<p><b>Abstract</b>—Performance analysis of concurrent executions in parallel systems has been recognized as a challenging problem. The aim of this research is to study approximate but efficient solution techniques for this problem. We model the structure of a parallel machine and the structure of the jobs executing on such a system. We investigate rich classes of jobs, which can be expressed by series, parallel-and, parallel-or, and probabilistic-fork. We propose an efficient performance prediction method for these classes of jobs running on a parallel environment which is modeled by a standard queueing network model. The proposed prediction method is computationally efficient, it has polynomial complexity in both time and space. The time complexity is <tmath>$O(C^{2}N^{2}K)$</tmath> and the space complexity is <tmath>$O(C^{2}N^{2}K)$</tmath>, where <tmath>$C$</tmath> is the number of job classes in the system, the number of tasks in each job class is <tmath>$O(N)$</tmath>, and <tmath>$K$</tmath> is the number of service centers in the queueing model. The accuracy of the approximate solution is validated via simulation.</p>