M/M/1 Queue Simulation Server

# System Architecture: LLM-MCP Integration for M/M/1 Queue Simulation ## Overall System Architecture ```mermaid graph TB subgraph Users["👥 User Layer"] U1[Simulation Researchers] U2[AI/LLM Developers] U3[Students & Educators] end subgraph Interface["💻 Interface Layer"] Claude[Claude Desktop/CLI] API[Claude API] end subgraph Protocol["🔌 Protocol Layer"] MCP[Model Context Protocol] STDIO[STDIO Transport] end subgraph Server["🚀 MCP Server: mcp-server-mm1"] direction TB Resources["📚 7 Resources • Schema • Parameters • Metrics • Formulas • Guidelines • Examples • Literature"] Tools["🔧 5 Tools • validate_config • calculate_metrics • run_simulation • compare_results • recommend_parameters"] Prompts["💬 4 Prompts • generate_simulation_code • explain_mm1_theory • analyze_results • debug_simulation"] end subgraph Core["⚙️ Core Engine"] SimPy["SimPy Discrete Event Simulation"] Theory["Theoretical Metrics M/M/1 Formulas"] end subgraph Distribution["📦 Distribution Channels"] PyPI["PyPI Registry pip install mcp-server-mm1"] Smithery["Smithery Registry uvx mcp-server-mm1"] GitHub["GitHub Repository Source Code"] end Users --> Interface Interface --> Protocol Protocol --> Server Server --> Core Distribution -.-> Server Resources --> Core Tools --> Core Prompts --> Tools style Server fill:#e1f5ff style Core fill:#fff4e1 style Distribution fill:#f0e1ff style Protocol fill:#e1ffe1 ``` ## Component Interaction Flow ```mermaid sequenceDiagram participant User as 👤 User participant Claude as 🤖 Claude participant MCP as 🔌 MCP Protocol participant Server as 🚀 MCP Server participant SimPy as ⚙️ SimPy Engine User->>Claude: "Simulate M/M/1 queue with λ=5, μ=8" Claude->>MCP: Request via STDIO MCP->>Server: validate_config(5, 8) Server-->>MCP: ✓ Valid (ρ=0.625) MCP->>Server: calculate_metrics(5, 8) Server-->>MCP: Theoretical results MCP->>Server: run_simulation(5, 8, 10000) Server->>SimPy: Execute discrete event simulation SimPy-->>Server: Simulation metrics Server->>Server: compare_results() Server-->>MCP: Combined analysis MCP-->>Claude: Structured response Claude-->>User: "System utilization: 62.5%..." ``` ## MCP Server Architecture ```mermaid graph LR subgraph "MCP Server Package" direction TB subgraph "Resources Layer" R1[mm1://schema] R2[mm1://parameters] R3[mm1://metrics] R4[mm1://formulas] end subgraph "Tools Layer" T1[validate_config] T2[calculate_metrics] T3[run_simulation] T4[compare_results] end subgraph "Core Layer" S1[schemas/mm1_schema.py] S2[simulations/mm1_queue.py] S3[utils/metrics.py] end Resources --> Core Tools --> Core Core --> S1 Core --> S2 Core --> S3 end ``` ## Technology Stack ```mermaid mindmap root((MCP Server mcp-server-mm1)) Framework FastMCP Python 3.10+ Model Context Protocol Simulation SimPy 4.0+ NumPy 1.24+ Exponential Distributions Distribution PyPI Registry Smithery Registry Docker Container Features 7 Resources 5 Tools 4 Prompts STDIO Transport ``` ## Deployment Architecture ```mermaid graph TB subgraph Development Code[Source Code] PyProject[pyproject.toml] Smithery[smithery.yaml] Docker[Dockerfile] end subgraph Build GitHub[GitHub Actions] Build[python -m build] DockerBuild[Docker Build] end subgraph Distribution PyPI[PyPI Registry] SmitheryReg[Smithery Registry] Container[Docker Hub] end subgraph Installation PipInstall["pip install mcp-server-mm1"] UvxInstall["uvx mcp-server-mm1"] ClaudeDesktop["Claude Desktop Config"] end Development --> Build Build --> Distribution Distribution --> Installation style Distribution fill:#e1f5ff style Installation fill:#e1ffe1 ``` ## Key Metrics - **7 MCP Resources**: Comprehensive M/M/1 knowledge base - **5 MCP Tools**: End-to-end simulation workflow - **4 MCP Prompts**: AI-assisted code generation and analysis - **100% PyPI Deployment**: Available worldwide via pip/uvx - **STDIO Protocol**: Native Claude Desktop/CLI integration