Systems thinking in mathematical form.
Engineering Applications
- Rate Limiting: Feedback loops for traffic shaping
- Autoscaling: PID controllers for resource management
- Observability: Measuring system state for control
- Circuit Breakers: State machines with feedback
- Queue Management: Backpressure and flow control
Core Concepts
Feedback Loop
Output → Sensor → Controller → Actuator → System → Output
Every stable system has feedback. Without measurement, no control.
Open Loop vs Closed Loop
| Type | Description | Example |
|---|---|---|
| Open Loop | No feedback, fire-and-forget | Scheduled job |
| Closed Loop | Continuous feedback and adjustment | Autoscaler |
Closed loops are more robust but more complex.
PID Control
u(t) = Kp*e(t) + Ki*∫e(t)dt + Kd*de(t)/dt
| Term | Purpose |
|---|---|
| P (Proportional) | React to current error |
| I (Integral) | Eliminate steady-state error |
| D (Derivative) | Dampen oscillations |
Stability
A system is stable if it returns to equilibrium after disturbance.
Signs of instability:
- Oscillation
- Runaway growth
- Cascading failures
System Design Connections
Rate Limiting as Control
- Measurement: Request count per window
- Setpoint: Requests per second limit
- Actuator: Accept/reject requests
- Feedback: Adjust based on current rate
Autoscaling as PID
- P: Scale based on current CPU/memory
- I: Account for sustained load
- D: Anticipate load changes (predictive scaling)
Circuit Breaker States
Closed → [failures > threshold] → Open
Open → [timeout] → Half-Open
Half-Open → [success] → Closed
Half-Open → [failure] → Open
This is a state machine with feedback.
Key Insight
Tests = Behaviour (what should happen)
OTEL = Physics (what did happen)
You need both to have control. Tests define the setpoint. Observability provides the measurement.
Related
- Systems Thinking
- Closed-Loop Telemetry Optimization – Control theory applied to software
- Building the Harness – Feedback loops in practice
- Probability
