Mean Value Analysis (MVA) has long been a standard approach for performance analysis of computer systems. While the exact load-dependent MVA algorithm is an efficient technique for computer system performance modeling, it fails to address multi-core computer systems with Dynamic Frequency Scaling (DFS). In addition, the load-dependent MVA algorithm suffers from numerical difficulties under heavy load conditions. The goal of our paper is to find an efficient and robust method which is easy to use in practice and is also accurate for performance prediction for multi-core platforms. The proposed method, called Approximate Performance Evaluation for Multi-core computers (APEM), uses a flow-equivalent performance model designed specifically to address multi-core computer systems and identify the influence on the CPU demand of the effect of DFS. We adopt an approximation technique to estimate resource demands to parametrize MVA algorithms. To validate the application of our method, we investigate three case studies with extended TPC-W benchmark kits, showing that our method achieves better accuracy compared with other commonly used MVA algorithms. We compare the three different performance models, and we also extend our approach to multi-class models.