If the problem is bandwidth, then depending on format, source bit rate, framesize etc you'll want to re-encode to a more optimal size for your intended purpose
ffmpeg -i "my.mp4" -f mp4 -vcodec mpeg4 -b 512k -r 30 -s 640x360 -acodec libfaac -ar 32000 -ab 128k -ac 2 -threads 8 -movflags faststart "my_reduced.mp4"
-b = video bit rate (lower value = smaller size of the video file... however it reduces the quality of video.
-s = resolution of the video, optimize it to match desired output (but remember to maintain the correct aspect ration)
-movflags = relocates metadata to the start of the file reducing buffering time
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