Congestion¶

Traffic buildup and its measurement.

What is Congestion?¶

Congestion occurs when demand for resources exceeds capacity, causing delays.

Congestion Indicators¶

Robots waiting for access
Increased travel times
Queue formation
Reduced throughput

Measuring Congestion¶

Wait Time¶

Time spent waiting for resources:

Wait time = Actual travel time - Theoretical travel time

Occupancy¶

Resource utilization over time:

Occupancy = Time occupied / Total time

Queue Length¶

Number of robots waiting:

Avg queue = Σ(queue_length × duration) / Total time

Congestion Levels¶

Free Flow¶

Occupancy: ████░░░░░░ (40%)
Wait time: ~0
Throughput: 100%

Robots move without delay

Light Congestion¶

Occupancy: ██████░░░░ (60%)
Wait time: Low
Throughput: 95%

Occasional brief waits

Moderate Congestion¶

Occupancy: ████████░░ (80%)
Wait time: Noticeable
Throughput: 80%

Frequent waits, queues forming

Heavy Congestion¶

Occupancy: ██████████ (100%)
Wait time: High
Throughput: 50%

Long queues, significant delays

Gridlock¶

Occupancy: ██████████ (100%)
Wait time: Infinite
Throughput: 0%

No movement, deadlock risk

Congestion Patterns¶

Hotspots¶

Locations with consistently high congestion:

Warehouse Map:
  ░░░░░░░░░░
  ░░░░██░░░░  ← Hotspot
  ░░░░░░░░░░
  ░░░░░░░░░░

Common hotspots: - Station approaches - Main intersections - Narrow passages

Time-Based Patterns¶

Congestion varies over time:

Congestion
    │
    │     ╱╲
    │    ╱  ╲
    │   ╱    ╲──────╱╲
    │  ╱              ╲
    │ ╱                ╲
    │╱                  ╲
    └─────────────────────── Time
         Peak   Off-peak

Wave Propagation¶

Congestion spreads from source:

t=0:   ░░░█░░░  Initial congestion
t=1:   ░░██░░░  Spreads backward
t=2:   ░███░░░  Wave grows
t=3:   ████░░░  Propagates further

Congestion Impact¶

On Individual Robots¶

Metric	Impact
Travel time	Increased
Task completion	Delayed
Battery usage	Increased (waiting)

On System¶

Metric	Impact
Throughput	Reduced
Predictability	Decreased
Resource utilization	May decrease

Congestion-Aware Routing¶

Standard Routing¶

Finds shortest path regardless of traffic:

Shortest: A → B → C (congested)

Congestion-Aware¶

Avoids congested areas:

routing:
  policy: congestion_aware
  congestion_weight: 1.5

May choose longer but faster path:

Alternative: A → D → E → C (clear)

Path Cost¶

cost = distance + congestion_weight × congestion_score

Congestion Metrics¶

Real-Time Metrics¶

Metric	Description
Current occupancy	Robots/Capacity ratio
Wait queue length	Robots waiting
Wait time (current)	Accumulated wait

Aggregate Metrics¶

Metric	Description
Avg occupancy	Mean over time period
Max occupancy	Peak congestion
Total wait time	Sum of all waits
Wait time per task	Average per completed task

Congestion Visualization¶

Heat Map¶

Traffic Density:
  ░ = Low    (0-25%)
  ▒ = Medium (25-50%)
  ▓ = High   (50-75%)
  █ = Full   (75-100%)

  ░░░░▒▒░░░░
  ░░▒▓▓▓▒░░░
  ░▒▓███▓▒░░
  ░░▒▓▓▓▒░░░
  ░░░░▒▒░░░░

Time Series¶

Occupancy %
100│        ███
   │      ███████
 75│    ███████████
   │  █████████████
 50│███████████████████
   │█████████████████████
 25│███████████████████████
   │█████████████████████████
  0└──────────────────────────
    0   5   10  15  20  25  30
              Time (min)

Managing Congestion¶

Prevention¶

Better route planning
Load balancing
Off-peak scheduling

Mitigation¶

Dynamic rerouting
Traffic signals
Priority systems

Design Solutions¶

Wider aisles at hotspots
Parallel routes
Better station placement

Configuration¶

traffic:
  # Congestion thresholds
  reroute_on_congestion: true
  reroute_threshold: 3.0  # Wait time trigger

routing:
  # Congestion-aware pathfinding
  policy: congestion_aware
  congestion_weight: 1.5

metrics:
  # Congestion monitoring
  track_congestion: true
  congestion_sample_interval_s: 10