I use php and laravel as my web service.
I want to know does laravel store and process requests in these situation?
Everything in PHP starts as a separate process. These processes are independent form each other until some shared resource comes in Picture.
In your case one user is handled one session and sessions are file based by default. The session file is shared resource for processes which means you can only make one call to PHP at a time for one user.
Multiple user can invoke any number of processes at once depending on your systems capabilities.