Reduce installation time and increase the installation speed using drush command "site-install"
Is there any min requirement in-terms of hardware to install the distribution via drush


No, there aren't any minimum hardware requirements. If your machine can run the software that Drush relies on, Drush can run.


  does it require any additional configuration in php.ini or httpd.conf config file


It depends on your environment - the project page has all the information you'll need.


  Is there any alternate way to install the distribution via drush with minimal time


I don't see how there would be. The Drush guys aren't going to have made that process intentionally slow, so it'll probably be as quick as it can be.


  Can anyone tell me how to increase the installation speed and reduce installation time using drush command "site-install"


That's down to the specs of your machine; the obvious (if slightly patronising) answer is simply to buy better hardware if yours isn't up to the task you want to use it for.

Bottom line, if you're installing a "larger size distribution" you can expect it take more resources. If that amount of resources is more than you have to give, it's time to look at buying better hardware.