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Temporal Dependency for Dynamic Verification of Temporal Constraints in Workflow Systems Polo Regionale di Como of the Pol...
Objectives at a glance <ul><li>Investigation of mutual dependency between temporal constraints  </li></ul><ul><li>Its effe...
Timed Workflow Representation (1/6) <ul><li>Notations </li></ul><ul><li>Consideration of  an arbitrary execution path in a...
Timed Workflow Representation (2/6) <ul><li>For a set of activities from ai to aj  (j≥i)  </li></ul><ul><ul><ul><li>Maximu...
Timed Workflow Representation (3/6) <ul><li>Some expressions </li></ul><ul><ul><li>rdl(ai)=adl(ai)-S(a1) </li></ul></ul><u...
Timed Workflow Representation (4/6) <ul><li>Temporal Constraint consistentcy at build-time </li></ul><ul><li>An upper boun...
Timed Workflow Representation (5/6) <ul><li>Temporal Constraint consistentcy at run-time </li></ul><ul><li>An upper bound ...
Timed Workflow Representation (6/6) <ul><li>Temporal Constraint consistentcy at run-time </li></ul><ul><li>The correspondi...
<ul><li>Upper bound constraints without mutual nesting relationships are relatively independent. </li></ul><ul><li>Three k...
Temporal Dependency Between Temporal Constraints(2/5) <ul><li>scenario 2   </li></ul><ul><li>The temporal dependency betwe...
Temporal Dependency Between Temporal Constraints(3/5) <ul><li>scenario 3 </li></ul><ul><li>The temporal dependency between...
Temporal Dependency Between Temporal Constraints(4/5) <ul><li>For scenario 4, an extension of scenario 1, we can prove by ...
Temporal Dependency Between Temporal Constraints(5/5) <ul><li>Mutual dependency of deadline constraints are also are impor...
Build-Time Temporal Verification(1/2) <ul><li>Temporal constraints’ dependecy at build-time has to be verified for the eff...
Build-Time Temporal Verification(2/2) <ul><li>For deadline constraints,  on one hand , we verify them based on the followi...
Run-Time Temporal Verification(1/4) <ul><li>At the instantiation stage </li></ul><ul><ul><li>no specific execution times. ...
Run-Time Temporal Verification(2/4) <ul><li>At the execution stage </li></ul><ul><ul><li>For those upper bound constraints...
Run-Time Temporal Verification(3/4) <ul><ul><li>Theorem 3.  At checkpoint  ap  between  ai  and  aj , if  Rcd(ak, ai-1)  ≤...
Run-Time Temporal Verification(4/4) <ul><li>For deadline constraints verification at the execution stage </li></ul><ul><ul...
Conclusions <ul><li>The dependency between temporal constraints and its effects on the temporal verification are investiga...
Comments <ul><li>Both Build-time and Run-time temporal verifications are shown.  </li></ul><ul><li>Checkpoint selection st...
References <ul><li>1. Bussler, C.: Workflow Instance Scheduling with Project Management Tools. In Proc. of the9th Workshop...
<ul><li>Thank You All </li></ul>
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  1. 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. 2. Objectives at a glance <ul><li>Investigation of mutual dependency between temporal constraints </li></ul><ul><li>Its effects on the verification of temporal constraints </li></ul><ul><li>Development of some new methods for more effective and efficient temporal verification </li></ul>
  3. 3. Timed Workflow Representation (1/6) <ul><li>Notations </li></ul><ul><li>Consideration of an arbitrary execution path in a timed acyclic workflow graph </li></ul><ul><li>For ith activity ai , the follwing notations are taken into acoount </li></ul><ul><ul><li>minimum duration d(ai) </li></ul></ul><ul><ul><li>maximum duration D(ai) </li></ul></ul><ul><ul><li>run-time start time S(ai) </li></ul></ul><ul><ul><li>run-time end time E(ai) </li></ul></ul><ul><ul><li>run-time real completion duration Rcd(ai) </li></ul></ul>
  4. 4. Timed Workflow Representation (2/6) <ul><li>For a set of activities from ai to aj (j≥i) </li></ul><ul><ul><ul><li>Maximum duration D(ai, aj) </li></ul></ul></ul><ul><ul><ul><li>Minimum duration d(ai, aj) </li></ul></ul></ul><ul><ul><ul><li>Run-time real completion durations Rcd(ai, aj) </li></ul></ul></ul><ul><ul><ul><li>Upper bound constraint upb(ai, aj) </li></ul></ul></ul><ul><ul><ul><li>Lower bound constraint lob(ai, aj) </li></ul></ul></ul><ul><ul><ul><li>Deadline constraint at build-time rdl(ai) </li></ul></ul></ul><ul><ul><ul><li>Deadline constraint at run-time adl(ai) </li></ul></ul></ul>
  5. 5. Timed Workflow Representation (3/6) <ul><li>Some expressions </li></ul><ul><ul><li>rdl(ai)=adl(ai)-S(a1) </li></ul></ul><ul><ul><ul><li>Ex: rdl(ai)=(12-5) sec.=7 sec. </li></ul></ul></ul><ul><ul><li>Rcd(ai, aj)=E(aj)-S(ai) . </li></ul></ul><ul><ul><ul><li>Ex. S(ai)=3 sec E(ai)=5 sec </li></ul></ul></ul><ul><ul><ul><li> S(aj)=6 sec E(aj)=8 sec </li></ul></ul></ul><ul><ul><ul><li> Rcd(ai, aj)=(8-3) sec=5 sec. </li></ul></ul></ul><ul><ul><li>D(ai, aj) = Σ D(a k ) where k>=i and k<= j </li></ul></ul><ul><ul><li>d(ai, aj) = Σ d(a k ) where k>=i and k<= j </li></ul></ul>
  6. 6. Timed Workflow Representation (4/6) <ul><li>Temporal Constraint consistentcy at build-time </li></ul><ul><li>An upper bound constraint is consistent at the build-time </li></ul><ul><ul><ul><li>if and only if D(ai, aj) ≤ upb(ai, aj) </li></ul></ul></ul><ul><li>Lower bound constraint is consistent at build-time </li></ul><ul><ul><ul><li>if and only if d(ai, aj) ≥ lob(ai, aj) . </li></ul></ul></ul><ul><li>Deadline constraint at the build-time stage for ai is consistent </li></ul><ul><li>if and only if D(a1, ai) ≤ rdl(ai) . </li></ul>
  7. 7. Timed Workflow Representation (5/6) <ul><li>Temporal Constraint consistentcy at run-time </li></ul><ul><li>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) </li></ul><ul><li>Example: Inconsitency at checkpoint at execution stage </li></ul>Rcd(ai, ap) +D(ap+1, aj) >upb(ai, aj) upb(ai, aj) Rcd(ai, ap) D(ap+1, aj) time
  8. 8. Timed Workflow Representation (6/6) <ul><li>Temporal Constraint consistentcy at run-time </li></ul><ul><li>The corresponding consistency condition for a lower bound constraint is </li></ul><ul><ul><ul><li>if and only if Rcd(ai, ap) + d(ap+1, aj) ≥ lob(ai, aj) . </li></ul></ul></ul><ul><li>Deadline constraint at ai is consistent at the instantiation stage </li></ul><ul><li>if and only if D(a1, ai) ≤ adl(ai)-S(a1) </li></ul><ul><li>consistentcy at checkpoint ap by ai (p≤i) at the execution stage </li></ul><ul><li>if and only if Rcd(a1, ap)+D(ap+1, ai)≤ adl(ai)-S(a1) </li></ul>
  9. 9. <ul><li>Upper bound constraints without mutual nesting relationships are relatively independent. </li></ul><ul><li>Three kinds of basic nesting relationships , based on Allen’s interval logic, between upper bound constraints A, B, C, and a basic nesting extension. </li></ul><ul><li>Scenario 1 </li></ul><ul><li>The temporal dependency between A and B is consistent in scenario 1 </li></ul><ul><li>if and only if D(ak, ai-1)+upb(A)+D(aj+1, al)≤ upb(B) </li></ul>Temporal Dependency Between Temporal Constraints(1/5)
  10. 10. Temporal Dependency Between Temporal Constraints(2/5) <ul><li>scenario 2 </li></ul><ul><li>The temporal dependency between A, B and C is consistent in scenario 2 </li></ul><ul><li>if and only if </li></ul><ul><li>D(am, ai-1)+upb(A)+D(aj+1, ak-1)+upb(B)+ D(al+1, an)≤ upb(C) </li></ul>
  11. 11. Temporal Dependency Between Temporal Constraints(3/5) <ul><li>scenario 3 </li></ul><ul><li>The temporal dependency between A, B and C is consistent in scenario 3 </li></ul><ul><li>if and only if D(am, ai-1)+upb(A)+upb(B)-D(ak, aj)+D(al+1, an)≤ upb(C) </li></ul>
  12. 12. Temporal Dependency Between Temporal Constraints(4/5) <ul><li>For scenario 4, an extension of scenario 1, we can prove by the following theorem </li></ul><ul><li>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. </li></ul><ul><ul><li>The temporal dependency between 2 non-adjucent upper bound constraints A1 and A3 is consistent in scenario 4 </li></ul></ul><ul><ul><li>if and only if D(ai3, ail-1)+upb(A1)+D(aj1+1, aj3)≤ upb(A3) </li></ul></ul>
  13. 13. Temporal Dependency Between Temporal Constraints(5/5) <ul><li>Mutual dependency of deadline constraints are also are important for mutual nesting relationships . </li></ul><ul><li>The dependency between two adjacent deadline constraints respectively at ai and aj (j>i) is consistent </li></ul><ul><ul><li>if and only if D(ai+1, aj)≤rdl(aj)-rdl(ai). </li></ul></ul><ul><li>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. </li></ul>
  14. 14. Build-Time Temporal Verification(1/2) <ul><li>Temporal constraints’ dependecy at build-time has to be verified for the effectiveness of the temporal verification. </li></ul><ul><li>For upper bound constraints, on one hand , we conduct verification computations according to definition 1. </li></ul><ul><ul><li>An upper bound constraint is consistent at the build-time stage if and only if D(ai, aj) ≤ upb(ai, aj) </li></ul></ul><ul><li>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. </li></ul>
  15. 15. Build-Time Temporal Verification(2/2) <ul><li>For deadline constraints, on one hand , we verify them based on the following definition. </li></ul><ul><ul><li>Deadline constraint at the build-time stage for ai is consistent </li></ul></ul><ul><li>if and only if D(a1, ai) ≤ rdl(ai) . </li></ul><ul><li>On the other hand , based on the following definition and theorem 2 </li></ul><ul><ul><li>The dependency between two adjacent deadline constraints respectively at ai and aj (j>i) is consistent </li></ul></ul><ul><ul><li>if and only if D(ai+1, aj)≤rdl(aj)-rdl(ai). </li></ul></ul><ul><ul><li>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. </li></ul></ul>
  16. 16. Run-Time Temporal Verification(1/4) <ul><li>At the instantiation stage </li></ul><ul><ul><li>no specific execution times. </li></ul></ul><ul><ul><li>The temporal constraint and dependency verification is the same as that of the build-time. </li></ul></ul>
  17. 17. Run-Time Temporal Verification(2/4) <ul><li>At the execution stage </li></ul><ul><ul><li>For those upper bound constraints without mutual nesting relationships, we conduct the temporal verification according to definition 2. </li></ul></ul><ul><ul><ul><li>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 </li></ul></ul></ul><ul><ul><ul><li>if and only if Rcd(ai, ap) +D(ap+1, aj) ≤ upb(ai, aj) </li></ul></ul></ul><ul><ul><li>For those nested one another, theorem 3 can be applied. </li></ul></ul>
  18. 18. Run-Time Temporal Verification(3/4) <ul><ul><li>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. </li></ul></ul><ul><ul><li>Theorem 3 is more efficient than that only based on definition 2 </li></ul></ul><ul><ul><ul><li>For definition 2, we still need to conduct significant extra computations. </li></ul></ul></ul>
  19. 19. Run-Time Temporal Verification(4/4) <ul><li>For deadline constraints verification at the execution stage </li></ul><ul><ul><li>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. </li></ul></ul><ul><ul><li>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. </li></ul></ul>
  20. 20. Conclusions <ul><li>The dependency between temporal constraints and its effects on the temporal verification are investigated. </li></ul><ul><li>Some new verification methods are presented which enable us to conduct more effective and efficient temporal verification. </li></ul><ul><li>All these discussions, relevant concepts, principles and new verification methods strengthen the current workflow time management. </li></ul>
  21. 21. Comments <ul><li>Both Build-time and Run-time temporal verifications are shown. </li></ul><ul><li>Checkpoint selection strategy is not mentioned. </li></ul><ul><li>No proof of theorem is provided. </li></ul>
  22. 22. References <ul><li>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 </li></ul><ul><li>(1998) 753-758 </li></ul><ul><li>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 </li></ul><ul><li>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 </li></ul><ul><li>4. Li, H., Yang, Y., Chen, T.Y.: Resource Constraints Analysis of Workflow Specifications.The Journal of Systems and Software, Elsevier, in press </li></ul><ul><li>5. Marjanovic, O.: Dynamic Verification of Temporal Constraints in Production Workflows. In Proc. of the Australian Database Conference. Canberra, Australia (2000) 74-81 </li></ul>
  23. 23. <ul><li>Thank You All </li></ul>

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