Waiting in lines is a staple of everyday human life. Without really noticing we are doing it when we go to buy a ticket at a movie theater stop at a bank to make an account withdrawal or proceed to checkout a purchase from one of our favorite department stores. Oftentimes waiting lines are due to overcrowded overfilling or congestion; any time there is more customer demand for a service than can be provided a waiting line forms. Queuing systems is a term used to describe the methods and techniques most ideal for measuring the probability and statistics of a wide variety of waiting line models. This book provides an introduction to basic queuing systems such as M/M/1 and its variants as well as newer concepts like systems with priorities networks of queues and general service policies. Numerical examples are presented to guide readers into thinking about practical real-world applications and students and researchers will be able to apply the methods learned to designing queuing systems that extend beyond the classroom. Very little has been published in the area of queuing systems and this volume will appeal to graduate-level students researchers and practitioners in the areas of management science applied mathematics engineering computer science and statistics.