A method for efficiently managing memory resources in a computer system having a graphics processing unit that runs several processes simultaneously on the same computer system includes using threads to communicate that additional memory is needed to avoid termination or less than optimal performance of a process. If the request indicates that termination will occur then other processes will reduce their memory usage to a minimum to avoid termination but if the request indicates that the process will not run optimally then the other processes will reduce their memory usage to 1/N where N is the count of the total number of running processes. The apparatus includes a computer system using a graphics processing unit and processes with threads that can communicate directly with other threads and with a shared memory which is part of the operating system memory.