An analysis of single server bulk queueing models with compulsory vacation and varied service

Abstract

Queueing theory plays an important role in the modern life and at every step we encounter in our daily activities. Such types of queues or waiting lines are found everywhere: newlinecomputer-communication networks, production systems, transportation services, etc. In newlineorder to efficiently utilize manufacturing and service enterprises, it is critical to effectively newlinemanage queues. The main objective of queueing theory is to develop formulae, expressions newlinefor performance measures such as average number of customers in a queue, mean waiting newlinetime in the system, etc. The results from queueing theory can directly be used to solve newlinedesign and capacity planning problems such as determining the number of servers, an optimum queueing discipline, schedule for service, number of queues, etc. Besides making newlinesuch strategic design decisions, queueing theory can also be used for tactical as well as newlineoperational decisions and controls. newlineA vacation queue is a queueing system in which the server is available for only a portion newlineof the time. At other times it is busy serving other stations or just not available due to newlineother activities. newlineQueueing systems with bulk arrival and bulk service with the possibility of server failures newlineand the effective utilization of server idle time by allocating the server to do some other newlinework (vacation models) are often important in real life. newlineIn this thesis, single server bulk queueing models with compulsory vacation and varied newlineservice are considered. Analytical treatment of all models considered in this thesis, is done newlineby using supplementary variable technique. newlineThis research work consists of eight chapters. The content of forthcoming chapters is newlinesummarized below.Chapter one introduces the concepts and techniques used in the thesis and also provides newlinea summary of the work done. newlineIn chapter two, we present the basic queueing model which forms the starting point newlinefor later investigations in the thesis which we develop for different queueing systems. newline