TRACON ATCS reported a loss of separation on final due to compression. Reporter stated a blocked frequency precluded timely alternate instructions.

Narrative

Aircraft X was catching Aircraft Y on final due to the fact that the Aircraft Y slowed to 100 KTS inside the FAF. His was the first aircraft to slow that much in this rush. This caused a greater than usual amount of compression in this sequence. I slowed Aircraft X to 160 KTS and then moments later slowed him to 'slowest practical speed'. I then canceled the approach clearance and issued pull-out instructions - AFTER waiting for a pilot to stop talking on frequency. This delay caused a critical loss of time which contributed to the loss of separation. It is possible that had I been able to talk to Aircraft X when I wanted/needed to; separation would have been preserved.Give controllers some kind of software tool that 'projects' the compression between all aircraft on final and alarms when the software determines that a loss of separation may/will occur due to compression. Compression is never the same twice depending on crews and aircraft types and changing wind and weather conditions. Also; develop a system where we can communicate to pilots without interruptions; blocks; etc. Until then; we really don't have control. The idea that a controller's critical transmission to a pilot in harm's way may not get to the pilot or may be blocked is unacceptable in this safety industry. Until such time; we don't have control - only the illusion of control.