It could be easily done by creating .maintenance file in the root of your WordPress instance. Your script should look like this:
// create maintenance file before starting the long lasting process
file_put_contents( ABSPATH . '.maintenance', '<?php $upgrading = ' . time() . ';' );
// do stuff ...
// after finishing working on your stuff remove maintenance file
unlink( ABSPATH . '.maintenance' );
WordPress checks whether or not maintenance file exists in the root and if it does, then checks $upgrading variable to show maintenance message only for 10 minutes.
By default WordPress shows standard message during maintenance mode. It contains following text:
Briefly unavailable for scheduled maintenance. Check back in a minute.
If you want to run your own script and generate unique maintenance output, then you can create maintenance.php file within your wp-content folder. WordPress loads that file if it exists and stops executing a process after calling the file.