The rapid growth and scope of multimedia applications has caused a tremendous impact on the way people communicate. The mission of next generation networks (NGN) is facilitating multimedia applications creation and deployment as well as supporting interoperability and network convergence. A key technology, IP Multimedia Subsystem (IMS) is the definitive means of achieving such goals. IMS has been proposed to support newly emerged multimedia IP based applications such as voice over IP (VOIP), video on-demand (VOD), IPTV and etc using a core IP backbone. Clearly, such applications cause huge amount of traffic load and require specified QoS constrains. It is worth pointing out that IP protocol only provides best effort service and use destination based routing which causes packets to reach their destination through different paths. Since multimedia applications require specified QoS constrains, IP cannot guarantee the reception of packets in order which is essential for the real-time applications. In this way traffic engineering (TE) is a technique which has been used to guarantee the QoS as well as optimal use of infrastructure networks. In order to implement TE, multiprotocol label switching (MPLS) is the useful solution among other existing techniques. This is because MPLS packets belong to a traffic source are routed through a same path which is essential for TE implementation. In addition to this, MPLS is one of the crucial protocols which have important rules in NGN. The major technical challenge in TE is the paths selection in which both QoS constraints and best possible resources utilization are satisfied. One of the key issues in providing QoS guarantees is the paths selection where both QoS constraints and best possible resources utilization are satisfied. The problem of finding such paths is known as QoS routing and is NP-complete problem in general. Such problems can be solved using heuristic algorithm in polynomial time. Although much work has been done on laying MPLS paths to optimize performance, most has focused on satisfying bandwidth requirements. Relatively little research has been done on QoS routing where QoS constraints is both bandwidth and delay. In this thesis we explain QoS based routing along with MPLS and TE requirements. We first propose a new Bandwidth and end to end delay Guarantee algorithm based on the LR-Servers theory that it decreases minmum end to end delay and increases maximum flow (MDMF).then a another algorithm porposed that it is proper for multiservice MPLS network(MDMFMS). Our simulation results are compared with previously published algorithms which are known as MHA, WSP, MIRA, BCRA, BGDG and MIRAD. The simulation results reveal that MDMF and MDMFMS present lower rejection rate compare to the rejection Key words Next Generation Network,Quality of Service, Traffic Engineering, MPLS, QoS-based routing