While modeling user performance in human-computer interaction has been actively conducted, the user input in a temporally constrained task has not been sufficiently studied. However, for tasks such as games where real-time human-computer interaction is crucial, it is essential to understand the impact of time constraints. Therefore, this paper proposed a cognitive model that understands the effects of input latency -- as a kind of temporal variable -- on user input, and predicts user input behavior in the moving-target acquisition (MTA) task. Then, as an application of the proposed model, a latency compensation method was developed to maintain players' performance regardless of input latency. This dissertation also verified the accuracy of the proposed model by analyzing play data of various games designed for the experiments and a game in actual service. Finally, a number of artificial players were created using the model's free parameters extracted from the actual game data. The virtual players and the model were used to develop a game design assisting tool that predicts the difficulty of MTA games. The proposed model was able to simulate user behavior with the presence of input delay with high accuracy, and it is expected to be applicable to interface design where temporal factors matter.