Direct solution techniques are expensive for the state transition lattice of a class of non-product form queuing modes. In this thesis, Autorouting with A* algorithm is adapted to decompose it as solvable subsets which can be solved sequentially and independently. Autorouting with A* algorithm is heuristics in problem solving. It also is one of a class of global optimization problems that are difficult to solve. Some queuing modes of type A will be decomposed in this thesis through Autorouting with A* algorithm.