This paper compares the performances of optimal routing as yielded by the pipe, hose, and intermediate models. The pipe model, which is specified by the exact traffic matrix, provides the best routing performance, but the traffic matrix is difficult to measure and predict accurately. On the other hand, the hose model is specified by just the total outgoing/incoming traffic from/to each node, but it has a problem in that its routing performance is degraded compared to the pipe model, due to insufficient traffic information. The intermediate model, where the upper and lower bounds of traffic demands for source-destination pairs are added as constraints, is a construction that lies between the pipe and hose models. The intermediate model, which lightens the difficulty of the pipe model, but narrows the range of traffic conditions specified by the hose model, offers better routing performance than the hose model. An optimal-routing formulation extended from the pipe model to the intermediate model can not be solved as a regular linear programming (LP) problem. Our solution, the introduction of a duality theorem, turns our problem into an LP formulation that can be easily solved. Numerical results show that the network congestion ratio for the pipe model is much lower than that of hose model. The differences in network congestion ratios between the pipe and hose models lie in the range from 27% to 45% for the various network topologies examined. The intermediate model offers better routing performance than the hose model. The intermediate model reduces the network congestion ratio by 34% compared to the hose model in an experimental network, when the upper-bound and lower-bound margins are set to 25% and 20%, respectively.