Abstract
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(nċm), 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.
Highlights
In recent years, liveness-enforcing supervisory control has been an active area of research for resource allocation systems characterized by processes with highly ordered, linear workflows
A process instance is allowed to advance to its stage only when it has been granted the complete set of required resources and only will it release the currently held resources that are not required for the following stage
In [15, 16], we model the A/DRAS using a subclass of Petri nets known as Generalized Augmented Marked Graphs (G-AMG)
Summary
Liveness-enforcing supervisory control has been an active area of research for resource allocation systems characterized by processes with highly ordered, linear workflows. We note that in [11], Xie and Jeng study resource allocation in systems with synchronizations by analyzing a class of ordinary Petri nets called extended resource control nets (ERCN) They develop structural characterizations for the ERCN quasi-liveness and liveness that are based on the notion of empty siphons. On the other hand, places more emphasis on the associated design and control problems, seeking first to find resource levels that guarantee quasi-liveness and to find resource allocation sequences that enable synchronization transitions.
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