Modeling and Analysis for Workflow Constrained by Resources and Nondetermined Time: An Approach Based on Petri Nets

Time and resource management and verification are two important aspects of workflow management systems. In this paper, we present a modeling and analysis approach for a kind of workflow constrained by resources and nondetermined time based on Petri nets. Different from previous modeling approaches, there are two kinds of places in our model to represent the activities and resources of a workflow, respectively. For each activity place, its input and output transitions represent the start and termination of the activity, respectively, and there are two timing functions in it to define the minimum and maximum duration times of the corresponding activity. Using the constructed Petri net model, the earliest and latest times to start each activity can be calculated. With the reachability graph of the Petri net model, the timing factors influencing the implementation of the workflow can be calculated and verified. In this paper, the sufficient conditions for the existence of the best implementation case of a workflow are proved, and the method for obtaining such an implementation case is presented. The obtained results will benefit the evaluation and verification of the implementation of a workflow constrained by resources and nondetermined time.