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Time Model

How time is represented and advances in Waremax.

Time Representation

SimTime

Time is represented as a floating-point number of seconds:

SimTime = f64 (seconds since simulation start)

Precision

  • Resolution: microsecond-level
  • Range: 0 to simulation duration
  • No fixed time steps

Time Advancement

Event-Driven

Time only advances when processing events:

current_time = 0.0s
process(event at 10.5s) → current_time = 10.5s
process(event at 10.5s) → current_time = 10.5s (same time)
process(event at 23.8s) → current_time = 23.8s

No Idle Steps

If nothing happens for 30 seconds:

  • Time-stepping: 30+ iterations
  • DES: 0 iterations, jump directly

Simulation Phases

Initialization (t = 0)

  • Create robots at starting positions
  • Initialize stations
  • Schedule first order arrival
  • Set up initial state

Warmup Period

0 ────────────── warmup_end ────────────── duration
    Warmup            |       Measurement
    (no metrics)      |       (collect metrics)

During warmup:

  • Events processed normally
  • Metrics not collected
  • System reaches steady state

Measurement Period

After warmup:

  • All metrics collected
  • KPIs calculated
  • Results meaningful

Termination

Simulation ends when:

  • current_time >= duration
  • Event queue is empty

Duration Configuration

simulation:
  duration_minutes: 60    # Total simulation time
  warmup_minutes: 10      # Warmup period

Effective Duration

Effective = duration_minutes - warmup_minutes

Example:

  • Duration: 60 minutes
  • Warmup: 10 minutes
  • Effective: 50 minutes of metrics

Time Calculations

Travel Time

travel_time = edge_length / robot_speed

Example:

  • Edge: 15 meters
  • Speed: 1.5 m/s
  • Time: 15 / 1.5 = 10 seconds

Service Time

Depends on distribution:

# Constant
time = base + per_item × items

# Lognormal
time = sample_lognormal(base, stddev) + per_item × items

# Exponential
time = sample_exponential(mean)

Battery Consumption

energy_per_second = power_w / 3600
time_at_idle = energy_consumed_wh / (idle_power_w / 3600)

Event Ordering

When events have the same time:

  1. Priority order by event type
  2. FIFO for same type

This ensures:

  • Deterministic behavior
  • Logical event ordering
  • Consistent results

Type Priorities

1. SystemEvents (highest)
2. OrderArrival
3. TaskAssignment
4. RobotDepart
5. RobotArrive
6. ServiceStart
7. ServiceEnd
8. MetricsSample (lowest)

Time Units in Configuration

Configuration uses minutes for readability:

simulation:
  duration_minutes: 60      # Minutes
  warmup_minutes: 10        # Minutes

Internally converted to seconds:

duration_s = duration_minutes × 60
warmup_s = warmup_minutes × 60

Common Time Scales

Activity Typical Duration
Edge traversal 2-30 seconds
Station service 5-60 seconds
Charging (full) 30-120 minutes
Maintenance 5-15 minutes
Order cycle 30-180 seconds