In transportation system demand modeling and simulation, agent-based models and microsimulations are current state-of-the-art approaches. However, existing agent-based models still have some limitations on behavioral realism and resource demand that limit their applicability. In this study, leveraging the emerging technology of large language models (LLMs) and LLM-based agents, we propose a general LLM-agent-based modeling framework for transportation systems. We argue that LLM agents not only possess the essential capabilities to function as agents but also offer promising solutions to overcome some limitations of existing agent-based models. Our conceptual framework design closely replicates the decision-making and interaction processes and traits of human travelers within transportation networks, and we demonstrate that the proposed systems can meet critical behavioral criteria for decision-making and learning behaviors using related studies and a demonstrative example of LLM agents' learning and adjustment in the bottleneck setting. Although further refinement of the LLM-agent-based modeling framework is necessary, we believe that this approach has the potential to improve transportation system modeling and simulation.