2026 , Volume 31, № 5, p.77-90

The aim of the research is to analyze the probabilistic and temporal characteristics of the process of filling an A-way associative cache with the memory blocks that most frequently requested by the processor. The study of the cache filling process is based on a model of ideal displacement of the most unused block in the cache group, which has the lowest probability of being in demand by the processor. Since the probabilities of different memory blocks being in demand by the processor are independent, the process of filling the cache with the most in-demand objects is distributed geometrically with a decreasing distribution parameter as the most in-demand memory blocks of the processor are loaded into the cache. Relationships have been identified between the probabilistic- temporal characteristics of the cache loading process and both associativity of the cache and the distribution pattern of processor requests for the addressable objects. It has been established that, as associativity increases, the peak values of the cache-filling probability function decrease and shift to the right along the “number of memory hierarchy access cycles” axis, while the distribution’s “tail” becomes “heavier”. The distribution function is shifted from the origin by A − 1 cycles of accessing hierarchical memory. The growth rate of the probability of filling the cache with the most in-demand items is determined by the value of their probability. The dependence of the average filling time for the cache, largely determined by the associativity of the cache and the type of allocation of the most in-demand memory blocks. A given level of probability of filling the cache with the most demanded processing objects is proposed as a criterion for cache loading. Due to the fact that the average cache filling time significantly depends on the value of the associativity parameter and the probabilistic value (mass) of the objects most in demand by the processor, it is reasonable to measure the “warm- up” time in terms of the average filling values. It is shown that with increasing associativity, the cache time allocation functions for the most demanded memory blocks converge in terms of the average. And for associativity values, the probability of filling the cache in the saturation region of the allocation function is practically invariant to the type of distribution of the demand for memory blocks by the processor, and for values above three averages, it can be assumed that the cache is full