Significant challenges has been introduced for IP networks with the advent of new emerging applications, such as VOIP and E-Commerce, that require delivering quality guarantees. However, IP networks were originally designed to support best effort delivery only.??Three Quality of Service (QoS) models, IntServ, DiffServ and MultiProtocol Label Switching (MPLS) have been standardized by the Internet Engineering Task Force (IETF). Although these methods guarantee delivery, they have drawbacks such as complexity, restrictions of pre-defined classes and higher end-to-end delay.In this paper, a new QoS mathematical model has been proposed. This model is based on the principles of Network Calculus in which an incoming traffic flow is regulated by an arrival curve that upper bounds its rate. Then, this traffic flow is lower bounded and delayed by a service latency time at each node on its way to the destination node. This model is compared with other IP QoS models, IntServ and DiffServ.The worst case end-to-end delay is derived and illustrated by a numerical example .The proposed model has achieved the lowest end-to-end delay compared with others.