The article proposes the approach for predicting the performance of big data processing center services. To simulate the process of parallel computing, the fork-join queuing system (QS) with a truncated Pareto distribution of service time and three variants of distributions for the incoming flow is used. The number of devices in each of the fork-join subsystems of the QS can be more than one. The performance scores are the average system response time and its tail delay (99th percentile of the response time distribution). The approach is based on a combination of simulation modeling and neural networks, as one of the methods of machine learning. For at least 93% of the data used to test the proposed method in the course of a numerical experiment the approximation error of both studied characteristics does not exceed 5%, while the maximum approximation error is not more than 10%.