Event-based prospective memory (PM) requires remembering to perform intended deferred actions when particular stimuli or events are encountered in the future. We propose a detailed process theory within Braver's (2012) proactive and reactive framework of the way control is maintained over the competing demands of prospective memory decisions and decisions associated with ongoing task activities. The theory is instantiated in a quantitative "Prospective Memory Decision Control" (PMDC) architecture, which uses linear ballistic evidence accumulation (Brown & Heathcote, 2008) to model both PM and ongoing decision processes. Prospective control is exerted via decision thresholds, as in Heathcote, Loft, and Remington's (2015) "Delay Theory" of the impact of PM demands on ongoing-task decisions. However, PMDC goes beyond Delay Theory by simultaneously accounting for both PM task decisions and ongoing task decisions. We use Bayesian estimation to apply PMDC to experiments manipulating PM target focality (i.e., the extent to which the ongoing task directs attention to the features of PM targets processed at encoding) and the relative importance of the PM task. As well as confirming Delay Theory's proactive control of ongoing task thresholds, the comprehensive account provided by PMDC allowed us to detect both proactive control of the PM accumulator threshold and reactive control of the relative rates of the PM and ongoing-task evidence accumulation processes. We discuss potential extensions of PMDC to account for other factors that may be prevalent in real-world PM, such as failures of memory retrieval.