How to push and install APK files from a PC over Internet? I want to push AND INSTALL apk files from PC like Play Store does (when I send install signal from web interface). How to do this?

Note: The PC and Android device may not be in same Wi-Fi network. So, I am asking for solution over Internet.
I am rooted..
Setup a VPN! Having your phone rooted will let you install OpenVPN . You should setup a server (and connect it too to the VPN) and your phone will be your client. 

Then you'll have a server and a client in the same network so you can use adb commands! Push, pull, install...