1335 Edge Review: Calculations and Power Optimization

1335.1 Learning Objectives

Time: ~20 min | Level: Intermediate | Unit: P10.C10.U03

By the end of this chapter, you will be able to:

Calculate Data Reduction: Apply formulas to compute bandwidth savings from downsampling, aggregation, and filtering
Estimate Battery Life: Calculate average current draw and battery duration for different sampling strategies
Analyze Latency Trade-offs: Quantify latency reduction benefits of edge versus cloud processing
Perform Cost Analysis: Calculate total cost of ownership for edge versus cloud deployments
Solve Practice Problems: Apply formulas to realistic IoT scenarios

1335.2 Prerequisites

Required Reading: - Edge Review: Architecture - Architecture patterns and decision frameworks - Edge Compute Patterns - Edge computing basics

Related Chapters: - Edge Review: Deployments - Real-world patterns - Edge Topic Review - Main review index

For Beginners: Why Calculations Matter

Edge computing is not just about where you process data - it is about quantifying the benefits. When your boss asks “Why should we invest in edge gateways?”, you need numbers:

“We will reduce bandwidth costs by 95%”
“Battery life increases from 45 days to 7 years”
“Response time drops from 180ms to 5ms”

This chapter gives you the formulas and practice to make those calculations confidently.

1335.3 Key Formulas

1335.3.1 Data Volume Reduction

Total Data Reduction Ratio: \[R_{total} = \frac{V_{raw}}{V_{transmitted}}\]

Where:

$V_{raw}$ = Raw sensor data volume
$V_{transmitted}$ = Data sent to cloud after edge processing

Example: 10,000 samples/hour reduced to 10 aggregates/hour = 1000x reduction

1335.3.2 Bandwidth Savings

Daily Bandwidth Calculation: \[B_{daily} = N_{sensors} \times S_{sample} \times F_{rate} \times T_{hours}\]

Where:

$N_{sensors}$ = Number of sensors
$S_{sample}$ = Sample size (bytes)
$F_{rate}$ = Sampling frequency (samples/hour)
$T_{hours}$ = 24 hours

Aggregation Bandwidth: \[B_{aggregated} = N_{sensors} \times S_{aggregate} \times F_{aggregated} \times 24\]

Savings: \[Savings = \frac{B_{daily} - B_{aggregated}}{B_{daily}} \times 100\%\]

1335.3.3 Power Consumption

Battery Life Estimation: \[L_{battery} = \frac{C_{battery}}{I_{avg}} \times \frac{1}{D_{safety}}\]

Where:

$C_{battery}$ = Battery capacity (mAh)
$I_{avg}$ = Average current draw (mA)
$D_{safety}$ = Safety factor (0.8 typical)

Average Current with Sleep Modes: \[I_{avg} = \frac{(I_{sleep} \times T_{sleep}) + (I_{active} \times T_{active}) + (I_{tx} \times T_{tx})}{T_{total}}\]

Example:

$I_{sleep}$ = 0.01 mA (deep sleep)
$I_{active}$ = 25 mA (sensor read)
$I_{tx}$ = 120 mA (Wi-Fi transmit)
If sleep 99% of time: $I_{avg} \approx 0.01 + 0.25 + 1.2 = 1.46$ mA

1335.3.4 Latency Components

Total Edge Latency: \[L_{total} = L_{processing} + L_{network} + L_{queue}\]

Cloud Latency: \[L_{cloud} = L_{local} + L_{wan} + L_{cloud\_proc} + L_{wan} + L_{local}\]

Latency Reduction Benefit: \[Benefit = \frac{L_{cloud} - L_{edge}}{L_{cloud}} \times 100\%\]

1335.3.5 Cost Analysis

Total Cost of Ownership (TCO) for Edge: \[TCO_{edge} = C_{hardware} + (C_{maintenance} \times Y_{lifetime}) + (C_{energy} \times Y_{lifetime})\]

Cloud Cost: \[TCO_{cloud} = (C_{bandwidth} + C_{storage} + C_{compute}) \times Y_{lifetime}\]

Break-even Analysis: \[Year_{breakeven} = \frac{C_{hardware}}{(TCO_{cloud}/year) - (TCO_{edge}/year)}\]

1335.4 Data Reduction Strategies

1335.4.1 Sensor-Level Reduction Techniques

Technique	Description	Reduction Factor	Power Impact
Lower Sampling Rate	Reduce from 1 Hz to 0.1 Hz	10x	10x battery life
Event-Driven Sampling	Transmit only on threshold breach	100-1000x	100x+ battery life
Simpler Sensors	Use binary instead of analog when sufficient	10x data size	Varies
Delta Encoding	Transmit only changes, not absolute values	2-5x	Minimal
Local Buffering	Batch multiple readings into single transmission	Variable	2-10x (reduce TX)

1335.4.2 Gateway-Level Reduction Techniques

Technique	Description	Example	Typical Reduction
Downsampling	Reduce temporal resolution	1 sample/min to 1/hour	60x
Spatial Aggregation	Average nearby sensors	10 sensors to 1 average	10x
Temporal Aggregation	Compute hourly/daily statistics	Min/max/avg per hour	100-1000x
Filtering	Remove outliers, noise, redundancy	Discard unchanged values	2-10x
Compression	gzip, delta encoding, dictionary coding	Text logs to binary	5-10x
Feature Extraction	Send derived metrics, not raw data	FFT coefficients instead of waveform	10-100x

1335.4.3 Combined Strategy Example

Scenario: 100 temperature sensors, 1 reading/minute

Without Edge Processing:

100 sensors x 60 readings/hour x 4 bytes = 24,000 bytes/hour
Daily: 576,000 bytes (562 KB)
Monthly: 16.9 MB

With Edge Processing:

Evaluate: Remove 5% invalid readings - 95 readings/hour/sensor
Aggregate: Compute hourly min/max/avg - 3 values/hour/sensor
Format: Compress to binary - 2 bytes/value
Result: 100 sensors x 3 values/hour x 2 bytes = 600 bytes/hour
Daily: 14,400 bytes (14 KB)
Reduction: 97.5% (40x)

1335.5 Power Optimization

1335.5.1 Current Consumption by Mode

Device State	Current Draw	Typical Duration	Use Case
Deep Sleep	0.01 mA	99% of time	Battery-powered sensors
Light Sleep	0.5 mA	Between readings	Quick wake-up needed
Active (CPU)	25 mA	1-10 seconds	Sensor reading, processing
Wi-Fi TX	120 mA	<1 second	Cloud upload
Cellular TX	200 mA	1-5 seconds	Remote locations
LoRaWAN TX	40 mA	<1 second	Long-range, low power

1335.5.2 Battery Life Scenarios

Scenario 1: Aggressive Sampling (No Edge Intelligence)

Sample every 10 seconds
Transmit immediately via Wi-Fi
Active time: 2s + 0.5s TX = 2.5s per cycle
Cycles per day: 8,640
Sleep time: ~21.6 hours
$I_{avg} = \frac{(0.01 \times 77400) + (25 \times 17280) + (120 \times 4320)}{86400} \approx 11$ mA
Battery life (2000 mAh): 182 hours (7.6 days)

Scenario 2: Intelligent Edge Sampling

Sample every 10 seconds locally
Aggregate hourly at edge gateway
Transmit once per hour via LoRaWAN
Active time: 2s per 10s cycle (local), 1s TX per hour
$I_{avg} = \frac{(0.01 \times 79164) + (25 \times 17280) + (40 \times 24)}{86400} \approx 5.1$ mA
Battery life (2000 mAh): 392 hours (16.3 days) - 2.1x improvement

Scenario 3: Event-Driven + Edge

Monitor threshold locally
Transmit only on 5 degree change (assume 2 events/day)
Deep sleep 99.9% of time
$I_{avg} = \frac{(0.01 \times 86350) + (25 \times 48) + (40 \times 2)}{86400} \approx 0.03$ mA
Battery life (2000 mAh): 66,667 hours (2,778 days / 7.6 years!)

1335.6 Practice Problems

1335.6.1 Problem 1: Bandwidth Calculation

Scenario: Smart building with 500 temperature sensors

Each sensor: 4-byte reading
Sampling rate: 1 reading/minute
No edge processing (all data to cloud)

Calculate:

Hourly data volume
Monthly bandwidth (30 days)
Annual cost if bandwidth = $0.10/GB

Solution

a) Hourly data volume: \[V_{hourly} = 500 \text{ sensors} \times 60 \text{ readings/hour} \times 4 \text{ bytes} = 120,000 \text{ bytes} = 117.2 \text{ KB/hour}\]

b) Monthly bandwidth: \[V_{monthly} = 117.2 \text{ KB/hour} \times 24 \text{ hours/day} \times 30 \text{ days} = 84,384 \text{ KB} = 82.4 \text{ MB}\]

c) Annual cost: \[Cost_{annual} = \frac{82.4 \text{ MB/month} \times 12 \text{ months}}{1000 \text{ MB/GB}} \times \$0.10 = \$0.099 \approx \$0.10\]

Note: Seems cheap, but multiply by thousands of buildings - significant cost

1335.6.2 Problem 2: Edge Reduction Benefits

Same scenario as Problem 1, but with edge gateway:

Gateway aggregates to hourly min/max/avg (3 values/sensor/hour)
Each aggregate value: 4 bytes

Calculate:

New hourly data volume
Reduction factor
Annual cost savings

Solution

a) New hourly volume: \[V_{edge} = 500 \times 3 \times 4 = 6,000 \text{ bytes} = 5.86 \text{ KB/hour}\]

b) Reduction factor: \[R = \frac{120,000}{6,000} = 20x \text{ reduction}\]

c) Annual cost: \[Cost_{edge} = \frac{5.86 \text{ KB} \times 24 \times 30 \times 12}{1,000,000} \times \$0.10 = \$0.005\]

Savings: $0.10 - $0.005 = $0.095 per building/year

For 1000 buildings: $95/year savings (plus reduced cloud processing costs)

1335.6.3 Problem 3: Battery Life Optimization

ESP32 environmental sensor:

Battery: 3000 mAh
Deep sleep: 0.01 mA
Active: 30 mA for 3 seconds
Wi-Fi TX: 150 mA for 0.5 seconds

Compare battery life for:

Transmit every 1 minute
Aggregate 10 readings, transmit every 10 minutes
Event-driven: transmit only on 10% change (assume 1 event/hour)

Solution

a) Every 1 minute:

Cycles/day: 1440
Active time: 1440 x 3s = 4320s
TX time: 1440 x 0.5s = 720s
Sleep time: 86400 - 4320 - 720 = 81360s

\[I_{avg} = \frac{(0.01 \times 81360) + (30 \times 4320) + (150 \times 720)}{86400} = \frac{813.6 + 129,600 + 108,000}{86400} = 2.76 \text{ mA}\]

Battery life: $3000 / 2.76 = 1087$ hours = 45 days

b) Every 10 minutes:

Cycles/day: 144
Active time: 144 x 3s x 10 readings = 4320s (same local sampling)
TX time: 144 x 0.5s = 72s
Sleep time: 86400 - 4320 - 72 = 81,808s

\[I_{avg} = \frac{(0.01 \times 81808) + (30 \times 4320) + (150 \times 72)}{86400} = 1.635 \text{ mA}\]

Battery life: $3000 / 1.635 = 1835$ hours = 76 days (1.7x improvement)

c) Event-driven (24 TX/day):

Active for local monitoring: 1440 x 3s = 4320s
TX time: 24 x 0.5s = 12s
Sleep time: 86400 - 4320 - 12 = 82068s

\[I_{avg} = \frac{(0.01 \times 82068) + (30 \times 4320) + (150 \times 12)}{86400} = 1.521 \text{ mA}\]

Battery life: $3000 / 1.521 = 1972$ hours = 82 days (1.8x improvement)

Key insight: TX dominates power budget, minimize transmissions for longest life

1335.6.4 Problem 4: Latency Analysis

Industrial control system:

Local edge: 5ms processing
Cloud: 80ms WAN + 20ms processing + 80ms WAN = 180ms round-trip

Questions:

What percentage latency reduction does edge provide?
If control loop requires <50ms response, which architecture works?
For 10,000 control decisions/day, how much total time saved by edge?

Solution

a) Latency reduction: \[Reduction = \frac{180 - 5}{180} \times 100\% = 97.2\%\]

b) Architecture selection:

Edge: 5ms (meets <50ms requirement)
Cloud: 180ms (exceeds requirement)
Only edge architecture is viable

c) Total time saved: \[Savings = (180 - 5) \text{ ms} \times 10,000 = 1,750,000 \text{ ms} = 29.2 \text{ minutes/day}\]

Over a year: 29.2 x 365 = 10,658 minutes (177.6 hours) saved

1335.6.5 Problem 5: Data Reduction Ratio

A sensor transmits 100 bytes every 10 seconds. An edge gateway aggregates to hourly averages (50 bytes). What is the data reduction ratio?

Solution

Raw data per hour: \[V_{raw} = 100 \text{ bytes} \times \frac{3600 \text{ s}}{10 \text{ s}} = 100 \times 360 = 36,000 \text{ bytes}\]

Aggregated data per hour: \[V_{aggregated} = 50 \text{ bytes}\]

Reduction ratio: \[R = \frac{36,000}{50} = 720x\]

The edge gateway achieves a 720x data reduction.

1335.6.6 Problem 6: Average Current Draw

An ESP32 device consumes 0.01 mA in deep sleep, 80 mA when transmitting (1 second), and sleeps 99% of the time. What is the average current draw?

Solution

Time allocation per 100 seconds:

Sleep: 99 seconds at 0.01 mA
Transmit: 1 second at 80 mA

Average current: \[I_{avg} = \frac{(0.01 \times 99) + (80 \times 1)}{100} = \frac{0.99 + 80}{100} = \frac{80.99}{100} = 0.81 \text{ mA}\]

Average current draw: 0.81 mA

With a 2000 mAh battery: $2000 / 0.81 = 2469$ hours = 103 days

1335.7 Summary and Key Takeaways

1335.7.1 Essential Formulas

Calculation	Formula	Typical Result
Data Reduction	$R = V_{raw} / V_{transmitted}$	10-1000x
Bandwidth Savings	$(B_{raw} - B_{edge}) / B_{raw}$	90-99%
Battery Life	$C_{battery} / I_{avg}$	Days to years
Latency Reduction	$(L_{cloud} - L_{edge}) / L_{cloud}$	80-99%

1335.7.2 Key Insights

Transmission dominates power - Minimize TX events for longest battery life
Aggregation is powerful - Hourly aggregates achieve 60-1000x reduction
Event-driven is optimal - Only transmit on significant changes for years of battery life
Latency matters for safety - Edge provides 95%+ latency reduction for critical applications
TCO analysis requires both CapEx and OpEx - Edge has upfront costs, cloud has ongoing costs

1335.8 What’s Next

Continue your edge computing review with:

Edge Review: Deployments - Real-world deployment patterns, technology stack, and security considerations

Return to: Edge Topic Review - Main review index