how do I write $#queue+1 and $#{$queue[0]}+1 with array refs instead?

$#$queue+1
$#{$queue->[0]}+1
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or simply

scalar @$queue          # number of elements
scalar @{$queue->[0]}
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(you don't need the scalar if it's in scalar context anyway, like with if (@$queue) )

Presuming the first element of the referenced array holds another array ref, that is (not sure what you intend to keep there...).