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13 Apr 2023 Workgroup and Workflow Management Systems 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 [email protected]
- presentation given on 19/01/2009 -
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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
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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)
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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)
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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) = ΣD(ak) where k>=i and k<= j
• d(ai, aj) = Σd(ak) where k>=i and k<= j
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Timed Workflow Representation (4/6)
Temporal Constraint consistentcy at build-time• An upper bound constraint is consistent at the
build-timeif and only if D(ai, aj) ≤ upb(ai, aj)
• Lower bound constraint is consistent at build-timeif and only if d(ai, aj) ≥ lob(ai, aj).
• Deadline constraint at the build-time stage forai is consistent
if and only if D(a1, ai) ≤ rdl(ai).
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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
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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)
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• 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)
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Temporal Dependency Between Temporal Constraints(2/5)
• scenario 2
• The temporal dependency between A, B and C is consistent in scenario 2if and only ifD(am, ai-1)+upb(A)+D(aj+1, ak-1)+upb(B)+ D(al+1, an)≤ upb(C)
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Temporal Dependency Between Temporal Constraints(3/5)
• scenario 3
• The temporal dependency between A, B and C is consistent in scenario 3if and only if D(am, ai-1)+upb(A)+upb(B)-D(ak, aj)+D(al+1, an)≤ upb(C)
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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 4if and only if D(ai3, ail-1)+upb(A1)+D(aj1+1, aj3)≤ upb(A3)
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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.
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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.
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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 forai 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.
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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.
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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 stageif and only if Rcd(ai, ap) +D(ap+1, aj) ≤ upb(ai, aj)
• For those nested one another, theorem 3 can be applied.
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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.
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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 afterap 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.
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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.
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Comments
• Both Build-time and Run-time temporal verifications are shown.
• Checkpoint selection strategy is not mentioned.
• No proof of theorem is provided.
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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
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Thank You All