3.2.3. Analysis of the Uniqueness of Global IDs
3.2.3. Analysis of the Uniqueness of Global IDs
The selection of a pseudo random Global ID is similar to the selection of an SSRC identifier in RTP/RTCP defined in Section 8.1 of [RTP]. This analysis is adapted from that document.
Since Global IDs are chosen randomly (and independently), it is possible that separate networks have chosen the same Global ID. For any given network, with one or more random Global IDs, that has inter-connections to other such networks, having a total of N such IDs, the probability that two or more of these IDs will collide can be approximated using the formula:
P = 1 - exp(-N**2 / 2**(L+1))
where P is the probability of collision, N is the number of interconnected Global IDs, and L is the length of the Global ID.
The following table shows the probability of a collision for a range of connections using a 40-bit Global ID field.
| Connections | Probability of Collision |
|---|---|
| 2 | 1.81*10^-12 |
| 10 | 4.54*10^-11 |
| 100 | 4.54*10^-09 |
| 1000 | 4.54*10^-07 |
| 10000 | 4.54*10^-05 |
Based on this analysis, the uniqueness of locally generated Global IDs is adequate for sites planning a small to moderate amount of inter-site communication using locally generated Global IDs.