Hello,

I would love to get an intuition for the lower bound of the P2P transmission delay of a file. To be more more specific, I understand the following about the elements of the max function:

**1.** \frac{F}{u_s}: Just the time of Alice to **upload** her file [understood]

**2. **\frac{F}{d_{min}}: The **download time** of the end system with the slowest download speed [understood]

**3. **\frac{3*F}{u_s + \sum_i (d_i)}: Here lies the problem. While the first argument capture the uploading of the file and the second argument captures the initial distribution of the file fragements, this 3rd argument should capture the **distribution of the file between the friends**, given that each friend already has their file fragment. For a given friend, let's say Bob, this means that the distribution delay is max(\frac{2*F/3}{u_b}, \frac{F/3}{min(d_c, d_d)}. For all of the 3 friends that are going to distribute files this would mean the total distribution delay is:

max(\frac{2*F/3}{u_b}, \frac{F/3}{min(d_c, d_d)} + max(\frac{2*F/3}{u_v}, \frac{F/3}{min(d_b, d_d)} + max(2*\frac{F/3}{u_f}, \frac{F/3}{min(d_b, d_b)}

Now if we assume that the upload speed is generally much slower than the download speed, this would result in

= \frac{2*F/3}{u_b} + \frac{2*F/3}{u_c} + \frac{2*F/3}{u_d}

which is the closest I could get the supplied term (while assuming that the upload speed in not parallelized). I know that you said that this is just an approximation and maybe there is nothing more to be understood about it, but I'd love to get the a bit of a mathematically intuition. - I do not understand why Alice's upload speed is included in the distribution time, since (from what I can remember, and this might be wrong) it was said that the 3 friends divide the fragments between themselves.

- Also I am confused by the 3F: In terms of uploading, I would have argued that each friend needs to upload 2 file fragments (i.e. 2 * F/3) which they would do simultaneously...

I hope I was able to properly explain my confusion :)