A History Equivalence Algorithm for Dynamic Process Migration

TL;DR

This work addresses dynamic migration of processes modeled as WF-nets by adopting history equivalence, a trail-based consistency model, to determine migration mappings. It introduces an algorithm that constructs reachability graphs for the old and new nets, computes for each state the finite set of Trace Transition Sets (TTSs) representing all possible past firings, and then matches old and new states by the intersection of their TTSs, with nonmatching states designated as the change region. The approach accommodates empty transitions and provides an intuitive correctness argument supported by examples, offering an automated, context-aware method for migrating dynamic workflows. The results enable precise, history-informed migration points and can improve disruption minimization when evolving business processes modeled by Petri nets.

Abstract

Dynamic changes in processes necessitate the notion of state equivalence between the old and new workflows. In several cases, the history of the workflow to be migrated provides sufficient context for a meaningful migration. In this paper, we present an algorithm to find the equivalence mapping for states from the old workflow to the new one using a trail-based consistency model called history equivalence. The algorithm finds history equivalent mappings for all migratable states in the reachability graph of the process under migration. It also reports all non-migratable states that fall in the change region for a given pair of old and new Petri Nets. The paper presents the algorithm, its working, and an intuitive proof. The working is demonstrated through a couple of illustrations.

Figures (6)

• Figure 1: A Petri Net that is a WF-net and a Petri Net that isn't
• Figure 5: WF-net with many complex paths in the reachability graph (Figure \ref{['fig:many_cycles_rg']})
• Figure 6: Reachability Graph for WF-net in Figure \ref{['fig:many_cycles_pn']}
• Figure 7: An example taken from A Taxonomy of Consistency Models in Dynamic Migration of Business Processesa_taxonomy
• Figure 8: Reachability for the old process from Figure \ref{['fig:empty_transitions']}