Amount of data stored in enterprises are increasing rapidly. Volume of data stored in database is approaching to terabyte size. Response time is directly proportional to the amount of data in databases. Requirement of fast response time under these circumstances have motivated the research of parallel database systems (PDS) during last decade. Despite distribution of data in PDS to various processing elements (PE), concurrency control algorithms uses centralized scheduling approach. This approach has inherent weakness, under heavy load conditions, such as - big lock table, more number of messages in the system, central overloaded scheduler. In this paper we distribute the scheduling responsibilities to the nodes where data is actually located. We also propose a new serializability criterion, parallel database quasi-serializability, to meet these requirements