How to bring down a application for certain period of time
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There is no direct support for something like this.
But, you could create a boolean constant you use to show/hide pages on a site, or other UI elements, to make that app non-/available to users.
where can we configure the constant
I am not sure what you want to know. I am talking about a constant in Appian.
docs.appian.com/.../Constants.html
OOTB you can use the 'Maintenance Window' feature in the Admin Console but this will apply to the whole environment, not to a specific Application. Otherwise you can do exactly as describes, to toggle the value of a constant which is used to hide the default landing pages for all of the roles involved in your application and replace with a blanket "This Application is undergoing maintenance" message or equivalent as the only User Interface they can see.
Apart from what both of these people said, if you are using tempo by any chance (that I assume you are not), then you can also unpublish the application. That should take all the records/actions away from tempo.