## 1 Introduction
### Literature Review of the Studies on Fatigue in ATCOs  
Existing research on fatigue has primarily focused on the effects of fatigue on performance, the factors influencing fatigue, and countermeasures. There is no univocal accepted definition of fatigue [9] because the concept is used in many fields. In simple terms, a person's fatigue means feeling sleep, tired, or exhausted [10; 11]. In the civil aviation field, fatigue has been researched extensively because it is an at-risk state and impairs a person's working performance. The International Civil Aviation Organization (ICAO) defines crewmember fatigue as \"[a] physiological state of reduced mental or physical performance capability resulting from sleep loss, extended wakefulness, circadian phase, and/or workload (mental and/or physical activity) that can impair a person's alertness and ability to perform safety-related operational duties\" [12]. The definitions reveal that fatigue is a state of diminished performance and capability. The effects of fatigue generally tend to be a continuum ranging from mild to severe and disabling manifestations such as exhaustion, overstrain, and chronic fatigue syndrome [13]. Under the influence of fatigue, people's alertness, motor skills, reflex ability, judgment, cognitive performance and decision-making will be impaired [1; 14]. It has been proven that heart rate and heart rate variability were also highly correlated with fatigue [15; 16]. The fatigue of ATCOs is related to numerous factors, including physiological features, circadian rhythmicity, homeostatic factors, and work tasks. [PERSON] et al. [17; 18] found that people in the age range of 31-45 had the highest chronic fatigue levels, poorest sleep quality, and shortest sleep time before a morning shift, and females had higher chronic fatigue levels and longer sleep times than males. [PERSON] et al. [19] reported that less sleep generally leads to low sleep quality and higher levels of fatigue. A number of studies summarized that circadian rhythmicity produced by sleep habit and the homeostatic drive to sleep produced by reduction in the quantity or quality of sleep, or the extension of time awake, were the main causes of fatigue [20; 21; 22]. It was stated that fatigue was caused by a lack of sleep and prolonged wakefulness or change in sleep-wake schedule [23]. Fatigue levels were significantly different between day and night shifts, time periods, and various work schedules [24]. Fatigue has been recognized as a major consequence of increased work intensity [25]. Duty cycles and short breaks during working hours were also considered factors that influence fatigue [26]. The ICAO [12] listed four scientific principles for fatigue management: the need for sleep, sleep loss and recovery, circadian effects on sleep and performance, and the influence of the workload, revealing the primary factor areas influencing fatigue. It can be summarized that the common form of ATCOs' fatigue includes the drive to sleep [27; 28], produced by circadian rhythmicity or sleep loss and meaning the need to sleep, and the biological drive for preoperative rest [22], produced by continuous or intense work and meaning the need to stop work to have a rest. In this study, we mainly focused on the drive to sleep. Several studies have focused on modeling fatigue and developing countermeasures to prevent fatigue in ATCOs during occupational activities. Modeling fatigue has potential uses on estimating fatigue on the basis of working hours, detecting fatigue, and warning and managing risk mitigation strategies [28]. A number of biomathematical models of fatigue such as a three-process model of alertness, a system for aircrew fatigue evaluation and sleep, activity, fatigue, and a task effectiveness model [21; 29; 30; 31] have been developed, providing theoretical references to predict fatigue and minimize the adverse impact of fatigue and develop countermeasures. The most common countermeasures for ATCOs are fatigue management.