Bandwidth calculation error

A file created with ‘constant quality’ cannot have a constant bandwidth.
‘Bandwidth’ has only indirectly to do with ‘quality’. If you want to learn about that a bit more, it is explained in a great way in this video:

With ‘constant quality’, the encoder uses whatever bandwidth is necessary to achieve the desired quality. And this varies very wildly over the course of the file.
That’s why Plex performs an in-depth bandwidth analysis, which provides a much better way to determine the real bandwidth of a file.
What you see as the file’s bandwidth with ‘mediainfo’ and the like is simply a mediated
file size/runtime calculation. This cannot reflect the ups and downs in bandwidth of a real-world video.

Here is a real-world bandwidth graph of a ‘constant quality’ video file

Either you create your videos with ‘average bitrate’ instead or you provide more bandwidth reserve from your server to your clients (if that is possible).