The efficiency of a large-scale multicomputer is critically dependent on the performance of its underlying interconnection network. Dimension-ordered routing has been employed to transmit messages in multicomputer networks as it requires a simple deadlock-avoidance algorithm, resulting in an efficient router implementation. The performance of this routing algorithm has been widely analysed under the assumption of the traditional Poisson arrival process, which is inherently unable to model traffic self-similarity revealed by many real-world applications. In an effort towards providing cost-effective tools that help investigating network performance under more realistic traffic loads, this paper proposes an analytical model for dimension-ordered routing in k-ary n-cube networks when subjected to self-similar traffic. As the service time, blocking probability and waiting time experienced by a message vary from a dimension to another with dimension-ordered routing, the design of this model poses greater challenges. The model validity is demonstrated by performance results obtained from Simulation experiments.