Multipath Protocol Label Switching (MPLS) is a routing mechanism (technology) used in modern telecommunication networks, which is built as a multi-service network with a certain Quality of Service (QoS). To maintain the required QoS in such complicated networks, the Traffic Engineering (TE) should be equipped with optimum traffic management, routing mechanism, and switching operations, which are what this paper tackles, where the TE is identified as the optimal distribution of flows in the

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... ing network. In this paper, an effective multipath routing mathematical model is developed based on several previous mechanisms to ensure the guaranteed desired QoS and loading balance according to the Telecommunication Network Systems (TCS) resources, to achieve the optimum TE, and hence improving the network usage efficiency. Moreover, the obtained mathematical optimization algorithm results are provided through the relative equations. Indeed the developed routing mathematical model in this paper is suitable for the dynamic distribution of information flows, which is the main improvement in the TE achieved in this work. Service (QoS) traffic polytypic users. Multipath Protocol Label Switching (MPLS) is a routing mechanism used to achieve the required QoS in the modern telecommunication networks, where the traffic management, routing and switching operations are considered as the main parameters for the Traffic En- , where TE is identified as the matter to optimize the distribution of the network data flow. In [3] , the QoS for hybrid telecommunication network is achieved by developing an adaptive routing method, where in [4] the optimum utilization for the resources of networks is investigated to achieve communication models accuracy that provides the required performance by improving the routing protocols. However, the network performance was improved in different ways than the routing methods, such as applying network coding as in [5] [6] [7], which shows that decreasing the number of the transmitted packets does improve the telecommunication traffic significantly in different applications such as wireless sensor network [5] [6], and long term evaluation advance mobile communication network [7]. General understanding and analysis for applying network coding in cooperative networks over lossy channels with the improvement of traffic is shown in [8] [9]. In [10], the author proposed rateless layered for multiple description video delivery through a relay, and it showed as well how the proposed scenario exploited the path delivery over a mobile network to show the advantages of the relaying when the network is optimized intern of routing and the unequal error detection. In this paper, an effective multipath routing mathematical model is developed which is derived from different existed multipath routing mechanisms to ensure obtaining the desired QoS and loading balance according to the Tele-Communication Systems (TCS) resources, and hence reaching the most effective TE, which is called the optimum TE. The optimum TE is the main requirement to improve the network usage efficiency. Accordingly, during the wireless communication system where one packet can be simultaneously transmitted along multiple paths, the optimum TE is providing balanced loading and helping to improve the TCR, especially high-speed and associated likelihood-time quality of service indicators. The rest of the paper is organized as following: in Section 2, the multipath routing solution general requirements is discussed, with the classification of the mathematical models of routing; Section 3 provides the required back ground for Grafokombinatornye routing algorithms and models; Then, the mathematical optimization algorithm is obtained and its theoretical results are provided through the relative equations; and finally, the paper concludes.