K-ary n-cubes have been one of the most popular interconnection networks for practical multicomputers due to their ease of implementation and ability to exploit communication locality found in many parallel applications. This paper describes an analytical model for k-ary n-cubes with dimension-ordered routing. The main feature of the model is its ability to captures network performance when an arbitrary number of virtual channels are used to reduce message blocking. Simulation experiments reveal that the latency results predicted by the analytical model are in good agreement with those provided by the simulation model.