Least-Cost Transition Firing Sequence Estimation in Labeled Petri Nets

This paper develops a recursive algorithm for estimating the least-cost transition firing sequence(s) based on the observation of a sequence of labels produced by transition activity in a given labeled Petri net. Each transition in the given net is associated with a nonnegative cost which could represent its likelihood (e.g., in terms of the amount of workload or power required to execute the transition). Given the structure of a labeled Petri net and the observation of a sequence of labels, we aim at finding the transition firing sequence(s) that has (have) the least total cost and is (are) consistent with both the observed label sequence and the Petri net. We develop a recursive algorithm that finds the least-cost transition firing sequence(s) with complexity that is polynomial in the length of the observed label sequence and is thus amenable to online event estimation and monitoring. An example of two parallel working machines is also provided to illustrate the algorithm