Filter-at-Edge Pattern: Quantifying the Trade-off Between Threshold and Bandwidth
The filter-at-edge pattern transmits only “interesting” events. Setting the threshold involves balancing bandwidth savings vs missed events:
Scenario: 1,000 temperature sensors, 1 sample/minute, transmit only when change >2 deg C from last reading
Statistical Model for temperature variation: \[
\Delta T \sim \mathcal{N}(0, 0.5^2) \quad \text{(normal variation is ±0.5°C per reading)}
\]
Probability of exceeding threshold: \[
P(|\Delta T| > 2°C) = 2 \times P(Z > \frac{2 - 0}{0.5}) = 2 \times P(Z > 4) \approx 0.00006
\] \[
\text{Transmission Rate} = 1,000 \text{ sensors} \times 1,440 \text{ readings/day} \times 0.00006 = 86 \text{ transmissions/day}
\]
Bandwidth Calculation: \[
\text{Without Filter} = 1,000 \times 1,440 \times 20 \text{ bytes} = 28.8 \text{ MB/day}
\] \[
\text{With Filter} = 86 \times 20 \text{ bytes} = 1.72 \text{ KB/day}
\] \[
\text{Reduction} = \frac{28.8 \text{ MB}}{1.72 \text{ KB}} = 16,744\times \quad \text{(99.994% savings)}
\]
Threshold Sensitivity (if we lower to 1 deg C): \[
P(|\Delta T| > 1°C) = 2 \times P(Z > 2) \approx 0.046
\] \[
\text{Transmissions} = 1,440,000 \times 0.046 = 66,240 \text{ readings/day}
\] \[
\text{Reduction} = \frac{1,440,000}{66,240} = 22\times \quad \text{(still 95.4% savings)}
\]
The sweet spot is setting thresholds at 3-4 standard deviations of normal variation: high enough to filter noise, low enough to catch real events.