Study of Memory Partitioning for Multiprogramming Systems with Virtual Memory

In this paper, we investigate the effect that the shape of the lifetime function has on the optimal partition of the main memory of a computer among N programs, where the criterion of optimality is maximization of CPU utilization. We used a simple queuing model as a base for understanding this interrelationship. The lifetime function is the average of the execution intervals of a program as a function of the amount of memory allocated. When the lifetime function is convex and is proportional to m
^α
, where m is the size of memory, then the optimal partition is obtained by dividing the main memory equally among q of the N programs (q is the optimal degree of multiprogramming). Thus, the best partition is always one of two policies; allocate all memory equally among the q programs or allocate all memory to one program. When the lifetime function has a degenerate S shape (is proportional to m
^α
when m ≤ m
0
and remains constant beyond m
0
), then there exists a memory size m such that no program can have a memory other than m or m
0
if any program has a memory size greater than m
0
each other program should have a memory size that is equal to or greater than m
0