Capturing the effects of fatigue and, more generally, the effectsof physical and mental states on human performance has beena topic of research for many years. Recent models, especiallythose developed in a cognitive architecture, have shown greatpromise in capturing these effects by providing insight into thespecific cognitive and other components involved in taskperformance (like perception and motor movement). Inparticular, separate models have been developed to account forboth time-of-day and time-on-task effects related to fatigue. Inthis paper, we present a novel unified model, developed in theACT-R cognitive architecture, that captures both time-of-dayand time-on-task effects with a single set of mechanisms andparameters. We demonstrate how this unified model accountsfor quantitative and qualitative aspects of fatigued performancefrom two experiments, one focused on time-on-task effectsunder conditions of moderate fatigue, the other focusing ontime-of-day effects under conditions of severe fatigue in astudy of long-term (88-hour) sleep deprivation.