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Second, when using iteration rather than explicitly backward edges, the conditional rollback may be considered as a continuation of the workflow instance execution. We believe that the use of iteration provides a much cleaner graphical notation to model cyclic activity workflows. To reduce the complexity and facilitate the management of conditional rollbacks, the only restriction we place on the conditional rollback is the following: A call to rollback to an activity node ndk can only be accepted if it comes from subactivity nodes or sibling activity nodes of ndk.

We restrict our discussion in the context of how to handle unexpected delays. A deeper study on such context can be found in Ruiz, Liu, and Pu (2002). Basic Notions Activity restructuring operators are used to reorganize the hierarchical structure of activity patterns with their activity dependencies remaining valid. Two types of activity restructuring operators are proposed by Liu and Pu (1998a): Activity-Split and Activity-Join. Activity-Split operators allow releasing committed resources that were updated earlier, enabling adaptive recovery and added concurrency (Liu & Pu, 1998b).

2) ∀ ndi, ndj ∈ N, if ndi* → ndj then ndj* → ndi does not hold. Copyright © 2005, Idea Group Inc. Copying or distributing in print or electronic forms without written permission of Idea Group Inc. is prohibited. TEAM LinG 20 Liu, Pu and Ruiz To illustrate the definition, let us recast the telephone service provisioning workflow procedure depicted in Figure 4(A) diagram and described in Figure 5 in terms of the above definition as follows: • • N = {(Begin, NeedService, not fired, simple), (A1, NeedService, not fired, simple), (A2, commit(A1), not fired, simple), (OS1, commit(A2), not fired, OR-Split), (A3, creditStatus = true, not fired, simple), (OS2, commit(A3), not fired, OR-Split), (A11, circuitAllocated = false, not fired, simple), (OJ2, circuitAllocated = true ∨ commit(A11), not fired, OR-Join), (B, terminate(OJ2), not fired, compound ), (OJ1, creditStatus = false ∨ commit(B), not fired, OR-Join), (End, terminate(OJ1), not fired, simple)} E = {Begin → A1, A1 → A2, A2 → OS1, OS1 → A3, OS1 → OJ1, A3 → OS2, OS2 → OJ2, OS2 → A11, A11 → OJ2, OJ2 → B, B → OJ1, OJ1 → End} Note that NeedService is a Boolean variable from the ActivityFlow runtime environment.

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