Abstract

This paper analyzes the problem of optimal control of two work-stealing deques in two-level memory (for example, registers—random access memory), where probabilities of parallel operations with deques are known. The classic sequential cyclic method for representing a deque in memory is considered. In the case of the deque overflowing in fast memory or emptying the FIFO-part or LIFO-part the necessary exchanges between fast and slow memory and shifts of elements in fast memory occur for relocation to the optimal state, which to be found. The task is to find the optimal partition of the total fast memory for deques and to determine the optimal state of each deque in each partition after the memory reallocation, i.e., to find the optimal number of elements, taken from both sides of the deque, to leave in the fast memory if the deque is filled or emptied. Optimality criteria for memory sharing is to maximize the sum of the mean operating times of each deque before the memory is redistributed and to maximize the lowest mean operating time of each deque before the memory is redistributed. The mathematical model in the form of an absorbing Markov chain are constructed. Simulation modeling, based on the proposed mathematical model, was carried out. The results of numerical experiments are presented.

中文翻译：

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关于两级内存中工作窃取双端队列的优化管理

摘要

本文分析了两级存储器（例如寄存器——随机存取存储器）中两个窃取工作的双端队列的最优控制问题，其中双端队列并行操作的概率是已知的。考虑了在内存中表示双端队列的经典顺序循环方法。在快速内存中的双端队列溢出或清空 FIFO 部分或 LIFO 部分的情况下，快速和慢速内存之间的必要交换以及快速内存中元素的移位发生，以重新定位到最佳状态，这将被找到。任务是为双端队列找到总快速内存的最佳分区，并确定内存重新分配后每个分区中每个双端队列的最佳状态，即找到最佳元素数，从双端队列两侧取出，如果双端队列被填满或清空，则留在快速内存中。内存共享的最优标准是在重新分配内存之前最大化每个双端队列的平均操作时间的总和，并在重新分配内存之前最大化每个双端队列的最低平均操作时间。建立了吸收马尔可夫链形式的数学模型。基于所提出的数学模型进行了仿真建模。给出了数值实验的结果。基于所提出的数学模型，进行了。给出了数值实验的结果。基于所提出的数学模型，进行了。给出了数值实验的结果。