Time Series Data¶

Metrics tracked over simulation time.

What is Time Series Data?¶

Time series data captures metric values at regular intervals throughout the simulation, showing how the system behaves over time.

Aggregate vs. Time Series¶

Aggregate: Single value for entire simulation

Average throughput: 1,000 tasks/hour

Time Series: Values at each time point

t=0m:  800 tasks/hour
t=5m:  950 tasks/hour
t=10m: 1,100 tasks/hour
t=15m: 900 tasks/hour

Why Time Series?¶

Identify Patterns¶

See trends and cycles:

Throughput
    │
    │    ╱╲      ╱╲
    │   ╱  ╲    ╱  ╲
    │  ╱    ╲  ╱    ╲
    │ ╱      ╲╱      ╲
    │╱
    └─────────────────── Time
         Peak hours pattern

Detect Issues¶

Find when problems occur:

Queue Length
    │
    │                 ████
    │           ████████████
    │     ██████████████████
    │ ████████████████████████
    └─────────────────────────── Time
                  ↑
         Problem starts here

Validate Warmup¶

Confirm system reaches steady state:

Utilization
    │        ─────────────
    │      ╱
    │     ╱
    │    ╱
    │   ╱
    │  ╱
    └────────────────────── Time
      ↑
    Warmup   Steady State

Common Time Series Metrics¶

Throughput Over Time¶

Time (min) | Tasks Completed | Rate (tasks/hr)
-----------|-----------------|----------------
0          | 0               | 0
5          | 68              | 816
10         | 152             | 912
15         | 241             | 964
20         | 335             | 1,005

Queue Lengths¶

Time | Station S1 | Station S2 | Total
-----|------------|------------|-------
0    | 0          | 0          | 0
5    | 3          | 2          | 5
10   | 5          | 4          | 9
15   | 4          | 3          | 7

Utilization Over Time¶

Time | Robot Util | Station Util
-----|------------|-------------
0    | 0%         | 0%
5    | 65%        | 58%
10   | 78%        | 72%
15   | 82%        | 80%
20   | 80%        | 78%

Configuration¶

Enable Time Series¶

metrics:
  timeseries:
    enabled: true
    interval_s: 60  # Sample every minute

Select Metrics¶

metrics:
  timeseries:
    include:
      - throughput
      - utilization
      - queue_length
      - wait_time
      - task_count

Sampling Interval¶

Interval	Use Case
1s	Detailed debugging
10s	Fine-grained analysis
60s	Standard monitoring
300s	Long simulations

Output Format¶

CSV Format¶

timestamp,throughput,robot_utilization,station_utilization,avg_queue_length
0,0,0.00,0.00,0.0
60,82,0.65,0.58,2.3
120,95,0.78,0.72,3.5
180,91,0.80,0.78,3.2

JSON Format¶

{
  "timeseries": [
    {
      "timestamp": 0,
      "throughput": 0,
      "robot_utilization": 0.00,
      "queue_length": 0.0
    },
    {
      "timestamp": 60,
      "throughput": 82,
      "robot_utilization": 0.65,
      "queue_length": 2.3
    }
  ]
}

Analysis Techniques¶

Trend Analysis¶

Identify overall direction:

Is throughput increasing, stable, or decreasing?

Early:   ████████░░ (800)
Middle:  ██████████ (1000)
Late:    ████████░░ (800)

Pattern: Peak in middle, degradation later

Moving Average¶

Smooth out noise:

Raw data:      82, 95, 78, 102, 85, 91, 88
3-point avg:   -, 85, 92, 88, 93, 88, -

Correlation¶

Find relationships:

Queue length ↑ → Wait time ↑
Utilization ↑ → Congestion ↑

These correlations help identify root causes

Visualization¶

Line Charts¶

Best for continuous metrics:

Throughput
1200│         ___
1000│    ____/   \____
 800│   /             \
 600│  /
 400│ /
 200│/
   0└─────────────────────
    0   15   30   45   60
              Time (min)

Stacked Area¶

For composition:

Time Breakdown (cumulative)
100%│████████████████████
    │████ Idle ██████████
    │████████████████████
 50%│▓▓▓▓ Travel ▓▓▓▓▓▓▓▓
    │▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓
    │░░░░ Working ░░░░░░░
  0%└─────────────────────

Heat Maps¶

For spatial-temporal data:

     t=0  t=5  t=10 t=15 t=20
N1   ░    ░    ▒    ▓    ▓
N2   ░    ▒    ▓    ▓    █
N3   ░    ░    ▒    ▒    ▓
N4   ░    ░    ░    ▒    ▒

░ = Low   ▓ = High
▒ = Med   █ = Max

Common Patterns¶

Warmup Period¶

      _______________
     /
    /
   /
  /
 /
/
  Warmup → Steady State

Exclude warmup from analysis.

Periodic Behavior¶

    /\    /\    /\    /\
   /  \  /  \  /  \  /  \
  /    \/    \/    \/    \

Regular cycles (e.g., order waves)

Degradation¶

________
        \
         \
          \
           \

Performance declining over time

Investigate cause (queue buildup, resource exhaustion).

Best Practices¶

Choose Appropriate Interval¶

Too short: Noisy data, large files
Too long: Miss important details

Rule of thumb: 30-100 data points per simulation.

Include Key Metrics¶

At minimum: - Throughput - Utilization - Queue length

Exclude Warmup¶

metrics:
  warmup_s: 300  # Exclude first 5 minutes

Align with Analysis Goals¶

Debugging: Short interval, many metrics Comparison: Standard interval, key metrics only