In: IEEE Trans. on Robotics and Automation, Vol. 11, No. 5, pages 748-753. 1995.
Abstract: The paper studies a Petri net model of a system composed of two processes sharing a resource. Conflicts may occur over the usage of the shared resource, thus making the system nondeterministic. Therefore, in the context of minimax algebra, it cannot be formulated as a linear system in order to computer its performance measures. However, if the sequence by which the resource is allocated to the two processes is known, the system can be transformed into a decision-free net. For this system with an imposed constraint on the resource allocation frequencies, the paper shows that the optimal allocation sequence is the most regular integer sequence satisfying that constraint. The periodic behavior of this system is also discussed under no constraints on the resource allocation frequencies.
Keywords: Petri nets, allocation sequences, minimax algebra, resource sharing.