Queueing theory is one of the most diversified fields of applied sciences that is widely used in a variety of areas including operations research, management science, computer science, telecommunication, production systems, and many others. The study of transient solution in queueing theory is an important which lead to optimal solutions and the control of the system. Thus, our aim in this book is to study the transient behavior of some queueing systems such as, single and multi server queue with some concepts (balking and reneging). In addition, when the parameters in the queueing system depend on time.