I would like to know that how I could make my own minecraft server for playing the start time and the end time. For example, Mineplex server is the time when the game ends or mccentral. I would think it to be a plugin or just command block of the system. And then when the time has been so players would get teleported spawn / lobby. Hope you can help ...
For servers like Mineplex, they most likely use a plugin, simply because they're more configurable and reliable.
If you want to shut down the server at a specified time, that can be easily done with various pre-existing plugins. From a Google search I found AutoShutdown. This basically shuts down and restarts the server at times you can specify, along with some other features. Just before the server shuts down you can kick all the players to a lobby using, maybe, BungeeTeleporter.
However, if you want to shut the server down when a game ends, that may be more complicated. Doing so would probably require that a specific condition be filled for the game to be counted as over, such as only 1 player left alive, or a timer runs out. I haven't found a plugin for this, but if you're proficient with Java and plugin development it's possible to make your own.
You may also want to reset the world when the game is over to prepare for a new match. I recommend WorldReset to automatically restore from a backup.