629 Address Collisions and the Birthday Problem
629.1 Learning Objectives
By the end of this module, you will be able to:
- Apply the Birthday Problem formula to calculate collision probability
- Explain why address collisions occur more often than intuition suggests
- Evaluate address space requirements for different deployment sizes
- Design IoT networks with appropriate address space sizing
- Calculate bandwidth requirements for IoT deployments
629.2 Module Overview
When designing IoT networks, engineers often assume that address collisions are extremely unlikely given the large address spaces available. However, the Birthday Problem reveals a surprising truth: collisions occur far more frequently than intuition suggests. This module explores the mathematics behind address collisions and provides practical guidance for network design.
This module is divided into three focused chapters:
629.3 Key Concepts Preview
629.3.1 The Birthday Problem
The Birthday Problem demonstrates why collisions occur more frequently than expected:
- With just 23 people, there’s a 50% chance of shared birthdays
- The probability depends on n squared (quadratic), not n (linear)
- For IoT: 300 devices in a 16-bit address space = 52% collision probability
629.3.2 Address Space Sizing
Design Guideline: Safe device count = sqrt(Address Space) x 0.85
| Address Size | Safe Device Count | Protocol Examples |
|---|---|---|
| 16-bit | ~220 devices | Zigbee short addresses |
| 32-bit | ~55,000 devices | LoRaWAN DevAddr |
| 64-bit | ~3.6 billion devices | EUI-64, BLE MAC |
| 128-bit | Unlimited for IoT | IPv6, UUIDs |
629.3.3 Bandwidth Reality Check
Most IoT sensor applications need Kbps, not Mbps:
- 500 soil sensors sending 50 bytes every 15 minutes = 13 Kbps total
- Upgrading from LoRaWAN (5 Kbps) to LTE-M (1 Mbps) often wastes money
- Bandwidth and latency are independent - more bandwidth doesn’t reduce response time
629.4 Start Learning
Begin with The Birthday Problem in IoT Networks to understand why address collisions occur far more often than intuition suggests, then continue through the module.
50% Collision Thresholds: - 16-bit: ~300 devices - 32-bit: ~77,000 devices - 48-bit: ~20 million devices - 64-bit: ~5 billion devices
Bandwidth Formula: Average = (Devices x Payload x Messages/Min) / 60 seconds
629.5 Summary
- The Birthday Problem explains why collisions occur sooner than expected
- Address space sizing is critical for network design
- Bandwidth requirements are often significantly overestimated
- Right-sizing networks saves cost while meeting requirements
629.6 What’s Next
Start with The Birthday Problem in IoT Networks, or if you’ve completed this module, continue to the Radio Propagation module.