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Performing deferred actions in the future relies upon Prospective Memory (PM). Often, PM demands arise in complex dynamic tasks. Not only can PM be challenging in such environments, the processes required for PM may affect the performance of other tasks. To adapt to PM demands in such environments, humans may use a range of strategies, including flexible allocation of cognitive resources and cognitive control mechanisms. We sought to understand such mechanisms by using the Prospective Memory Decision Control (Strickland, Loft, Remington, & Heathcote, 2018) model to provide a comprehensive, quantitative account of dual task performance in a complex dynamic environment (a simulated air traffic control conflict detection task). We found that PM demands encouraged proactive control over ongoing task decisions, but that this control was reduced at high time pressure to facilitate fast responding. We found reactive inhibitory control over ongoing task processes when PM targets were encountered, and that time pressure and PM demand both affect the attentional system, increasing the amount of cognitive resources available. However, as demands exceeded the capacity limit of the cognitive system, resources were reallocated (shared) between the ongoing and PM tasks. As the ongoing task used more resources to compensate for additional time pressure demands, it drained resources that would have otherwise been available for PM task processing. This study provides the first detailed quantitative understanding of how attentional resources and cognitive control mechanisms support PM and ongoing task performance in complex dynamic environments. © 2019 American Psychological Association.