Mathematical Modelling of Distributed Memory System

Several mathematical models are considered in the paper to make a strict comparison of the storage models used both in artificial systems and probably in Nature. The very first artificial model was proposed by M. Tsetlin, who called it “The Pile of Books” in his publication in 1961, where he expected some valuable properties in comparison to the typical librarian book storage. Same model was re-discovered by Hendriks in 1972. In 1973 Burville and Kingman obtained mathematical results for corresponding Markov Chain. This Pile of Books model later found use in the Internet search approaches. The main attention in the present paper is paid to our “Distributed Memory” model, which contained additional parameters—the numbers of copies of the same elements stored in the memory. This model demonstrated some new useful applications for search in Internet as multiple storage sites in Internet is widely used. The most important result of the paper is that some features exhibited in the distributed model turned out to be in close similarity with the properties described in a book of biology by A. Levi and S. Sikevits who mentioned rather unusual organization used in biological cells for storage and extraction of enzymes. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.