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In this paper, a new method is proposed to evaluate the performance of concurrent systems. A concurrent system consisting of multiple processes that communicate via message passing mechanisms is modeled by a Petri net, which is in turn represented by a set of ordinary differential equations (ODEs) of a restricted type. The equations describe the system state changes, and the solutions, also called state measures, can be used for the performance analysis such as estimating response time, throughput and efficiency. This method can avoid a state explosion problem encountered by the conventional methods based on Continuous-Time Markov Chains. Its application to an IBM business system is given as an example.