The underlying object of this book is to provide foundational prologue to modeling and analysis of queueing system. In order to predict the performance of a queueing system, we have investigated various model using probabilistic approaches. Work done in the present book will provide an insight to production engineers and decision makers to improve the quality of products by minimizing the interruption due to server breakdown, machine downtimes, blocking of resources, etc. The book will also meet the requirements of academicians as well as research scholars and students in mathematics and statistics. Constructive comments and suggestions from the reader for further improvement of the book will be gratefully acknowledged.