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Parallel processing is an important pattern in cluster systems. To analyze the performance of parallel processing systems, we leveraged the fork-join queueing network (FJQN) models. However, there are no easy solutions to these models, especially for the multi-class closed ones. In this paper, a novel and efficient method named horizontal decomposition has been proposed. The main idea of our method is to approximate a non-product-form FJQN with some closed and open product-form networks. So the computational complexity can be dramatically reduced compared with the traditional hierarchical decomposition approach. And the algorithms for solving single-class and multi-class closed FJQNs have been developed respectively based on the horizontal decomposition. With these algorithms, the response time and throughput of each service center in a FJQN can be approximately calculated. The evaluation results show that 90 percentile of relative errors of most service centers are less than 15% except for the shared ones. The evaluation results also showed that the number of iterations in the algorithm for the multi-class FJQNs almost grows linearly with the population of networks.