A systematical approach is proposed in this paper for approximating the overflow process with an IPP under a multi-class isochronous traffic environment when an optimal channel assignment algorithm is employed. The three-moment matching method is employed during the approximation process, which can be efficiently implemented by use of matrix-partitioning techniques. Using this approach, the performance of a single-hop parallel-link network under a sequential routing scheme can be analyzed as the superposition of several independent links.