## 3 Model Validation  
### Design  
The model in this study represents the cognitive process of task switching as self-interruption according to the imposed mental demands, followed by a decision as to whether to switch tasks based on the task attributes. To validate the model, an illustrative model of a dual task was developed based on the modeling method, and the simulated results of the model were compared with the results of an empirical test. The dual task used in this study includes a primary task that has several mental demand levels and a secondary task that is easy in comparison to the primary task. The primary task involves a memory game, usually referred to as a concentration or pair game. In the memory game, a deck of cards that includes pairs of matching images is used. The goal of this game is to match all the pairs. All cards are laid face down at the start of the game. The players then flip two cards sequentially. If the flipped cards match, they are kept facing upwards; if not, they are flipped to face downwards. The memory game has been altered in various ways in certain studies to meet their respective goals [21; 42]. Therefore, this game was slightly altered for the experiment in this study, such that there were 20 cards consisting of ten pairs arranged in a 5 \(\times\) 4 matrix, as shown in Figure 4a. The cards depicted four types of images, depending on the level of difficulty, as shown in Table 1.  
The secondary task in the experiment involved a visual attention task called a subitizing task [43]. In this type of task, several visual objects are presented to the subject, and the subject must identify the number of objects present [44]. In the experiment, the subject must identify the number of target cards with only one diamond on the screen and then click on the card corresponding to the number of identified target cards (see Figure 4b). The number of target cards varied between five and nine. Because this secondary task is less demanding than the easiest version of the primary task, it can result in a switch to the secondary task when the primary task is too difficult. Additionally, at least five visual objects must be identified in this task, which prevents the rehearsal of the primary task when performing the secondary task. In other words, the subitizing task was chosen for the experiment. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Difficulty** & **Image Form** & **Alternative Image Form** & **Instance** \\ \hline Level 1 & Diamond at playing card & Diamond at playing card & (see Figure 4a) \\ Level 2 & Three-letter word & Reverse order of the word & DOG, GOD \\ Level 3 & Simple calculation & Simple calculation with the same answer & 2 \(\times\) 3, 4 + 2 \\ Level 4 & Simple equation & Simple equation with the same answer & X + 2 = 3, 2X + 3 = 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Four types of images on the cards in the primary task. Figure 4: Interface of the primary task (**a**) and the secondary task (**b**). The primary task, i.e., the memory game, includes a subgoal of matching a pair of cards by repeating a small unit of a task to select and click on a card, and the primary task is to perform the repetition of the subtask associated with the subgoal ten times. According to the characteristics of the memory game, three results concerning task switching can be expected based on the abovementioned accounts of task switching. First, most task switching will be performed just after achieving a subgoal, that is, when cognitive resources are free because of the completion of the subtask of matching a pair of cards, in accordance with accounts based on the availability of cognitive resources. Second, according to difficulty-based accounts, the greater the difficulty of the memory game, the greater the task switching that occurs during the execution of a subtask. If the level of difficulty of the memory game is high, each time a card is identified, it will consume considerable cognitive resources and increase the likelihood of switching to another task.