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- 1. Temporal Dependency for Dynamic Verification of Temporal Constraints in Workflow Systems Polo Regionale di Como of the Politecnico di Milano Workgroup and Workflow Management Systems Jalal Uddin Ahammad jalal.ahammad@mail.polimi.it - presentation given on 19/01/2009 -
- 2. Objectives at a glance Investigation of mutual dependency between temporal constraints Its effects on the verification of temporal constraints Development of some new methods for more effective and efficient temporal verification
- 3. Timed Workflow Representation (1/6) Notations Consideration of an arbitrary execution path in a timed acyclic workflow graph For ith activity ai , the follwing notations are taken into acoount minimum duration d(ai) maximum duration D(ai) run-time start time S(ai) run-time end time E(ai) run-time real completion duration Rcd(ai)
- 4. Timed Workflow Representation (2/6) For a set of activities from ai to aj (j≥i) Maximum duration D(ai, aj) Minimum duration d(ai, aj) Run-time real completion durations Rcd(ai, aj) Upper bound constraint upb(ai, aj) Lower bound constraint lob(ai, aj) Deadline constraint at build-time rdl(ai) Deadline constraint at run-time adl(ai)
- 5. Timed Workflow Representation (3/6) Some expressions rdl(ai)=adl(ai)-S(a1) Ex: rdl(ai)=(12-5) sec.=7 sec. Rcd(ai, aj)=E(aj)-S(ai) . Ex. S(ai)=3 sec E(ai)=5 sec S(aj)=6 sec E(aj)=8 sec Rcd(ai, aj)=(8-3) sec=5 sec. D(ai, aj) = Σ D(a k ) where k>=i and k<= j d(ai, aj) = Σ d(a k ) where k>=i and k<= j
- 6. Timed Workflow Representation (4/6) Temporal Constraint consistentcy at build-time An upper bound constraint is consistent at the build-time if and only if D(ai, aj) ≤ upb(ai, aj) Lower bound constraint is consistent at build-time if and only if d(ai, aj) ≥ lob(ai, aj) . Deadline constraint at the build-time stage for ai is consistent if and only if D(a1, ai) ≤ rdl(ai) .
- 7. Timed Workflow Representation (5/6) Temporal Constraint consistentcy at run-time An upper bound constraint between ai and aj is consistent at checkpoint ap between ai and aj (j≥p, p≥i) at the execution stage if and only if Rcd(ai, ap) +D(ap+1, aj) ≤ upb(ai, aj) Example: Inconsitency at checkpoint at execution stage Rcd(ai, ap) +D(ap+1, aj) >upb(ai, aj) upb(ai, aj) Rcd(ai, ap) D(ap+1, aj) time
- 8. Timed Workflow Representation (6/6) Temporal Constraint consistentcy at run-time The corresponding consistency condition for a lower bound constraint is if and only if Rcd(ai, ap) + d(ap+1, aj) ≥ lob(ai, aj) . Deadline constraint at ai is consistent at the instantiation stage if and only if D(a1, ai) ≤ adl(ai)-S(a1) consistentcy at checkpoint ap by ai (p≤i) at the execution stage if and only if Rcd(a1, ap)+D(ap+1, ai)≤ adl(ai)-S(a1)
- 9. Upper bound constraints without mutual nesting relationships are relatively independent. Three kinds of basic nesting relationships , based on Allen’s interval logic, between upper bound constraints A, B, C, and a basic nesting extension. Scenario 1 The temporal dependency between A and B is consistent in scenario 1 if and only if D(ak, ai-1)+upb(A)+D(aj+1, al)≤ upb(B) Temporal Dependency Between Temporal Constraints(1/5)
- 10. Temporal Dependency Between Temporal Constraints(2/5) scenario 2 The temporal dependency between A, B and C is consistent in scenario 2 if and only if D(am, ai-1)+upb(A)+D(aj+1, ak-1)+upb(B)+ D(al+1, an)≤ upb(C)
- 11. Temporal Dependency Between Temporal Constraints(3/5) scenario 3 The temporal dependency between A, B and C is consistent in scenario 3 if and only if D(am, ai-1)+upb(A)+upb(B)-D(ak, aj)+D(al+1, an)≤ upb(C)
- 12. Temporal Dependency Between Temporal Constraints(4/5) For scenario 4, an extension of scenario 1, we can prove by the following theorem Theorem 1. If the dependency between any two adjacent upper bound constraints is consistent, the dependency between any two non-adjacent upper bound constraints must be consistent. The temporal dependency between 2 non-adjucent upper bound constraints A1 and A3 is consistent in scenario 4 if and only if D(ai3, ail-1)+upb(A1)+D(aj1+1, aj3)≤ upb(A3)
- 13. Temporal Dependency Between Temporal Constraints(5/5) Mutual dependency of deadline constraints are also are important for mutual nesting relationships . The dependency between two adjacent deadline constraints respectively at ai and aj (j>i) is consistent if and only if D(ai+1, aj)≤rdl(aj)-rdl(ai). Theorem 2. If the dependency between any two adjacent deadline constraints is consistent, the dependency between any two non-adjacent deadline constraints must be consistent.
- 14. Build-Time Temporal Verification(1/2) Temporal constraints’ dependecy at build-time has to be verified for the effectiveness of the temporal verification. For upper bound constraints, on one hand , we conduct verification computations according to definition 1. An upper bound constraint is consistent at the build-time stage if and only if D(ai, aj) ≤ upb(ai, aj) On the other hand , we verify the temporal dependency according to the conditions applied for upper bound constraints with mutual nesting relationships described in previous section.
- 15. Build-Time Temporal Verification(2/2) For deadline constraints, on one hand , we verify them based on the following definition. Deadline constraint at the build-time stage for ai is consistent if and only if D(a1, ai) ≤ rdl(ai) . On the other hand , based on the following definition and theorem 2 The dependency between two adjacent deadline constraints respectively at ai and aj (j>i) is consistent if and only if D(ai+1, aj)≤rdl(aj)-rdl(ai). Theorem 2. If the dependency between any two adjacent deadline constraints is consistent, the dependency between any two non-adjacent deadline constraints must be consistent.
- 16. Run-Time Temporal Verification(1/4) At the instantiation stage no specific execution times. The temporal constraint and dependency verification is the same as that of the build-time.
- 17. Run-Time Temporal Verification(2/4) At the execution stage For those upper bound constraints without mutual nesting relationships, we conduct the temporal verification according to definition 2. An upper bound constraint between ai and aj is consistent at checkpoint ap between ai and aj (j≥p, p≥i) at the execution stage if and only if Rcd(ai, ap) +D(ap+1, aj) ≤ upb(ai, aj) For those nested one another, theorem 3 can be applied.
- 18. Run-Time Temporal Verification(3/4) Theorem 3. At checkpoint ap between ai and aj , if Rcd(ak, ai-1) ≤ D(ak, ai-1) , then, if A is consistent, B must be consistent. Theorem 3 is more efficient than that only based on definition 2 For definition 2, we still need to conduct significant extra computations.
- 19. Run-Time Temporal Verification(4/4) For deadline constraints verification at the execution stage Theorem 4. At the execution stage, at checkpoint ap , if a deadline constraint D after ap is consistent, any deadline constraint after D must be consistent. According to theorem 4, at a checkpoint, we need not verify any deadline constraints after a consistent one. Obviously, this will improve the verification efficiency.
- 20. Conclusions The dependency between temporal constraints and its effects on the temporal verification are investigated. Some new verification methods are presented which enable us to conduct more effective and efficient temporal verification. All these discussions, relevant concepts, principles and new verification methods strengthen the current workflow time management.
- 21. Comments Both Build-time and Run-time temporal verifications are shown. Checkpoint selection strategy is not mentioned. No proof of theorem is provided.
- 22. References 1. Bussler, C.: Workflow Instance Scheduling with Project Management Tools. In Proc. of the9th Workshop on Database and Expert Systems Applications (DEXA’98). Vienna, Austria (1998) 753-758 2. Chinn, S., Madey, G.: Temporal Representation and Reasoning for Workflow in EngineeringDesign Change Review. IEEE Transactions on Engineering Management 47(4) (2000)485-492 3. Eder, J., Panagos, E., Rabinovich, M.: Time Constraints in Workflow Systems. In Proc. Of the 11th International Conference on Advanced Information Systems Engineering(CAiSE’99). Lecture Notes in Computer Science, Vol. 1626. Springer-Verlag, Germany (1999) 286-300 4. Li, H., Yang, Y., Chen, T.Y.: Resource Constraints Analysis of Workflow Specifications.The Journal of Systems and Software, Elsevier, in press 5. Marjanovic, O.: Dynamic Verification of Temporal Constraints in Production Workflows. In Proc. of the Australian Database Conference. Canberra, Australia (2000) 74-81
- 23. Thank You All