I see that you are using LWP::UserAgent module. That's where your problem lies, because I believe the user agent is a single threaded process that waits for the GET to complete before processing the next request.

So if you change your scheduler to the following, it should HTTP get all your scheduled jobs without waiting for them to complete:

foreach $url ( @scheduled_jobs ) {
    my $ua = new LWP::UserAgent;
    my $req = new HTTP::Request GET => $url;

    my $pid = fork();
    if ($pid == 0)
    {
        # in the child
        my $res = $ua->request($req);
        exit(0);
    }
    
    # in the parent, carry on with next job...
}
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I haven't tested the code, but I believe if you do something along the line, it should work.