## 1 Introduction  
Research in the fields of chronobiology and sleep science distinguishes between people of two distinct chronotypes: morning and evening types or, in short, M- and E-types [1; 2]. If M-types are most alert in the morning, E-types are most alert in the evening, and, in addition, they prefer early awakening-early bedtime and late awakening-late bedtime, respectively [3]. Links are presented in the literature between the chronotype and individual differences in various domains, including the domains of neurophysiology, psychiatry, cognitive psychology, personality, and mental and physical health (reviewed in [4]).  
According to a growing body of experimental research, the positions of endogenous circadian phases show, at least, a 2 h difference between chronotypes [5; 6; 7; 8; 9; 10]. When workers/students work/study Monday to Friday, and then have two days without work/study, they might be tempted to \"catch up\" on sleep. However, the simulations of weekday and weekend sleep times with a sleep-wake regulation model [11] suggest that, despite complete freedom to sleep in and nap during the two weekend days, the reduction in sleep during the week cannot be reversed by the extension of weekend sleep beyond its normal, adequate duration [12; 13; 14; 15; 16]. The simulations also suggest a more profound weekday sleep loss in E-types than M-types because E-types have to advance their weekday times by more relative to weekend waking times [12; 13].  
It appears that negative impacts of the disparity between chronotypes in weekday sleep loss underlie the complaints about \"the tyranny of the early risers/birds\" (e.g., [17; 18]). This disparity rests upon the tradition of setting working and school start-times too early. Consequently, given that our work/study culture is biased towards the circadian clocks of M-types, E-types are forced to sacrifice a larger amount of sleep on weekdays to arrive at their place of work/study at the M-type-oriented start-times. The recent \"natural experiment\" during \"lockdown\" demonstrated that, when home-workers/students were suddenly able to choose their own waking times, most slept later. Notably, this \"experiment\" also confirmed the model-based prediction of a failure to decrease the weekend sleep duration during lockdown, in response to the increase in weekday sleep duration leading to the decrease in weekday sleep loss [14].  
Therefore, a question arises of whether the simulations of data on sleep timing of M- and E-types can help in the overthrowing of such a \"tyranny of the early risers\" by changing sleep times of E-types; that is, can the simulations based on a sleep-wake regulating model be implicated in the development of a method to correct the sleep times of E-types required to equalize the irrecoverable weekday sleep loss of the two chronotypes?  
Consequently, the aim of this paper was to apply the model-based simulations of sleep times self-reported by M- and E-types for the development of a methodology for the estimation of the delay in the waking times of E-types relative to the waking times of M-types required to overthrow the \"tyranny of the early risers\". Our hypothesis was that, since the literature suggested a >2 h difference between the two chronotypes in the positions of their endogenous circadian phases, such estimates would indicate that permitting a >2 h difference in weekday waking times of M- and E-types can be recommended to equalize the irrecoverable sleep losses on weekdays.