Long-range dependencies in reading memory pages in the man-computer system interaction

Abstract

The modern computer systems consist of many interdependent subsystems. There are two possible approaches to their analysis. The first one is based on the idea of reductionism proposed by Descrates[1] and can be considered as a still ruling paradigm in the case of computer science and engineering. The second one can be related to the still new idea of the complex systems approach, where in order to understand the behaviour of such systems one needs to have the knowledge about the behaviour of system components and also, that is more important, how they act together [2, 3, 4, 5, 6, 7, 8]. This specific paradigm change can be even shown in the case of the idea of Turing machines and new approach for consideration in the case of interactive processing – even the opinion that “the computer engineering is not a mathematical science” was presented [9]. It should be noted that the Turing machine is a mathematical idea [10] while its implementations are the physical ones [11], but if the physical nature of computer systems was indicated, there is a need to have an appropriate physical (thermodynamical) basis for deliberations in such a case. In [12] it has been shown that the analysis of processes in the computer systems can be based on non-extensive thermodynamics. However, this analysis considers only spatial correlations, meanwhile in this paper we will focus on time dependencies leading to a long-memory effect. The paper is divided into 5 sections. In Section 2 the conception of the hierarchical structure of memory system in the computer is presented. This proposal was given in [11] where its influence on computer thermodynamics was discussed. In Section 3 there is a short survey about long-range dependencies whereas Section 4 discusses practical usage of theoretical considerations. The last section concludes the paper.