QUEUEING MODELING OF REPAIRABLE MACHINING SYSTEMS WITH SERVICE INTERRUPTION

Abstract

The queueing theory and performance models have become the essential tools for the system designers/organizations to deal with unavoidable interruption of machining systems and also have potential industrial applications in computer and communication networks, traffic control, nuclear and power plants, distribution and power supply systems, production and assembly lines etc. In the industrial scenario, the primary objective of system designers is to design the machining system which may be fault tolerable. Many engineering systems which are prone to failures and operate in a machining environment can be improved by appropriate choice of redundancy as well as maintainability. Keeping in mind the vital role of queueing modeling of machining system with service interruptions due to unavailability of the server, in the present thesis some of queueing models for machining system with service interruption have been explored in different frameworks. In the present work our prime objective is to develop both transient as well as steady state queueing models for the repairable machining system with service interruption to investigate queueing and reliability indices of the concerned system. A variety of prominent features namely control policies, threshold policies, vacation, working vacation, server breakdown, provision of standby support, reboot and recovery process have been incorporated to dealt with the interruptions occurred in machining environment. Furthermore optimal system parameters have been obtained to determine the optimal cost of the system. The thesis is organized into 10 chapters including the first chapter devoted to general introduction on the relevant topics of work done in the thesis. The literature review, basic concepts and methodology used are also discussed in the first chapter. The chapters 2-8 and chapter 9-10 explore Markovian and non-Markovian models of machining system, respectively. The study done is concluded by highlighting the noble features and future scope in the end of the thesis. The relevant references are listed in the alphabetical order. The investigation presented in the chapters 1-10 of the thesis are as follows: Chapter 1 entitled ‘General Introduction’ presents the motivation, the overview of the relevant research works, methodological aspects, solution techniques, survey of the literature and contents of the thesis. Chapter 2 deals with the time-dependent analysis of an M/M/1 queueing model with state dependent rates and optional multiple working vacations. Chapter 3 is concerned with admission control of maintenance for unreliable server machining system ii with working vacation. The chapter 4 presents the admission control policy for the fault tolerant system comprising of multi-components operating machines and multi types of warm standbys under the maintenance of single unreliable server. The concepts of F-policy which deals with the controlling of admission of failed machines and imperfect coverage are incorporated to make Markov model more realistic. Chapter 5 deals with the performance modeling of finite Markov M/M/1/L working vacation model for the fault tolerant machining system (FTMS). The concepts of redundancy along with the provision of dissimilar warm standbys are considered to maintain the pre-required high reliability of the system. In chapter 6, Markov model of multi-component machining system comprising of two unreliable heterogeneous servers and mixed type of standby support has been studied. In chapter 7, the performance prediction of fault tolerant machining system with imperfect coverage, reboot and server vacation is described. This study is concerned with the performance modeling of a fault tolerant system consisting of operating units supported by a combination of warm and cold spares. In chapter 8, Markovian model for FTS multi-component machining system with imperfect coverage, standby support and working vacation is investigated. In chapter 9, the availability analysis of M/G/1 FTS system for R-out-of-M: G configuration is described. The study of imperfect fault coverage and availability analysis of redundant machining system having the facility of recovery and replacement has been done. In chapter 10, the M/G/1 model for the multi-component fault tolerant machining system by incorporating the features of common cause shock failure and standby support has been investigated. Finally noble features and future scope of investigations done are presented in the conclusion section given after chapter 10. The queueing models developed in the present thesis provide valuable insights for the system design and may be successfully used in abundant congestion situations encountered in machining environment. Keeping in mind a variety of problems have been explored using different methodologies. It is hoped that the queueing models developed for machining systems in this thesis may be helpful to system analysts, developers, and practitioners to frame more optimal and efficient design of the concerned system.