M/M/1 Queue Simulation Server

\documentclass[aspectratio=169]{beamer} \usepackage{tikz} \usepackage{xcolor} \usepackage{amsmath} \usepackage{amssymb} \usepackage{hyperref} % Theme \usetheme{Madrid} \usecolortheme{default} % Colors \definecolor{mcpblue}{RGB}{33, 150, 243} \definecolor{mcpgreen}{RGB}{76, 175, 80} \definecolor{mcporange}{RGB}{255, 152, 0} \definecolor{mcppurple}{RGB}{156, 39, 176} % Title \title{\textbf{LLM-MCP Integration for M/M/1 Queue Simulation}} \subtitle{Enhancing Simulation Accessibility through Model Context Protocol} \author{WSC 2025 Research Project} \institute{Winter Simulation Conference 2025} \date{} \begin{document} \begin{frame}[plain] \titlepage \end{frame} \begin{frame}{System Architecture Overview} \begin{columns}[T] % Left Column \begin{column}{0.48\textwidth} \begin{block}{Architecture Layers} \small \textbf{1. User Interface Layer} \begin{itemize} \item Simulation researchers \item Students \& educators \item Natural language via Claude Desktop/CLI \end{itemize} \vspace{0.3cm} \textbf{2. Protocol Layer} \begin{itemize} \item Model Context Protocol (MCP) \item STDIO transport \item Secure data exchange \end{itemize} \vspace{0.3cm} \textbf{3. MCP Server (mcp-server-mm1)} \begin{itemize} \item \textcolor{mcpblue}{7 Resources} (Schema, Metrics, Formulas...) \item \textcolor{mcpgreen}{5 Tools} (Validate, Calculate, Simulate...) \item \textcolor{mcporange}{4 Prompts} (Generate, Explain, Analyze...) \end{itemize} \end{block} \end{column} % Right Column \begin{column}{0.48\textwidth} \begin{block}{Core Components} \small \textbf{4. Simulation Engine} \begin{itemize} \item SimPy 4.0+ discrete event simulation \item Theoretical M/M/1 formulas \end{itemize} \vspace{0.2cm} Key Formulas: \begin{align*} \rho &= \lambda / \mu \quad \text{(Utilization)} \\ L_q &= \rho^2 / (1-\rho) \quad \text{(Queue Length)} \\ W_q &= \rho / (\mu(1-\rho)) \quad \text{(Wait Time)} \end{align*} \vspace{0.3cm} \textbf{5. Distribution Channels} \begin{itemize} \item PyPI: \texttt{pip install mcp-server-mm1} \item Smithery: \texttt{uvx mcp-server-mm1} \item GitHub: Open-source repository \end{itemize} \end{block} \end{column} \end{columns} \end{frame} \begin{frame}{Interaction Flow \& Key Innovations} \begin{columns}[T] \begin{column}{0.48\textwidth} \begin{block}{User-to-Simulation Flow} \scriptsize \begin{enumerate} \item \textbf{User}: ``Simulate M/M/1 with $\lambda=5$, $\mu=8$'' \item \textbf{Claude}: Interprets and calls MCP tools \item \textbf{MCP Server}: \begin{itemize} \item \texttt{validate\_config(5, 8)} $\rightarrow$ Valid ($\rho=0.625$) \item \texttt{calculate\_metrics(5, 8)} $\rightarrow$ Theory \item \texttt{run\_simulation(5, 8, 10000)} $\rightarrow$ SimPy \item \texttt{compare\_results()} $\rightarrow$ Analysis \end{itemize} \item \textbf{Results}: \begin{itemize} \item Utilization: 62.5\% \item Avg queue length: 1.04 \item Avg waiting time: 0.208 \item Accuracy: 98.5\% \end{itemize} \end{enumerate} \end{block} \end{column} \begin{column}{0.48\textwidth} \begin{block}{Key Innovations} \small \textbf{\textcolor{mcpblue}{1. Structured Knowledge}} \begin{itemize} \item 7 Resources = Comprehensive M/M/1 domain \item Zero-hallucination via theoretical validation \end{itemize} \textbf{\textcolor{mcpgreen}{2. Workflow Automation}} \begin{itemize} \item End-to-end: Validate $\rightarrow$ Execute $\rightarrow$ Analyze \item Automated theory vs. simulation comparison \end{itemize} \textbf{\textcolor{mcporange}{3. AI-Assisted Development}} \begin{itemize} \item Production-ready SimPy code generation \item Interactive debugging and optimization \end{itemize} \textbf{\textcolor{mcppurple}{4. Universal Accessibility}} \begin{itemize} \item One-command install: \texttt{uvx mcp-server-mm1} \item Native Claude Desktop/CLI integration \end{itemize} \end{block} \end{column} \end{columns} \vspace{0.5cm} \begin{center} \fbox{% \begin{minipage}{0.9\textwidth} \centering \textbf{Key Achievement:} First production MCP server for discrete event simulation, \\ bridging LLMs and queueing systems through natural language interaction. \end{minipage} } \end{center} \end{frame} \begin{frame}{Technical Implementation \& Impact} \begin{columns}[T] \begin{column}{0.48\textwidth} \begin{block}{Technical Specifications} \small \textbf{Implementation Stack} \begin{itemize} \item Framework: FastMCP (Python 3.10+) \item Simulation: SimPy 4.0+ \item Numerical: NumPy 1.24+ \item Protocol: STDIO transport \end{itemize} \vspace{0.3cm} \textbf{Package Structure} \begin{verbatim} mcp_server_mm1/ ├── server.py ├── schemas/mm1_schema.py ├── simulations/mm1_queue.py └── utils/metrics.py \end{verbatim} \vspace{0.3cm} \textbf{Deployment} \begin{itemize} \item PyPI: \href{https://pypi.org/project/mcp-server-mm1}{pypi.org/project/mcp-server-mm1} \item GitHub: Public repository \item Docker: Containerized \item Smithery: MCP registry \end{itemize} \end{block} \end{column} \begin{column}{0.48\textwidth} \begin{block}{Research Contributions} \small \textbf{1. Novel Integration Pattern} \begin{itemize} \item First production MCP for DES \item LLM-simulation interoperability \item Reusable for M/M/c, M/G/1, networks \end{itemize} \textbf{2. Educational Impact} \begin{itemize} \item Natural language access to theory \item Interactive learning through simulation \item Automated code generation for students \end{itemize} \textbf{3. Workflow Acceleration} \begin{itemize} \item From ``write code'' to ``describe needs'' \item Instant validation and stability checking \item Auto theory-simulation comparison \end{itemize} \end{block} \begin{block}{By the Numbers} \centering \begin{tabular}{ll} \textcolor{mcpblue}{7 Resources} & Domain knowledge \\ \textcolor{mcpgreen}{5 Tools} & Complete workflow \\ \textcolor{mcporange}{4 Prompts} & AI assistance \\ \textcolor{mcppurple}{100\% deployed} & PyPI + Smithery \\ \end{tabular} \end{block} \end{column} \end{columns} \end{frame} \end{document}