With the urbanization process, an increasing number of sensors are being deployed in transportation systems, leading to an explosion of big data. To harness the power of this vast transportation data, various machine learning (ML) and artificial intelligence (AI) methods have been introduced to address numerous transportation challenges. However, these methods often require significant investment in data collection, processing, storage, and the employment of professionals with expertise in transportation and ML. Additionally, privacy issues are a major concern when processing data for real-world traffic control and management. To address these challenges, the research team proposes an innovative Multi-agent framework named Independent Mobility GPT (IDM-GPT) based on large language models (LLMs) for customized traffic analysis, management suggestions, and privacy preservation. IDM-GPT efficiently connects users, transportation databases, and ML models economically. IDM-GPT trains, customizes, and applies various LLM-based AI agents for multiple functions, including user query comprehension, prompts optimization, data analysis, model selection, and performance evaluation and enhancement. With IDM-GPT, users without any background in transportation or ML can efficiently and intuitively obtain data analysis and customized suggestions in near real-time based on their questions. Experimental results demonstrate that IDM-GPT delivers satisfactory performance across multiple traffic-related tasks, providing comprehensive and actionable insights that support effective traffic management and urban mobility improvement.