The parallel packet switch (PPS) attracts a lot of attention from the communications equipment vendors. However, lack of the detailed analysis and understanding of the issues involved in congestion management has slowed down its recognition and deployment. In this paper, we analyze the conditions of stable working for PPS with buffered input demultiplexors. By comparing PPS with reference switch, we present a definition of stable working for the PPS architecture. The necessary and sufficient condition of stable working for a PPS is proposed and proved. Then we describe a family of dispatch algorithms for the PPS, and give the restriction of algorithms for guaranteeing stable working. Finally the minimum bound of PPS layers and core speedup are analyzed.