M/M/1 Queue Simulation Server

# MCP Server for M/M/1 Queue Simulation A [Model Context Protocol](https://modelcontextprotocol.io/) server that provides comprehensive resources, tools, and prompts for M/M/1 queuing system simulation and analysis. [](https://www.python.org/downloads/) [](https://opensource.org/licenses/MIT) [](https://modelcontextprotocol.io/) ## What is M/M/1? M/M/1 is a fundamental queuing model in operations research: - **First M**: Markovian (Poisson) arrivals - **Second M**: Markovian (exponential) service times - **1**: Single server This MCP server enables LLMs like Claude to: - Access structured M/M/1 theory and formulas - Validate simulation parameters - Calculate theoretical performance metrics - Generate and execute SimPy simulations - Compare simulation results with theory ## Features ### 📚 Resources (7) - `mm1://schema` - Complete M/M/1 system schema - `mm1://parameters` - Parameter definitions with constraints - `mm1://metrics` - Performance metrics catalog - `mm1://formulas` - Theoretical formulas - `mm1://guidelines` - Implementation best practices - `mm1://examples` - Pre-configured scenarios - `mm1://literature` - References and citations ### 🔧 Tools (5) - `validate_config` - Validate M/M/1 parameters and check stability - `calculate_metrics` - Compute theoretical performance metrics - `run_simulation` - Execute SimPy discrete event simulation - `compare_results` - Analyze simulation accuracy - `recommend_parameters` - Suggest optimal configuration ### 💬 Prompts (4) - `generate_simulation_code` - Create production-ready SimPy code - `explain_mm1_theory` - Educational content on M/M/1 theory - `analyze_results` - Interpret simulation outcomes - `debug_simulation` - Troubleshoot common issues ## Installation ### Option 1: Using `uvx` (Recommended) ```bash uvx mcp-server-mm1 ``` ### Option 2: Using `pip` ```bash pip install mcp-server-mm1 mcp-server-mm1 ``` ### Option 3: From Source ```bash git clone https://github.com/yourusername/mcp-server-mm1.git cd mcp-server-mm1 uv pip install -e . mcp-server-mm1 ``` ## Usage with Claude Desktop Add to your `claude_desktop_config.json`: ### macOS Location: `~/Library/Application Support/Claude/claude_desktop_config.json` ### Windows Location: `%APPDATA%\Claude\claude_desktop_config.json` ### Configuration ```json { "mcpServers": { "mm1-simulation": { "command": "uvx", "args": ["mcp-server-mm1"] } } } ``` Restart Claude Desktop and the server will be available! ## Example Usage in Claude ### 1. Get M/M/1 Schema ``` User: Show me the M/M/1 queue schema Claude uses: mm1://schema resource ``` ### 2. Validate Configuration ``` User: Is λ=5, μ=8 a valid M/M/1 configuration? Claude uses: validate_config tool Result: ✓ Valid, ρ=0.625 ``` ### 3. Calculate Theoretical Metrics ``` User: Calculate theoretical metrics for λ=5, μ=8 Claude uses: calculate_metrics tool Result: - Utilization: 0.625 - Avg queue length: 1.0417 - Avg waiting time: 0.2083 - Avg system time: 0.3333 ``` ### 4. Run Simulation ``` User: Run a simulation with λ=5, μ=8 for 10,000 time units Claude uses: run_simulation tool Result: Simulation metrics + theoretical comparison + accuracy analysis ``` ### 5. Generate Code ``` User: Generate SimPy code for λ=3, μ=10 Claude uses: generate_simulation_code prompt Result: Complete, production-ready Python code ``` ## Development ### Setup Development Environment ```bash # Clone repository git clone https://github.com/yourusername/mcp-server-mm1.git cd mcp-server-mm1 # Install dependencies uv pip install -e ".[dev]" ``` ### Run Tests ```bash pytest ``` ### Code Quality ```bash # Format code black src/ tests/ # Lint ruff check src/ tests/ # Type check mypy src/ ``` ### Local Testing Use the MCP Inspector to test the server locally: ```bash # Install MCP inspector (if not already installed) npm install -g @modelcontextprotocol/inspector # Run server with inspector mcp dev src/mcp_server_mm1/server.py ``` This opens a web interface where you can: - Browse available resources - Test tool invocations - Try prompt templates - Inspect JSON-RPC communication ## Architecture ``` src/mcp_server_mm1/ ├── server.py # FastMCP server with resources/tools/prompts ├── schemas/ │ └── mm1_schema.py # M/M/1 system schema definition ├── simulations/ │ └── mm1_queue.py # SimPy simulation implementation └── utils/ └── metrics.py # Theoretical calculations ``` ## M/M/1 Theory Quick Reference ### Key Formulas Given arrival rate λ and service rate μ: - **Utilization**: ρ = λ/μ - **Avg Queue Length**: L_q = ρ²/(1-ρ) - **Avg Time in Queue**: W_q = ρ/(μ(1-ρ)) - **Avg Time in System**: W = 1/(μ(1-ρ)) ### Stability Condition System must satisfy **ρ < 1** (λ < μ) If ρ ≥ 1, the queue grows unbounded! ## Contributing Contributions are welcome! Please: 1. Fork the repository 2. Create a feature branch 3. Make your changes with tests 4. Submit a pull request ## License MIT License - see [LICENSE](LICENSE) file for details. ## Related Work This MCP server was developed as part of research on LLM-assisted simulation code generation for the Winter Simulation Conference (WSC) 2025. ## References - [Model Context Protocol Documentation](https://modelcontextprotocol.io/) - [SimPy Documentation](https://simpy.readthedocs.io/) - [M/M/1 Queue - Wikipedia](https://en.wikipedia.org/wiki/M/M/1_queue) ## Support - **Issues**: [GitHub Issues](https://github.com/yourusername/mcp-server-mm1/issues) - **Discussions**: [GitHub Discussions](https://github.com/yourusername/mcp-server-mm1/discussions) --- **Made with ❤️ for the simulation and LLM communities**