PEA Challenges

Worked solutions to performance-evaluation case studies, combining JMT/JMVA queueing models with Python analytical solvers.

🌟 Highlights

• 18 independent case studies, from staffing a medical center to sizing a hybrid-cloud deployment.
• Every challenge pairs a JMT/JMVA network model (.jsimg) with a Python script that solves the same problem analytically.
• Reusable queueing solvers for classic models: M/M/c/K, multiclass MVA, M/G/1.
• Each script generates its own plots (utilization, response time, cost curves) alongside the numerical results.
• A consistent folder layout across all challenges, so any solution can be reused as a template for a new problem.

ℹ️ Overview

This repository collects solved assignments from the Performance Evaluation and Applications course. Each challenge starts from a short description of a real system — a medical center, a RAID array, an online shop, a car maintenance facility — and asks questions like: how many servers are needed? What response time can be expected? What's the optimal trade-off between cost and performance?

Every problem is worked out in two complementary ways: a queueing-network model built with JMT/JMVA (Java Modelling Tools), and a Python script that solves the same model analytically. The repository is meant for students and practitioners who want to see performance-evaluation techniques — queueing networks, mean value analysis, cost optimization — applied to concrete, end-to-end examples instead of isolated formulas.

🧩 How It Works

Each challenge follows the same pipeline:

1. Assignment — a short problem statement describes the system, its workload, and the questions to answer (see each challenge's own README.md).
2. Modeling — the system is represented as a queueing network, either as a JMT/JMVA model file (.jsimg) or as an analytical model in Python.
3. Solving — a Python solver (e.g. MMcKSolve, MVAmcmsSolve, MG1Solve) computes performance indices such as utilization, throughput, response time, and cost.
4. Visualization — results are plotted with matplotlib and saved as figures for quick inspection.

🚀 Usage

Run any challenge's solution script directly with Python:

cd challenges/A13-cache-performance/solution
python3 A13_solution.py

For example, the solver in A05-car-maintenance-facility/solution searches for the number of service nodes that minimizes total cost, using an M/M/c/K queueing model:

from MMcK import MMcKSolve

sol = MMcKSolve(D, c, K, Lambda)   # solve the M/M/c/K queue
cost = n * (Cfix + sol['Uave'] * Cvar) + Cpen * sol['Dr']

Running the script prints the optimal configuration and saves a cost-vs-capacity plot in the same folder.

The .jsimg files under each challenge's models/ folder are JMT (Java Modelling Tools) projects and can be opened with JMT itself.

⬇️ Installation

Requirements

• Python 3.9+
• NumPy and Matplotlib
• JMT (Java Modelling Tools) and a Java runtime, only if you want to open the .jsimg model files

Setup

git clone https://github.com/AlessandroAssini/SystemPerformanceModels.git
cd SystemPerformanceModels
pip install numpy matplotlib

There is no shared build step: each challenge is self-contained under challenges/<challenge-name>/solution/.

📁 Project Structure

SystemPerformanceModels/
├── challenges/
│   ├── A01-medical-center/
│   │   ├── README.md        # assignment description and folder contents
│   │   ├── models/          # JMT/JMVA .jsimg models
│   │   └── figures/         # generated plots
│   ├── A12-microservice-cost-minimization/
│   │   ├── notes/           # assignment notes
│   │   └── solution/        # Python solvers and scripts
│   └── ...                  # 18 challenges in total
└── README.md

🛠️ Technologies

• Language: Python 3
• Numerical computing: NumPy
• Visualization: Matplotlib
• Queueing-network modeling: JMT / JMVA (.jsimg model files)
• Documentation: Markdown

✍️ Authors

• Alessandro Assini

Developed as part of the Performance Evaluation and Applications university course.

🤝 Contributing

This repository mainly documents solved coursework, but suggestions are welcome:

• Open an issue to report a mistake or suggest an improvement.
• Submit a pull request to propose a fix or an additional challenge.

📄 License

This project is licensed under the MIT License.

📖 Further Reading

Each challenge has its own README.md describing the specific problem and folder contents:

• A01-medical-center
• A02-local-versioning-service
• A03-3d-printing-service
• A04-electric-car-charging-facility
• A05-car-maintenance-facility
• A06-microcontroller
• A07-insurance-backend
• A08-raid-1-comparison
• A09-city-transport-system
• A10-production-plant-inspections
• A11-server-on-off-features
• A12-microservice-cost-minimization
• A13-cache-performance
• A14-secure-system-balancing
• A15-media-decoder
• A16-hybrid-cloud
• A17-online-shop
• A18-secure-transaction-system