With the recent surge in personalized learning, Intelligent Tutoring Systems (ITS) that can accurately track students' individual knowledge states and provide tailored learning paths based on this information are in demand as an essential task. This paper focuses on the core technology of Knowledge Tracing (KT) models that analyze students' sequences of interactions to predict their knowledge acquisition levels. However, existing KT models suffer from limitations such as restricted input data formats, cold start problems arising with new student enrollment or new question addition, and insufficient stability in real-world service environments. To overcome these limitations, a Practical Interlinked Concept Knowledge Tracing (PICKT) model that can effectively process multiple types of input data is proposed. Specifically, a knowledge map structures the relationships among concepts considering the question and concept text information, thereby enabling effective knowledge tracing even in cold start situations. Experiments reflecting real operational environments demonstrated the model's excellent performance and practicality. The main contributions of this research are as follows. First, a model architecture that effectively utilizes diverse data formats is presented. Second, significant performance improvements are achieved over existing models for two core cold start challenges: new student enrollment and new question addition. Third, the model's stability and practicality are validated through delicate experimental design, enhancing its applicability in real-world product environments. This provides a crucial theoretical and technical foundation for the practical implementation of next-generation ITS.