1. 30 déc., 2025 2 validations
    • Hamadou Ba's avatar
      feat: Phase 4 - Jackson's theorem analytical module · 92152fa2
      Hamadou Ba a écrit
      Implement analytical analysis using Jackson's theorem for open networks
      
      Jackson's Theorem Implementation:
      - analytics/jackson.py: Complete Jackson theorem analyzer
        - Calculate effective arrival rates (λᵢ)
        - Calculate utilizations (ρᵢ = λᵢ/μᵢ)
        - Stability check (ρᵢ < 1 for all queues)
        - M/M/1 formulas: L = ρ/(1-ρ), W = L/λ
        - System-wide metrics using Little's Law
        - Handles both stable and unstable queues
      
      Mathematical Formulas:
      - Effective arrival rates for network topology
      - Utilization: ρᵢ = λᵢ / μᵢ
      - Average customers: Lᵢ = ρᵢ / (1 - ρᵢ)
      - Average time: Wᵢ = Lᵢ / λᵢ (Little's Law)
      - Average wait: Wq = W - 1/μ
      - Total system: L_total = Σ Lᵢ, W_total = L_total / λ₀
      
      Comparison Module:
      - analytics/comparison.py: Compare analytical vs simulation
        - QueueComparison for per-queue metrics
        - NetworkComparison for system-wide comparison
        - Percentage difference calculations
        - Formatted comparison reports
      
      Testing & Validation:
      - tests/test_analytics.py: 7 tests validating Jackson's theorem
        - Simple M/M/1 queue (analytical vs theory)
        - Unstable queue detection (ρ > 1)
        - Network with multiple servers
        - Little's Law validation (L = λW)
        - Probability conservation
        - Effective arrival rates
        - Multi-server stability
      
      Demo & Examples:
      - demo_analytical.py: Compare analytical vs simulation for scenarios
        - Runs scenarios 1-3
        - Shows theoretical predictions
        - Shows simulation results
        - Detailed comparison tables
        - Percentage differences
      
      Results:
      -  All 7 analytical tests pass
      -  Little's Law validated for all queues
      -  Stability detection working correctly
      -  Comparison reveals expected statistical variation
      
      Observations:
      - Analytical predictions are accurate for stable systems
      - Simulation shows statistical variation (finite sample)
      - Unstable queues detected correctly (ρ ≥ 1)
      - Differences increase with higher utilization
      
      Phase 4 Complete ✓
      Next: Phase 5 - Backend API implementation
      92152fa2
    • Hamadou Ba's avatar
      feat: Phase 2 - Core simulation engine implementation · bca9b73c
      Hamadou Ba a écrit
      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
      bca9b73c