Optimal management of two parallel stacks in two-level memory

Abstract

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.The research was supported by the Russian Foundation for Basic Research, grants 01-01-00113 and 03-01-06415.Large stack. We make the stack very large and assume that an overflow will never occur; an overflow causes abnormal termination.Demand fed single element stack manager. In this case the top of stack is hardware realised as a circular buffer and the rest of the stack is stored in the memory. As an overflow or underflow of the stack occurs, an element (or several elements) are moved from the buffer to the memory or vice versa.Paging stack manager. The top of stack is software realised as a part of dedicated memory. When the top of stack is emptied, the half of the buffer is copied from the memory, and when a stack overflow occurs, the lower half of the buffer is moved to the memory and the upper half is moved to the beginning of the buffer.

The Optimal Control of Two Work-Stealing Deques, Moving One After Another in a Shared Memory

“…In [17] and [31] the mathematical models of optimal control of one and two stacks in two-level memory were proposed, in [32]-models of the optimal control of FIFO-queues. In practice, various architectures have hardware implemented a number of methods for managing stacks in two-level memory as an alternative to the classic cache memory [33].…”

Optimal Implementation of Two FIFO-Queues in Single-Level Memory

“…In [2][3][4][5][6] a mathematical model of the process was constructed as twodimensional random walk in a triangle with two reflecting and one absorbing barriers. In [7][8] we consider the problem of one and two stacks managing in two-level memory. This paper proposes mathematical models and optimal algorithms of two FIFO-queues control [9].…”