Bulk Queueing models with unreliable server restricted admissions and threshold policies for vacations

Abstract

Queueing theory is an important branch of applied probability and it involves the mathematical study of queues or waiting lines. The formation of waiting lines is a common phenomenon which occurs whenever the current demand for a service exceeds the current capacity to provide that service. In this thesis, bulk queueing models with re-service, service interruptions, variant threshold policies for secondary jobs (multiple vacations, modified vacations and vacation interruptions), and restricted admissions on arrivals are developed. The proposed models of this research work are theoretically developed and numerically justified. In chapter 2, a bulk queueing system with server s choice of admitting re-service, multiple vacations and setup time is analyzed. A bulk arrival general bulk service queueing system with variant threshold policies for vacations is discussed in chapter 3. In chapter 4, a bulk queueing system with multiple vacations under restricted admissibility policy of arriving batches is considered. A single server bulk service queueing system with interrupted secondary job (vacation) is considered in chapter 5. A single server batch arrival queueing system with unreliable server and single vacation is analyzed in chapter 6. In chapter 7, a batch arrival single server retrial queue with modified vacations under N- policy is analyzed. For this model, the probability generating function of the steady state orbit size distribution at an arbitrary time epoch is obtained. A batch arrival general bulk service retrial queueing model with constant retrial rate is studied in chapter 8. The probability generating function of the steady state orbit size distribution at an arbitrary time epoch is obtained. Chapter 6 is studied by the embedded Markov chain technique and level crossing analysis. All the remaining chapters are discussed by the supplementary variable technique.