Studies on Extended Cumulative Damage Models and Their Applications to Garbage Collections

Abstract

This dissertation proposes several maintenance policies for extended cumulative damage models in reliability theory and their applications to garbage collection policies for a generational garbage collector in computer science. Using the tech-niques of cumulative processes, the expected costs per unit of time, i.e., expected cost rate models, are obtained, and optimal policies which minimize them are discussed analytically and computed numerically. An initial chapter gives introduction which is constructed by review of literatures and organization of dissertation. Extended cumulative damage models in theory and their optimizations are proposed in the following chapters: Chapter 2 proposes two basic preventive maintenance policies for a used system with an initial variable damage level. Chapter 3 considers three replacement policies that are com-bined additive with independent damages. Chapter 4 takes up three maintenance policies for an operating system which works at random times for jobs. Chapter 5 proposes a standard cumulative damage model in which the notion of “whichever occurs last” is applied, which is called maintenance last. As applications, two stochastic models based on the working schemes of a generational garbage collector are proposed in Chapter 6. In the end of dissertation, the results are summarized and future problems are given. The models proposed in Chapter 2-5 are derived from practical systems as introduced in every chapter and could be applied to them by suitable modifications and extensions. The theoretical methods proposed in Chapter 6 could provide some useful information to computer programmers to design more efficient collectors.