A method and apparatus are provided for managing the amount of memory available to processes within the computer system. Additional virtual address spaces are dynamically created to make more memory available to computer processes. The computer processes executing in each virtual address space access a shared memory region. Also, when a user requests a new connection to the computer system to form a new user session, it is determined to which of the existing virtual address spaces the new user session would best be assigned so as to maintain a load balance among the existing virtual address spaces.