Congestion Metrics¶

Measuring and analyzing traffic congestion.

Why Congestion Metrics?¶

Congestion directly impacts performance:

Longer travel times
Reduced throughput
Wasted energy
Deadlock risk

Measuring congestion enables:

Identifying bottlenecks
Comparing routing policies
Optimizing layout

Core Congestion Metrics¶

Wait Time¶

Time robots spend waiting for resources:

Wait Time = Actual Travel - Free Flow Travel

Example:

Free flow: 10s
Actual: 18s
Wait time: 8s

Aggregate Wait Metrics¶

Metric	Formula
Total wait	Σ wait_time for all robots
Avg wait	Total wait / Task count
Wait ratio	Total wait / Total travel time

Occupancy¶

Resource utilization over time:

Occupancy = Time Occupied / Total Time

For nodes:

Node N5: Occupied 720s out of 3600s
Occupancy: 20%

For edges:

Edge E1: Occupied 1800s out of 3600s
Occupancy: 50%

Queue Length¶

Robots waiting for resources:

Instantaneous: Current queue at time t
Average: Mean queue over time period
Maximum: Peak queue length

Station queues:

Station S1 Queue:
  Avg: 3.2 robots
  Max: 8 robots
  Time > 5: 15% of simulation

Congestion Hotspot Metrics¶

Hotspot Identification¶

Find locations with highest congestion:

Node Congestion Ranking:
1. N15 (intersection): 85% occupancy, 12s avg wait
2. N22 (station approach): 72% occupancy, 8s avg wait
3. N8 (crossing): 65% occupancy, 6s avg wait

Congestion Score¶

Composite metric for each location:

Score = occupancy × wait_time × blocking_events

Higher score = worse congestion.

Time-Based Congestion¶

Congestion Over Time¶

Track how congestion varies:

Time    | Avg Occupancy | Avg Wait | Blocked Events
--------|---------------|----------|----------------
0-15m   | 15%           | 1.2s     | 45
15-30m  | 45%           | 5.8s     | 180
30-45m  | 62%           | 9.3s     | 320
45-60m  | 38%           | 4.1s     | 125

Peak Congestion¶

When congestion is highest:

Peak Congestion Period: 30-45 minutes
  - Coincides with order peak
  - Focus optimization here

Deadlock Metrics¶

Deadlock Count¶

Total deadlocks detected:

Deadlocks: 3
  - t=1823s: R5, R12 at N15/N16
  - t=2156s: R3, R8, R21 at intersection
  - t=3012s: R7, R15 at station approach

Resolution Metrics¶

Metric	Value
Avg resolution time	2.3s
Robots affected	8
Tasks delayed	12

Spatial Congestion Analysis¶

Congestion Heat Map¶

Warehouse Map (congestion intensity):

░░░░░░░░░░░░░░░░░░░░
░░░░░▒▒▒▒░░░░░░░░░░░
░░░▒▒▓▓▓▓▒▒░░░░░░░░░
░░▒▓▓████▓▓▒░░░░░░░░  ← Hotspot
░░░▒▒▓▓▓▓▒▒░░░░░░░░░
░░░░░▒▒▒▒░░░░░░░░░░░
░░░░░░░░░░░░░░░░░░░░

░ = Low    ▓ = High
▒ = Med    █ = Critical

Path Congestion¶

Average congestion along common paths:

Path A→B (via main aisle): Avg wait 8.5s
Path A→B (via side aisle): Avg wait 2.1s

Throughput Impact¶

Congestion vs. Throughput¶

Congestion Level | Throughput | Efficiency
-----------------|------------|------------
Low (<20%)       | 1,000/hr   | 100%
Medium (20-40%)  | 920/hr     | 92%
High (40-60%)    | 780/hr     | 78%
Critical (>60%)  | 550/hr     | 55%

Marginal Impact¶

Each 10% increase in congestion → ~8% throughput decrease

Configuration¶

Enable Congestion Tracking¶

metrics:
  congestion:
    enabled: true
    track_locations: true
    track_timeseries: true
    sample_interval_s: 30

Hotspot Detection¶

metrics:
  congestion:
    hotspot_detection: true
    hotspot_threshold: 0.5  # 50% occupancy
    top_n_hotspots: 10

Detailed Tracking¶

metrics:
  congestion:
    per_node: true
    per_edge: true
    wait_time_breakdown: true

Output Example¶

Summary¶

=== Congestion Summary ===
Total wait time: 4,523s
Avg wait per task: 3.6s
Peak congestion: 62% at t=2100s

Hotspots:
  1. N15: 85% occupancy
  2. N22: 72% occupancy
  3. N8: 65% occupancy

Deadlocks: 3
Avg resolution: 2.3s

JSON Detail¶

{
  "congestion": {
    "total_wait_s": 4523,
    "avg_wait_s": 3.6,
    "peak_occupancy": 0.62,
    "peak_time_s": 2100,
    "hotspots": [
      {"node": "N15", "occupancy": 0.85, "avg_wait_s": 12.3},
      {"node": "N22", "occupancy": 0.72, "avg_wait_s": 8.1}
    ],
    "deadlocks": {
      "count": 3,
      "avg_resolution_s": 2.3
    }
  }
}

Using Congestion Metrics¶

Identify Problems¶

High wait time + Low throughput = Congestion issue

Look at:
1. Hotspot locations
2. Peak congestion times
3. Deadlock frequency

Guide Solutions¶

Finding	Solution
Single hotspot	Increase capacity or add bypass
Widespread congestion	Reduce fleet or improve layout
Time-based peaks	Adjust order scheduling
Frequent deadlocks	Improve traffic policies

Validate Improvements¶

Before: Avg wait 8.5s, 3 deadlocks
After:  Avg wait 3.2s, 0 deadlocks

Improvement: 62% reduction in wait time