Automation is a necessity in modern society. People sometimes are inclined to trust automation too much. On the other hand, they sometimes tend to not be willing to use automation. To prevent these mistakes, this study explores factors of reaching an appropriate reliance on automation systems by using cognitive modeling. We have conducted psychological experiments on this problem using a simple line-tracing (driving) task where the participants had to track the line with a circle by pressing the arrow key on the keyboard (manual control) or rely on automation (auto control). They could switch between auto and manual control during the task. The success probabilities of each control mode were systematically varied. The ACT-R model that simulates these experiments was constructed by representing the reliance on the automation as utilities of rules. The model performs this task by firing rules that manage the perceptual/motor modules. The perceptual module finds and attends to the vehicle and the road on the screen, and the motor module press the keys depending on the current controlling modes or the current positional relation between the vehicle and the road. The utilities of these rules are updated based on the rewards in every screen update. This utility module is also compatible to a previous computational model of automation reliance. A preliminary run of this model simulated several qualitative features of the behavioral data. The ways it does not fit suggest that the model should be more sophisticated in its representation of space and process.