Parallel and distributed computing have become widespread as one of the main ways to improve the performance of computing environments when processing big data. The issue of assessing the main performance indicators of such systems remains relevant to the present time due to the complexity of such analysis. A fork-join queuing system is well suited for modeling parallel data processing. The article explores the possibility of estimating the average response time of the system using an analytical expression for the upper bound of the maximum order statistics. Two options are described, depending on the amount of knowledge available about the operation of a high-performance environment. The results of the numerical experiment confirm the efficiency of the approach for a fairly wide range of parameters, one of the main advantages of which is the ease of use.