## 2 ACT-R Modeling for Task Switching
### Theoretical Background
Accounts of the positive effects of the time spent on a task on task switching can be interpreted as implying that task switching can be rational when any subgoal in the task is not complete, despite the accumulated demands. Alternatively, other accounts have also been suggested in various studies [19; 28; 29], which stated that the task switching likelihood increases according to the declining rate of return as time is spent on the ongoing task. However, some accounts have demonstrated the opposite effect of time spent on an ongoing task. For instance, with vulnerabilities in memory, according to the memory-for-goal theory, task switching can be intentionally inhibited to avoid abandoning the accumulated memory of an ongoing task [28]. Therefore, the inhibition of switching can be increased when more time is spent on the ongoing task, because a longer time spent on the ongoing task will naturally accumulate more ongoing task-relevant memory. Combining the accounts of task switching in terms of the time spent on an ongoing task, it could be interpreted that the decisions to switch from the ongoing task can be made based on the demands of the task and the memory accumulated when performing it. Finally, similar to the abovementioned accounts of task switching decisions based on attributes such as accumulated demands and memory, several studies have represented task switching in terms of a process of deciding which task to perform in discretionary multitasking. For instance, [PERSON] and his colleagues developed strategic task overload management (STOM) [30; 31; 32], which addresses multitasking behaviors in overloaded multitasking environments. The model focuses exclusively on the decision process of which task to perform or which task to continue performing, and it is based on multiple task attributes, including difficulty, interest, priority, salience, and time on the task [30]. In particular, in terms of difficulty, the STOM model assumes that easier alternative tasks can be more attractive than difficult ones; the validation study of the STOM model demonstrated that the greater the difficulty of an ongoing task, the more \"sticky\" is the inhibition to switch away [31]. Moreover, [PERSON] et al. [28] presented the conclusion concerning the task attribute of difficulty as _task end-expectancy_. The greater the time spent on an ongoing task, the greater is the expectation of completing a subgoal of the task execution process, which could lead to a decision to intentionally increase the inhibition of task switching. In this manner, it can be determined that task switching is executed through the decision process in accordance with the attributes of the current tasks, such as the difficulty and time spent on the task in relation to task end-expectancy. Moreover, [PERSON] et al. [21] examined changes in human pupil size during forced and voluntary task switching. The results showed an increase in pupil dilation for the voluntary condition, which could be attributed to the decision to switch. In summary of the abovementioned accounts of task switching, in discretionary multitasking, imbalanced states can cause self-interruptions, which can indicate the point at which a decision is made regarding what task to perform. In addition, the point at which a subtask is completed can also be the time to decide whether to find another task to perform. The decision regarding what task to perform is made by comparing the task attributes of the ongoing task, where task switching is executed if it is rationally determined that a task other than the ongoing task needs to be performed. Accordingly, we herein propose an ACT-R modeling method to represent the process of task switching by self-interruptions based on the abovementioned accounts. Prior to presenting the proposed model, we first discuss the ACT-R cognitive architecture.