||In this thesis, the study of the multi-class traffic model consists of three main parts. They are 1) graphical method, 2) update sequence and convergence, 3) Upstream-Downstream Algorithm. Multi-class traffic refers to the networks which have more than one type of resource transferring in it. A class of traffic refers to a distinct pair of source and sink node in this thesis. For the first part, I will explain how this problem is approached initially, but this method was too slow for practical use. For the second part, I will explain the effects of different chemical potential update sequences on the final solution. For the third part, I will further explain how to improve the graphical method with the help of upstream-downstream states, and current distribution and chemical potential distribution will be discussed. Network allocation optimization problems have been studied for the use in Internet routing and the telephone networks. Both packet-switched and circuit-switched networks need to optimize the usage of the whole network, in order to reduce traffic jam and maintain good quality of service. I found that the optimal solution is given by finding the chemical potentials at the nodes subject to friction on the links. The method is compared with Dijkstra's algorithm, which is the most commonly used shortest path finding algorithm. It is fast, however, it cannot deal with large amount of routing. However, our model can route a batch of calls simultaneously. An advantage is that as long as calls are routed from the same source and destination the computation time is independent of the number of calls. Also, our optimal solution is obtained in real numbers while those of Dijkstra's algorithm are integers. Therefore, our model can provide a better solution for the case of packet-switched networks. For the speed of the program, we believe that when the number of calls is large, our model can definitely be faster than Dijkstra's algorithm.