, in which competition and broadcast were realised through reverberating populations of spiking neurons. In the present model, unlike the previous one, the wiring of the workspace is not predefined but constructed in a stochastic fashion on the fly, which is far more biologically plausible. We demonstrate that the new model exhibits the same capacity for broadcast and competition as the previous one. We conclude with a short discussion of a brain-inspired cognitive architecture that incorporates a global workspace of the sort described.