Packet Collisions

Collisions

Collisions occur if any part of the two packets overlap. The probability of collision is

$$\frac{\text{vulnerable period}}{\text{transmission window}}=\frac{2T_{\text{adv}}}{T_{\text{adv\_interval}}+\text{avg}(t_{\text{adv\_delay}})}$$

Definition (Packet Reception Rate)

The Packet Reception Rate is the odds that a transmitted advertisement packet will be received.

$$\text{PRR}=1-(\text{probability of collisions})$$

Definition (Data Reception Rate)

The rate at which at least one packet is received in $M$ redundant advertisements are sent.

$$\text{DRR}=1-(\text{probability of collisions}{)}^N$$

where $N$ is the number of packets. In general, redundancy results in high DRR even with many devices. Send less packets/s to reduce congestion or send more to gain from redundancy?

If many devices ($>400$), send less. If less, redundancy is better.

BLE Advertisement Frequency

Advertisements occur periodically, $10-20ms$ or $T_{\text{adv\_interval}}$. There is a random delay before each transmission at $0-10ms$ or $T_{\text{adv\_delay}}$. The data payload is up to $31$ bytes.