Multiple processors are employed to improve the performance of database systems and the parallelism can be exploited at three levels in query processing: intra-operation, inter-operation, and inter-query parallelism. Intra-operation and inter-operation parallelism are also called intra-query parallelism which has been studied extensively recently. In contrast inter-query parallelism has received little attention particularly for multiple dependent queries. In this paper, we develop a decompression algorithm, CPS, for coping with multiple dependent queries which are represented by a directed graph, and the algorithm makes use of the activity analysis of critical path analysis, and the resource scheduling and levelling of project management. A simulation study has been conducted and the results show that the proposed algorithm outperforms other existing methods and is able to provide a global optimal solution when the number of processors available is sufficient.