MCP Server for M/M/1 and M/M/c Queue Simulation

A Model Context Protocol server that provides comprehensive resources, tools, and prompts for M/M/1 and M/M/c queuing system simulation and analysis.

New in v0.2.0: Full M/M/c support with comparison tools!

What is M/M/1 and M/M/c?

M/M/1 and M/M/c are fundamental queuing models in operations research:

• First M: Markovian (Poisson) arrivals

• Second M: Markovian (exponential) service times

• 1 or c: Number of servers (1 for M/M/1, c for M/M/c)

This MCP server enables LLMs like Claude to:

• Simulate both M/M/1 and M/M/c systems

• Compare separate queues vs pooled queue strategies

• Validate simulation parameters

• Calculate theoretical performance metrics

• Generate and execute SimPy simulations

• Analyze real-world scenarios (supermarkets, banks, etc.)

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 (8)

• validate_config - Validate M/M/1 parameters and check stability

• calculate_metrics - Compute theoretical performance metrics

• run_simulation - Execute M/M/1 simulation (legacy)

• run_mmc_simulation - Execute M/M/c simulation (NEW!)

• compare_mm1_vs_mmc - Compare separate vs pooled queues (NEW!)

• analyze_cashier_problem - Supermarket scenario analysis (NEW!)

• 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)

Option 2: Using pip

Option 3: From Source

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

Restart Claude Desktop and the server will be available!

Example Usage in Claude

1. Get M/M/1 Schema

2. Validate Configuration

3. Calculate Theoretical Metrics

4. Run Simulation

5. Generate Code

Development

Setup Development Environment

Run Tests

Code Quality

Local Testing

Use the MCP Inspector to test the server locally:

This opens a web interface where you can:

• Browse available resources

• Test tool invocations

• Try prompt templates

• Inspect JSON-RPC communication

Architecture

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 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

• SimPy Documentation

• M/M/1 Queue - Wikipedia

Support

• Issues: GitHub Issues

• Discussions: GitHub Discussions

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