Optimal management of two parallel stacks in two-level memory

We consider the problem to manage two stacks in two-level memory. It is assumed that the tops of the stacks grow towards one another in the fast memory to which several processors are allowed to have simultaneous access, and the size of the stacks exceeds that of the fast memory. The fast memory stores the tops of the stacks only, while the remaining parts are stored in the second level memory. If the top of one of the stacks becomes empty or the stacks fill all the fast memory, that is, the stack overflow occurs, then a swapping to the second level memory is performed in such a way that each time a certain state of the memory is set and the next step starts. We study how to choose such a state of the memory in order to maximise the average time before the next swapping to the second level memory.