AbstractThe problem of optimal nonbifurcated routing in virtual circuit (VC) communication networks, such as the X.25 packet‐switched networks, the frame‐relay networks or the ATM networks, is considered. To describe the related characteristic of the generally asymmetrical transmit and receive traffic in such networks, a related multicommodity flow (RMCF) model with two traffic matrices is proposed. For solving the optimal flow assignment problem with this model, we present an algorithm which incorporates the transmit receive (TR) relation, an important practical constraint existing in most of the operational VC networks.A comparison of the RMCF model with the symmetrical multicommodity flow (SMCF) model shows that the former is superior with respect to the network delay. Furthermore, performance degradation has been observed, which is caused by using the traditional multicommodity flow (MCF) model due to the lack of VC bandwidth reservation of the receive traffic. We also show the dependency of the network throughput on the traffic symmetry versus the TR ra