Associativity between Weak and Strict Sequencing

Qiao and Bochmann, University of Ottawa

Gregor v. Bochmann

Department of Electrical Engineering and Computer Science

University of OttawaCanada

presentation at the SAM Conference

September 2014, Valence (Spain)

Associativity betweenWeak and Strict Sequencing

Overview

Introduction– Weak and strict sequencing– Examples – Associativity

System design: collaborations and partial orders– Structure of global behaviors: collaborations and roles– Initiating and terminating roles– Definition of weak and strong sequencing

Association rules– Associativity of weak and of strict sequencing– No associativity for mixed sequencing– Consideration of initiating and terminating roles

Conclusions– Possible impact on performance measures

– How to avoid the ambiguity of mixed sequencing

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Gregor v. Bochmann, University of Ottawa

Partial order of events

Lamport [1978] pointed out that in a distributed system, there is in general no total order of events, only a partial order.

– The events taking place at a given component can be totally ordered (assuming sequential execution).

– The reception of a message is after its sending.

– The after-relation is transitive.

For example, we have b after a and c after b; but d and e are unrelated (no order defined - concurrent), also j and i are concurrent. d after a by transitivity.

a bc

j

a

e

f

d

i

k

hg

Gregor v. Bochmann, University of Ottawa

Example of strong and weak sequencing

strongly sequenced(yellow after red)

can be enforce by

weakly sequenced(yellow afterw red)

how to enforce ?(there are often race conditions)

Coordination message

Examples

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Construction project The King’s Concert

Examples (priority for strict sequencing)

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Construction project The King’s Concert

Examples (priority for weak sequencing)

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Construction project The King’s Concert

Overview

Introduction– Weak and strict sequencing– Examples – Associativity

System design: collaborations and partial orders– Structure of global behaviors: collaborations and roles– Initiating and terminating roles– Definition of weak and strong sequencing

Association rules– Associativity of weak and of strict sequencing– No associativity for mixed sequencing– Consideration of initiating and terminating roles

Conclusions– Possible impact on performance measures

– How to avoid the ambiguity of mixed sequencing

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Global behaviors: collaborations and roles

[Castejon, Bochmann, Braek 2013]

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role-1 role-2 role-3

A B

(a)

role-1 role-2 role-3

A

B

(b)

role-1 role-2 role-3

A

(c)

Initiating actions:(no earlier actions)

Terminating actions:(no later actions)

Partial order of actions

Sequencing of collaborations

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Defining weak and strong sequencing by partial orders

Considering onlyinitiating and terminatingroles

Overview

Introduction– Weak and strict sequencing– Examples – Associativity

System design: collaborations and partial orders– Structure of global behaviors: collaborations and roles– Initiating and terminating roles– Definition of weak and strong sequencing

Association rules– Associativity of weak and of strict sequencing– No associativity for mixed sequencing– Consideration of initiating and terminating roles

Conclusions– Possible impact on performance measures

– How to avoid the ambiguity of mixed sequencing

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Associativity

Three collaborations A, B and C executed in sequence A ; B ; C

Case of weak sequence: A ;w B ;w C Associativity: (A ;w B) ;w C = A ;w (B ;w C)

Associativity for strong sequencing: (A ;s B) ;s C = A ;s (B ;s C)

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Partial orders showing associativity

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No associativity for mixed sequencing

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In general: no associativity

Two additional dependencies for (A ;s (B ;w C) ) as compared with ( (A ;s B) ;w C) :

Additional dependency for RC: The roles only involved in C only have to wait for all roles to have completed activity AAdditional dependency for RAC: The roles involved in A and C (but not in B) have to wait for all roles to have completed activity A.

Note: The case of weak and strict order interchanged (i.e. A ;w B ;s C ) can be treated similarly by reversing the direction of time.

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Condition for associativity

We have (A ;s (B ;w C) ) = ( (A ;s B) ;w C) if there is no role in the sets RC and RAC

However, this condition is not necessary.See example:

Proposition: We have (A ;s (B ;w C) ) = ( (A ;s B) ;w C) iff each initiating role of C is also involved in B.

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A

B

C

RC

Overview

Introduction– Weak and strict sequencing– Examples – Associativity

System design: collaborations and partial orders– Structure of global behaviors: collaborations and roles– Initiating and terminating roles– Definition of weak and strong sequencing

Association rules– Associativity of weak and of strict sequencing– No associativity for mixed sequencing– Consideration of initiating and terminating roles

Conclusions– Possible impact on performance measures

– How to avoid the ambiguity of mixed sequencing

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Conclusions

The meaning of a mixture of weak and strong sequencing for distributed workflow applications is in general ambiguous.

This can have an impact on – the possible ordering of actions performed by the

different parties involved in the distributed processes

– the performance properties of the global collaboration (see for instance [Israr 2011 and 2014])

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Conclusions (suite)

The identified ambiguity can be avoided:1.By defining priority for either the weak or the strict sequencing operator.2.By using a notation of parenthesis.

– However, often graphical notations are used.

– In UML Activity Diagrams, the notation of regions may be used to show the order in which the sequencing operations should be applied.

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Questions ??

Comments ??

These slides can be downloaded fromhttp://www.site.uottawa.ca/~bochmann/talks/w-s-sequencing.pdf