Recently a number of studies have indicated that network traffic exhibits noticeable self-similar behaviour, i.e., traffic is bursty over a wide range of time scales. This fractal-like nature of traffic has received significant attention in the networking community as it has a considerable impact on queueing performance. Thus, it is very necessary to examine the performance properties of interconnection networks in the presence of self-similar traffic before practical implementations show their potential faults. However, adopting the simulation approach to evaluate system performance under self-similar workloads may be very costly and time-consuming because the convergence of simulations to a steady state is often very slow as burstiness appears over many time scales. This paper proposes the first analytical performance model for k-ary n-cubes with self-similar traffic. The validity of the model is demonstrated by comparing analytical results to those obtained through simulation experiments of the actual system.