I don't think ThreadPool will help here. I ran the code in a Process pool and a Thread pool and the runtime was somewhat similar. I also double checked how much data is being sent between the MATLAB client and workers and it is not a lot:
BytesSentToWorkers BytesReceivedFromWorkers
__________________ ________________________
1 576198886.00 614.00
2 576198886.00 614.00
3 576198886.00 614.00
4 576198886.00 614.00
5 576198886.00 614.00
6 576199557.00 1081.00
7 576199557.00 1081.00
8 576198886.00 614.00
Total 4609592430.00 5846.00
ThreadPool can certainly help when working with large data, but I do not think it is the culprit here.
I think the culprit is multi-threading. Running the code serial took me 33 seconds and running it on a single worker with no multi-threading took 78 seconds. This means that some multi-threading is happening behind the scenes.
I think you had the right idea of giving your parallel workers access to more threads. For example, in serial the code took 33 seconds. I then started a single worker and gave it access to 8 threads and that ran in 38 seconds (5 seconds for overhead is reasonable). I think as the problem scales up and you can have more workers with more threads you will get more of a benefit from MATLAB Parallel Server.
P.S. you may want to explore using sliced input variables as your data gets larger, so you can send chunks of data to the workers instead of the entire matrix/array.
