Studies on some queueing models with heterogeneous service and vacations

Abstract

In this thesis attempts have been made to investigate some M/G/1 type of queueing models with two phases of heterogeneous services associated with various types of vacations and as well as without vacations. The thesis consists of 7 (seven) chapters in two parts. The first part includes the queueing system with two phases of heterogeneous service and in the second part the queueing system with Bernoulli vacation schedule is considered. In this course of study, various new results are obtained as well as some existing well known results are generalized. The following is a brief description of the work done in the thesis. Chapter I-Introduction The chapter I is the general introduction which includes historical aspects, basic terminology, the anatomy of the queueing system where the various types of queueing processes and the techniques used in this thesis are discussed elaborately. PART I (Queueing system with two phases of heterogeneous service) In the part I of the thesis, the M/G/1 type of queueing system with two phases of heterogeneous services associated with single as well as batch arrival queueing models are considered and the various useful aspects are discussed thoroughly. The part I of the thesis is divided into three different chapters which are organized as follows. Chapter II deals with an M/G/1 queueing system with two phases of heterogeneous service where after completion of first phase of service of an unit, it may leave the system or may go immediately for a second phase of service. By using the embedded Markov chain technique along with the Markov regenerative process the following aspects have been discussed under the present study of this chapter: The queue size distribution at departure epoch The queue size distribution due to busy periods of the server The busy period distribution The waiting time distribution The recursive solution of the departure point queue size distribution Finally some numerical results have been presented to compute the limiting probabilities of the queue...