Problèmes corrigés:
1. average_customers_in_system était toujours 0 (non calculé)
2. Comparaison utilisait γ₀ au lieu de λ₀ (erreur 101%)

Modifications:
- simulation.py: Ajout calcul L = λ₀ × W (Loi de Little)
- jackson.py: Ajout champ external_arrival_rate (λ₀)
- comparison.py: Utilisation de λ₀ au lieu de γ₀ pour L total
- analytics.py: Mise à jour API response model
- simulation.ts: Ajout external_arrival_rate dans types

Tests: ✓ 21/21 tests passent

Backend (Python):
- Collecte de données de séries temporelles (échantillonnage toutes les 1000 unités)
- Comptage du nombre de clients par file au fil du temps
- Génération d'histogramme des temps de traitement (20 bins)
- Calcul de statistiques: min, max, moyenne, écart-type
- Ajout des champs time_series_data et histogram_data à SimulationResults
- Méthode _create_histogram() pour génération automatique des bins

Frontend (React + TypeScript):
- Nouveau composant TimeSeriesChart: graphique de l'évolution du nombre de clients
  * Affiche la convergence vers l'état stable
  * Utilise Chart.js Line chart
  * Responsive avec Material-UI Paper
- Nouveau composant ProcessingTimeHistogram: distribution des temps de traitement
  * Barres montrant la distribution exponentielle
  * Statistiques affichées (min, moyenne, écart-type, max)
  * Utilise Chart.js Bar chart
- Intégration dans ResultsDisplay onglet Visualisations
- Nouveaux types TypeScript: TimeSeriesData, HistogramData

Améliorations TP:
✓ Visualisation de la convergence vers l'état d'équilibre
✓ Validation de la distribution exponentielle (M/M/1)
✓ Graphiques scientifiques pour le rapport

Build: ✓ 720.12 kB (gzip 231.51 kB)

Add Pydantic models for API validation and 5 project scenarios

Pydantic Models:
- models/config.py: SimulationConfigModel with full validation
  - ServerConfig for each server in the network
  - Probability conservation validation
  - Conversion to internal SimulationConfig

- models/results.py: Complete results models for API responses
  - QueueStatisticsModel per queue
  - TimeSeriesDataModel for evolution tracking
  - HistogramDataModel for processing time distribution
  - SimulationResultsModel with all metrics

Predefined Scenarios:
- scenarios.py: 5 scenarios from project requirements
  - Scenario 1: 1 fast server (120ms) - instability test
  - Scenario 2: 1 fast + 1 slow server (120ms/240ms)
  - Scenario 3: 3 slow servers (240ms each)
  - Scenario 4: 1 fast + 1 medium (120ms/190ms) - compare with scenario 3
  - Scenario 5: Parameter sensitivity (vary λ and p)

- Theoretical utilization calculations for each scenario
- Scenario registry for easy access
- list_scenarios() function for API

Testing:
- test_all_scenarios.py: Comprehensive test of all scenarios
- Runs all 5 scenarios with variations
- Compares theoretical vs simulation results
- Summary table for performance comparison

Results Analysis:
- All scenarios execute successfully
- Stable systems show ρ < 1 as expected
- Some scenarios show slight instability (ρ ≈ 1.0) due to high load
- Parameter sensitivity variations demonstrate impact of λ and p

Phase 3 Complete ✓
Next: Phase 4 - Analytical module (Jackson's theorem)

Implement event-driven discrete simulation for queueing networks

Core Components:
- events.py: Event and EventType for discrete event simulation
  - Priority queue ordering by time
  - ARRIVAL and SERVICE_END event types

- request.py: Request entity with full visit tracking
  - QueueVisit records for each queue visited
  - Automatic calculation of wait/service/system times
  - Journey tracking through network

- random_utils.py: Random number generation
  - Exponential distribution (inverse transform method)
  - Probabilistic choice for routing decisions
  - Seed control for reproducibility

- queues.py: M/M/1 Queue implementation
  - FIFO discipline with single server
  - Complete statistics collection (utilization, avg times)
  - Exponential service times

- router.py: Probabilistic routing logic
  - Route from coordinator: exit (p) or server (qi)
  - Route from server: always return to coordinator
  - Probability conservation validation

- simulation.py: Main event-driven simulator
  - Priority queue (heapq) for event scheduling
  - Warmup period to reach steady state
  - Complete statistics generation
  - Support for multiple servers

Testing:
- test_random_utils.py: Validate exponential distribution (mean, reproducibility)
- test_simulation.py: End-to-end simulation tests
  - Stable and unstable systems
  - Multiple servers
  - Reproducibility with seeds

Demo:
- demo_simulation.py: Scenario 1 demonstration (1 fast server)
- Theoretical vs simulation comparison
- All 14 tests passing ✓

Phase 2 Complete ✓
Next: Phase 3 - Statistics collection and multi-server scenarios

Initialize Turborepo monorepo with Python backend and React frontend

- Setup Turborepo configuration with workspaces
- Configure Python FastAPI backend
  - Create project structure (core, analytics, api, models)
  - Add requirements.txt with FastAPI, Uvicorn, Pydantic, etc.
  - Basic FastAPI app with health endpoints
  - CORS middleware for frontend integration
- Configure React + TypeScript + Vite frontend
  - Install dependencies (Chart.js, D3.js, Zustand, Axios)
  - Setup Tailwind CSS with PostCSS
  - Create component directory structure
  - Basic landing page with Tailwind styling
- Add comprehensive README files
- Configure .gitignore for Python and Node.js

Phase 1 Complete ✓
Next: Phase 2 - Core simulation engine implementation