Let me use my crystal ball again... are you trying to run the "qsub script" from the first code sample and get it's output? If so, use backticks.

my $PBS_ARRAYID = '123' ;
my @output = `/usr/bin/perl /chongle/jeri/timecheck/MUSCLEHMM.pl $PBS_
+ARRAYID > /chongle/jeri/timecheck/output.$PBS_ARRAYID.txt 2> /chongle
+/jeri/timecheck/error.$PBS_ARRAYID.txt` ;
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