On the memory sharing problem

This paper presents an alternative proof for the structure of the optimal policy for the memory sharing problem, where several types of users share a common finite memory (or any other finite resource) and a policy is needed to allocate this memory among different types of service request. It is known that the optimal policy when there are two or three user types is “simple”. The proofs given here are also for the case of two or three user types, and they show that any nonsimple policy can be improved upon by adding and/or removing some points from its state space until it becomes simple