Due to the increased evolution of multimedia applications deployed on the global network - the Internet, interests in this eld focused on the network s reliability and performance. The concern is to estimate network link sizes in an optimum way which imposes multiple challenges. One of these challenges is the allocation of resources among competitive demands of various applications taking into account the cost of the resources and the QoS requirements of traffic delivery. Without proper network planning, deploying multimedia applications in an IP network does not promise an acceptable QoS level to the end-user. There is a di erence between the theoretical values of the quality and quantity of any data transmitted over an IP network and those which exist in practice. This is because network resources could be shared by multiple users. In this book, we aim to study analytically the distribution of the number of multimedia connections over IP networks. The study is also conducted over networks that implement various call admission control (CAC) schemes. CAC are used in nowadays networks to enhance its reliability and improve application performance.