I have the following requirement.
what is size resolution that is best for what internet speeds?
I have already configured dispatcher environment with Apache server.
I have to test on dispatcher below one case by case.
Chrome has OOTB option to set custom download speed., you could also use tools like Charles proxy to do similar.
 Network Analysis Reference | Tools for Web Developers | Google Developers
Most of the modern video providers already have options to serve content based on user download speed, e.g. they request the bitrate depending on the users speed.
Please replicate video to publish environment and check, if still not appearing then clear cache and try.
I want to test video resolution and internet speed on cached page.
and Can I set different video resolutions as I can set custom download speed using chrome developer tools?
And I have second question.
I have added video(AEM front end testing(HD1080P).mp4) file like below one and published it in author environment.
But the video doesn't display like below one in publish environment.
I don't know why.
Have you tested your videos on AEM pages that are not cached. If you select a tool as Peter suggests - you should be able to test the videos on Cached pages.