Recently Lee et al. developed an approximation algorithm for the performance evaluation of the open queueing networks with blocking. This algorithm, which solves the exponential queueing networks with general configuration, is developed based on the symmetrical decomposition approach and is reported to have many advantages over the previous algorithms. In addition to being very accurate, this algorithm is reported to be quite simple, pretty fast and solves very general configurations. In this study, we show that if a network has a tree-like configuration, the algorithm developed by Lee et al. always converges to the unique solution. To prove the theoretical results pertaining to the algorithm, some properties associated with symmetrical decomposition approach are exploited. The results obtained in this study such as the proofs of convergence of the algorithm as well as uniqueness of the solution would contribute to the theoretical study for the non-tandem configuration of open queueing networks.
