To establish reliable communicate between end users, alleviation of the congestion of packets in the communication networks is the most important problem. Many approaches have been attempting to resolve such a problem. As one of the effective routing strategies for reliable communication, we have also proposed a routing strategy with chaotic neurodynamics. By a refractory effect which is the most important effect of chaotic neuron, the routing strategy shows high performance for communication networks as compared to the shortest path approach. In addition, we improved the routing strategy by combining information of the shortest paths and waiting times at adjacent nodes. As a result, we confirmed that the routing strategy using chaotic neurodynamics is the most effective policy to alleviate the congestion of the packets in the communication network. However, in the previous works, the chaotic routing strategy was evaluated for ideal communication networks; each node has same transmission capability for routing the packets and same size of buffer for storing the packets. From a view point of realistic application of the chaotic routing strategy, it is important to evaluate the performance of the routing strategy under realistic conditions. In 2007, M.Hu et al. proposed a realistic communication network in which the largest storage capacity and processing capability are introduced. Thus, in this paper, we evaluate the chaotic routing strategy for the realistic communication networks. Results show that the chaotic routing strategy keeps the highest arrival rate of the packets as compared to the conventional routing strategies by avoiding the congestion of the packets effectively. Also, we confirmed that the chaotic routing strategy has much possibility for application in the real communication networks.