Abstract
Poor code locality in virtual memory systems is one of the reasons for page faults and, consequently, slow operation of an entire system. Despite the extensive body of research dedicated to minimizing page faults, the proposed solutions, which are predominantly based on clustering techniques, fail to provide approximation errors relative to an unknown optimal or near-optimal solution. We use Working Set strategy and geometric interpretation of the computational process, which clarifies the subtleties of optimization and facilitates the development of a mathematical model for minimization of page faults. Our approach includes functionals and constraints that define a set of possible solutions, which may be useful for future research aimed at developing an algorithm to achieve an optimal or ε-optimal solution. The results pave the way for researching and finding an efficient and cost-effective replacement algorithm similar to the working set approach.