Cluster-based systems have emerged as a promising technology for providing cost-effectiveness in high-performance computing and communication systems. Performance studies on communication networks in cluster-based systems have been reported based on the simplified assumptions that the traffic follows the non-bursty Poisson process and the message destinations are uniformly distributed over all network nodes. However, the uniform distribution of message destinations is not always realistic in practice. Moreover, the communication locality, a typical example of the non-uniform destination distribution, has been shown to be an important phenomenon in the communication networks of cluster systems. Many recent measurement studies have revealed that the traffic generated by many real-world applications exhibits a high degree of burstiness. In order to have a comprehensive understanding of the system performance, this paper proposes a new analytical model for communication networks in multi-cluster systems under the bursty message arrivals with communication locality. The model is validated through extensive simulation experiments.