I'm reading the white-paper about the tangle. In pages 8 to 10, the author is calculating the average time for first approval of a tip on a stationary tangle.
The first result is that under low load:
The first approval happens on an average timescale of order λ −1
where λ is the rate of arrival of new transactions. This result is clear to me.
But I must be missing something (maybe obvious) when the author present the result for a tangle under heavy load (page 10):
Let us now consider the high load regime, the case where L0 is large. As mentioned above, one may assume that the Poisson flows of approvals to different tips are independent and have an approximate rate of 2λ/L0. Therefore, the expected time for a transaction to receive its first approval is around L0/(2λ) ≈ 1.45h (1)
- L0 is the number of tips (large under heavy load).
- h is the average hidden time of a transaction (a transaction is hidden during the execution of the pow)
I don't see from where comes this factor: 1.45
I looked into reference "Sheldon M. Ross (2012) Introduction to Probability Models. 10th ed." (page 312) to have better understanding of the Poisson Process, but it didn't help me to understand why we obtain this result.