By far the greatest amount of time is being spent evaling the data structure into existence:

        my $e = eval( $p );
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There's not a lot you can do about that. Writing your own parser would be complicated, error prone and almost certainly eons slower.

The second largest amount of time is being spent building and executing those two complicated SQL statements:

$stmt = qq(INSERT INTO ACCU_USAGE  VALUES ($Mobil ...
...
$stmt = qq(INSERT INTO ACCU_USAGE  VALUES ($MobileNumber, ...
...
$rv = $dbh->do($stmt) or die $DBI::errstr;
...
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Now that you can do something about. By pre-preparing the statement using placeholders:

my $sql = $dbh->prepare( q[ INSERT INTO ACCU_USAGE  VALUES( ?, ?, ?, ?
+, ?, ?, ?, ? ) ] ) 
    or die $DBI::errstr;
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and then binding the vars when executing the statement:

                    $rv = $sql->execute(
                        $MobileNumber,
                        $value->{'subscriberGroupName'},
                        $value->{'absoluteAccumulated'}->{'counters'}-
+>[0]->{'bidirVolume'},
                        $value->{'absoluteAccumulated'}->{'counters'}-
+>[0]->{'name'},
                        $value->{'selected'},
                        $value->{'absoluteAccumulated'}->{'expiryDate'
+}->{'volume'},
                        $value->{'absoluteAccumulated'}->{'previousExp
+iryDate'}->{'time'},
                        $value->{'absoluteAccumulated'}->{'previousExp
+iryDate'}->{'volume'}
                    ) or die $DBI::errstr;
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Not only will you give the DB engine the best chance of performing the inserts optimally; you can also make your code look a lot cleaner and simpler to maintain. It won't reduce your cpu usage; but it should result in your program finishing more quickly.

I hope you'll agree this is much nicer to look at and understand:

#!/usr/bin/perl
use Data::Dumper;
use DBI;
use File::Basename;
#use warnings;

@ARGV = qw[ NUL junk.dat CON CON ]; ## crude hack for local testing.

open( FH, "<", $ARGV[0] );
open( AH, "<", $ARGV[1] );
open( OUT, ">", $ARGV[2] );
open( LOG, ">", $ARGV[3] );

#Conneting to database
my $dbExt = "db";
my $driver = "SQLite";

#my $file = basename($ARGV[1]);
#my @fileName = split(/\./, $file);
#$file = $fileName[0] . ".$dbExt";
my $dbFileName = 'junk.db'; #dirname( $ARGV[1] )  ."/" . $file;


if(-e $dbFileName) {
    unlink ($dbFileName);
}

my $database = "$dbFileName";
my $dsn = "DBI:$driver:dbname=$database";
my $userid = "";
my $password = "";

my $dbh = DBI->connect($dsn, $userid, $password, { RaiseError => 1, Au
+toCommit => 0 })
    or die $DBI::errstr;

my $stmt = <<EOS;
    CREATE TABLE ACCU_USAGE (
        MOBILE VARCHAR2(50),
        PLANNAME  VARCHAR2(50),
        PLANUSAGE CHAR(50),
        COUNTER CHAR(20),
        STATUS VARCHAR2(20),
        EXPIRY_DATE CHAR(20),
        PREEXP_TIME CHAR(20),
        PREEXP_VOLUME CHAR(20)
    );
EOS

my $rv =  $dbh->do($stmt);
if($rv < 0){
    unlink($dbFileName) if(-e $dbFileName);
    $dbh->disconnect();
    print LOG $DBI::errstr;
    exit(1);
}

my $sql = $dbh->prepare( q[ INSERT INTO ACCU_USAGE  VALUES( ?, ?, ?, ?
+, ?, ?, ?, ? ) ] )
    or die $DBI::errstr;

my $SubsSize= -s $ARGV[0];
my $AccuSize= -s $ARGV[1];
my $SubsCount=0;
my $AccuCount=0;
my $finalCount=0;
my $rowCount = 0;

while( <AH> ) {
    chomp;
    my $line = $_;
    $AccuCount++;
    my $MobileNumber;

    if( $line =~ /subscriberId:(\w+)\(\"(\d+)\"\)/ ) {
        $MobileNumber = $2;
    }
    else {
        $MobileNumber = "''";
    }

    my $plan = $line;
    $plan =~ s/\\//g;
    my @AccVolume;

    if( $plan =~ /usageControlAccum:(\w+)\(\"(.*)\"\)/ ) {
        my $p = $2;
        $p =~ s/:\{/ => {/g;
        $p =~ s/:\[/ => [/g;
        $p =~s/\"/\'/g;
        $p =~  s/\':/\'=>/g;
        $p =~ s/\}n/\}/g;

#        print $p,"\n";
        my $e = eval( $p );

        if ( @$ ) {
            push (@AccVolume,"error");
        } else {
            #print Dumper($e);
            foreach my $value ( @{$e->{'reportingGroups'}} ) {
                if ( exists ( $value->{'absoluteAccumulated'}->{'count
+ers'} ) ) {
                    $rv = $sql->execute(
                        $MobileNumber,
                        $value->{'subscriberGroupName'},
                        $value->{'absoluteAccumulated'}->{'counters'}-
+>[0]->{'bidirVolume'},
                        $value->{'absoluteAccumulated'}->{'counters'}-
+>[0]->{'name'},
                        $value->{'selected'},
                        $value->{'absoluteAccumulated'}->{'expiryDate'
+}->{'volume'},
                        $value->{'absoluteAccumulated'}->{'previousExp
+iryDate'}->{'time'},
                        $value->{'absoluteAccumulated'}->{'previousExp
+iryDate'}->{'volume'}
                    ) or die $DBI::errstr;
                }
                elsif ( exists ( $value->{'absoluteAccumulated'}->{'bi
+dirVolume'} ) ) {
                    $rv = $sql->execute(
                        $MobileNumber,
                        $value->{'subscriberGroupName'},
                        $value->{'absoluteAccumulated'}->{'bidirVolume
+'},
                        $value->{'absoluteAccumulated'}->{'name'},
                        $value->{'selected'},
                        $value->{'absoluteAccumulated'}->{'expiryDate'
+}->{'volume'},
                        $value->{'absoluteAccumulated'}->{'previousExp
+iryDate'}->{'time'},
                        $value->{'absoluteAccumulated'}->{'previousExp
+iryDate'}->{'volume'}
                    ) or die $DBI::errstr;
                }
                if($rv < 0) {
                    print LOG "Failed to insert $stmt query. Exiting..
+.\n";
                    unlink($dbFileName) if(-e $dbFileName);
                    print LOG $DBI::errstr;
                    $dbh->disconnect();
                    exit(1);
                }
                else {
                    $rowCount++;
                    if($rowCount == 5000) {
                        $dbh->commit();
                        $rowCount = 0;
                    }
                }
            }
        }
    }
}
close(AH);
$dbh->commit();
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