# Process Mining IPTV Customer Eye Gaze Movement Using Discrete-Time Markov Chains +
## 4 Results
### DTMC-\"Content Viewing\" Screens  
After developing the DTMC model, it was revealed that given the restricted time allotted for this particular activity, participants did not focus on certain blocks as they did in previous tasks. Therefore, the state space of the DTMC model is finalised as \(S=\{B,D,E,F,G,\)\(H,I,J,K,L,M,N,O,P,Q,R,S,T\}\). The Markov Modelling of the \"**content viewing**\" screen is implemented in R Studio by the \"markovovain\" package and R functions belonging to it, which was previously discussed in Section 3.4.2. In R studio, after the DTMC object is created, the properties of the model can be checked by calling the object itself as well as specific functions, see Figure 19. In the example, the created DTMC object is named \"dtmcA\", and the R function \"communicateingClasses()\" is executed. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**AOI/State Name** & **Expected Time to Absorption** \\ \hline A & 9.67 s \\ B & 9.67 s \\ C & 9.59 s \\ D & 9.54 s \\ Z & 9.49 s \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Expected time to absorption from each state–DTMC for screen B.  
Figure 19: Markov Model properties–content viewing screen. Observe that there is only one communicating class in the model and that all states communicate. When a participant looks at one block on the page, there is always a path in the subsequent n steps of the gaze movement by which they will finally look at the remaining blocks in the DTMC model. In addition, it strengthens the likelihood that participants explored the page across all AOIs throughout the trial. There is no absorbing state, i.e., participants are unlikely to concentrate on a single AOI for the duration of the experiment. The transition matrix of the DTMC, as well as the matrix of mean first passage times (see Equation (14)), are presented in the 18 \(\times\) 18 matrices in Figures 20 and 21 below. In the row of R of the transition matrix (Figure 20), besides the diagonal cell (R,R), all other values in the cell are small. On the basis of this data, we may conclude that when participants notice AOI R (background image), they tend to study it further rather than moving on to other places. In addition, columns R and T have the greatest number of values, indicating a high chance of transition from other states in the Markov Model, indicating  
Figure 21: Matrix of mean first passage time–”content viewing” screen [16]. Figure 20: Transition matrix–”content viewing” screen [16]. that participants are likely to shift their attention to AOI-R or AOI-T from other AOIs. It indicates that the backdrop image is appealing to participants for AOI-R. T represents non-AOI portions of the display; it is a segment between many blocks. Participants shift their eyes to AOI-T, presumably because they will observe another AOI via T.  
In Figure 21, the value in each cell is related to the number of steps before the DTMC reaches the destination state from the initial state. The diagonal values are 0 s because it takes no step to reach the state from itself. The values can also reflect the actual time (time = step number \(\times\) eye tracker recording interval) participants spend to move their gaze from one block to another. On the other hand, the values also reflect the connections between every two blocks regarding the page layout. For instance, from the initial state H, it takes the chain Six steps to reach state R (cell(H, R)). Six is the minimum value among all other cases at which the chain reaches state R from the other initial states. The reason is that, according to the page layout (Figure 5), block H is adjacent to block R. Moreover, cell (H,R) has the lowest value in the matrix, indicating that once participants see the music button, they will quickly gaze at the backdrop image. In addition, column H has the highest average value compared to the other columns, indicating that it takes the longest time for the chain to reach state H from other states.