I suspect you're creating the parallel.pool.Constant using data created on the client. It's much more efficient to have the workers create the data, if possible. Consider two cases:
% Case 1: data created on the client
parallel.pool.Constant(ones(1e4));
% Case 2: use the Constant constructor with a function handle to create
% the contents directly on the worker
parallel.pool.Constant(@() ones(1e4));
This results in the following memory usage pattern. In the screen-shot, case 1 is indicated with a red arrow, and case 2 with a green arrow.
As you can see, case 2 happens in parallel, and avoids the data transfer from the client to the workers (it's the data transfer that really causes the lack of parallelism).
If you really cannot create the data on the workers, you can use the parallel.pool.Constant constructor that accepts a Composite, like this:
% Build an empty Composite
c = Composite();
% Transfer the data from client only to worker 1
c{1} = ones(1e4);
c(2:end) = {[]};
spmd
% Use labBroadcast to copy data to all workers (labBroadcast
% is more efficient than the client/worker communication)
c = labBroadcast(1, c);
end
% Build the Constant from the Composite
c = parallel.pool.Constant(c);
% Flush memory on the workers by executing an empty SPMD block
spmd, end
