I think Cron:: is a bad top level namespace when the module is not specific to cron at all.

What about using Process:: instead? Something like Process::AvoidConcurrentRuns or Process::AvoidMultipleInstances or Process::Singleton

Also if you put this on CPAN, you might think about different possible use cases:

• Users might want to use it exactly as you have shown
• Users might want to use it as you've shown, but without the verbose output
• Users might want to just query if another instance is already running, and behave as they see fit

The interfaces for that might look like this:

# first case:
use Process::Singleton qw(:auto_verbose);

# second case:
use Process::Singleton qw(:auto);

# third case:
use Process::Singleton qw(is_running);
if (is_running()) {
   ...
} else {
   ...
}
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This is of course just an example, but I want to encourage you to think more about the interface.