Process Completing Sequences for Resource Allocation Systems with Synchronization - Song Foh Chew; Shengyong Wang; Mark A. Lawley (Journal of Control Science and Engineering)
This paper considers the problem of establishing live resource allocation in workflows with synchronization stages. Establishing live resource allocation in this class of systems is challenging since deciding whether a given level of resource capacities is sufficient to complete a single process is NP-complete. In this paper, we develop two necessary conditions and one sufficient condition that provide quickly computable tests for the existence of process completing sequences. The necessary conditions are based on the sequence of completions of 𝑛 subprocesses that merge together at a synchronization. Although the worst case complexity is O(2𝑛), we expect the number of subprocesses combined at any synchronization will be sufficiently small so that total computation time remains manageable. The sufficient condition uses a reduction scheme that computes a sufficient capacity level of each resource type to complete and merge all 𝑛 subprocesses. The worst case complexity is O(𝑛⋅𝑚), where 𝑚 is the number of synchronizations. Finally, the paper develops capacity bounds and polynomial methods for generating feasible resource allocation sequences for merging systems with single unit allocation. This method is based on single step look-ahead for deadly marked siphons and is O(2𝑛). Throughout the paper, we use a class of Petri nets called Generalized Augmented Marked Graphs to represent our resource allocation systems.