Abstract: In cloud computing and grid computing environment,there is a need of powerful graphical and mathematics tools for modeling and analyzing concurrent tasks scheduling because these tasks have dynamic,distributed,and heterogeneous properties．Petri nets are promising tools for modeling and analyzing events that are characterized as being concurrent,asynchronous,and dynamic．The weighted timed Petri net(WTdPN) model for concurrent tasks was given in this paper．Reachable marking graph is a very important tool to analyze the dynamic properties of Petri nets,but the concurrent relation of transitions in Petri nets can not be represented by reachable marking graph．Especially,it is not convenient to analyze time performance of system modeled by Petri net for the reachable marking graph．This paper presented the concept of concurrent scheduling marking graph(CSMG) and gave an algorithm for constructing concurrent scheduling marking graph of WTdPN．Finally,we analyzed the time performance of parallel download system using CSMG of WTdPN．

Key words: Timed Petri net,Concurrent scheduling marking graph,Concurrent task,Modeling and analysis