Research on sleep loss and vigilance both focus on declines in cognitive performance, but theoretical accounts have developed largely in parallel in these two areas. In addition, computational instantiations of theoretical accounts are rare. The current work uses computational modeling to explore whether the same mechanisms can account for the effects of both sleep loss and time on task on performance. A classic task used in the sleep deprivation literature, the Psychomotor Vigilance Test (PVT), was extended from the typical 10‐min duration to 35 min, to make the task similar in duration to traditional vigilance tasks. A computational cognitive model demonstrated that the effects of time on task in the PVT were equivalent to those observed with sleep loss. Subsequently, the same mechanisms were applied to a more traditional vigilance task—the Mackworth Clock Task—providing a good fit to existing data. This supports the hypothesis that these different types of fatigue may produce functionally equivalent declines in performance.