There has been growing interest in the performance of transaction systems that have significant response time requirements. These requirements are usually specified as hard or soft deadlines on individual transactions, and a concurrency control algorithm must attempt to meet the deadlines as well as preserve data consistency. This paper proposes a class of simple and efficient abort-oriented concurrency control algorithms based on the notion of compatibility. The schedulability of a transaction system is improved by aborting transactions that introduce excessive blockings. We consider different levels of the aborting relationship among transactions and evaluate the impacts of the aborting relationship when the relationship is built in an on-line or off-line fashion.