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 mα, 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 mα when m ≤ m0 and remains constant beyond m0), then there exists a memory size m such that no program can have a memory other than m or m0 if any program has a memory size greater than m0 each other program should have a memory size that is equal to or greater than m0
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