Snap-stabilizing Committee Coordination

Snap-stabilizing Committee Coordination

Borzoo BonakdarpourStephane DevismesFranck Petit

IEEE International Parallel and Distributed Processing Symposium (IPDPS’11)

May17, 2011

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Motivation

• Generation distributed code from high-level component-

based models.

May 17, 2011 IEEE International Parallel and Distributed Processing Symposium (IPDPS'11)

Behavioral atomic

components

Synchronizing with a set of rendezvous interactions

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Simple Rendezvous


s

Sender

r1

Receiver1

Interactions: sr1r2r3

Priorities:

s r1

r2

Receiver2

r2

r3

Receiver3

r3

r2Most process algebras have similar syntax and semantics

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Motivation


How do we generate distributed code by starting from such high-level models?

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Motivation


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Conflict resolution(exclusion)

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Committee Coordination Problem

Professors in a certain university have organized themselves into committees. Each committee has an unchanging membership roster of one or more professors. From time to time a professor may decide to attend a committee meeting; it starts waiting and remains waiting until a meeting of a committee of which it is a member is started. All meetings terminate in finite time. The restrictions on convening a meeting are as follows:

1. (synchronization) meeting of a committee may be started only if all members of that committee are waiting, and

2. (exclusion) no two committees may convene simultaneously, if they have a common member.

The problem is to ensure that if all members of a committee are waiting, then a meeting involving some member of this committee is convened


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Distributed Committee Coordination


C1 C3C2

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Committee Coordination Problem

1988• Chandy and Misra propose a solution by reduction to dining/drinking

philosophers problem

1989• Bagrodia introduces a solution based on message counts to ensure

synchronization and reduction to dining/drinking philosophers problems to solve exclusion

• Bagrodia presents simulation results to analyze the tradeoff between decentralization and communication overhead

1990• The line of research dies!


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Implementing Committee Coordination


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Why another Committee Coordination Algorithm?


[1] B. Bonakdarpour, M. Bozga, M. Jaber, J. Quilbeuf, J. Sifakis, From high-level component-based models to distributed implementations, EMSOFT’10

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Current Open Questions

• Number of components that can run simultaneously• Maximal/maximum concurrency

• Each component/interaction eventually gets an execution chance• Fairness

• Starting from an arbitrary configuration the systems reaches a legitimate configuration• Self-stabilization

• The amount of time that some component must wait for execution• Waiting time

• The number of rounds a component must wait• Service time

• The effect of time spent in an interaction• Utilization


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Maximal Concurrency


C1 C3C2

The meetings lasts

indefinitely

An idle meeting

eventually convenes

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Professor Fairness

Every professor wants to participate in a committee meeting infinitely often.


Every professor eventually participates in a committee meeting that it is a member of.

Assumption

Fairness

Otherwise, distributed committee

coordination is impossible [2]

[2] Y.-K. Tsay and R. Bagrodia. Some impossibility results in interprocesssynchronization. Distributed Computing, 6(4):221–231, 1993.

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Impossibility of Fairness and Maximal Concurrency


C1 C3C2

MaximalConcurrency

MaximalConcurrency

We design an algorithm for each property

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2-Phase Discussion Time


C1 C2

Phase1Essential discussion

(all professors have to participate)

Phase2Voluntary discussion

The meeting continues for a finite time

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Snap-stabilization

• A snap-stabilizing protocol guarantees that, starting from an arbitrary system configuration, the protocol always behaves according to its specification.

• Thus, a snap-stabilizing protocol is a time optimal self-stabilizing protocol (because it stabilizes in 0 rounds).


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Snap-stabilizing Committee Coordination


• A snap-stabilizing committee coordination protocol guarantees that, every meeting convened after the last transient faults satisfy every requirement of the committee coordination.

Note that a snap-stabilizing committee coordination protocol provides no guarantee for the meetings started during the transient faults, except that they do not interfere with the execution of the other meetings.

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Snap-stabilization 2-Phase CC


CommitteeCoordination

Self-stabilizing Circulating

Token||

Our algorithm is parallel composition of two modules

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Snap-stabilizing 2-Phase CC


C1 C3C2

Step1 Looking for a committee to participate

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L

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C1 C3C2

Step2 Choosing a committee, where all other members are also looking

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C1 C3C2

Step3 Getting ready to participate in committee, where all members are looking or waiting

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L

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C1 C3C2

Step3 Committee meeting convenes, where all members are waiting.

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L

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W

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W

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Snap-stabilizing 2-Phase CC with Maximal Concurrency


C1 C3C2

Step4 After essential discussion, professors may leave the meeting. A token holder releases the token.

L

W

W

W

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W

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D

DD

D

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Maximal Snap-stabilization 2-Phase CC with Maximal Concurrency

¬LegitimateStates(p) (∧ State = idle) Pointer := null;

¬LegitimateStates (p) ^ (State = idle) State := looking, Pointer := null;


Stabilizing Actions

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Snap-stabilization 2-Phase CC with Fairness• The algorithm is similar to the previous algorithm, except

that we use the token circulation to ensure fairness.

• Let A be a committee coordination algorithm that satisfies Professor Fairness. Let professors remain in the meeting for infinite time. Under such assumption the system reaches a quiescent state where the status of all professors do not change any more. The Degree of Fair Concurrency of A is then the minimum number of meetings held in a quiescent state.


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Snap-stabilization 2-Phase CC with Fairness

The degree of fair concurrency for a committee coordination algorithm that satisfies professor fairness is the size of minimum maximal matching of the system.


Theorem

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Conclusion

• Summary– We considered the distributed committee coordination problem– We showed that satisfying fairness and maximal concurrency is

impossible even if professors desire to participate in meetings infinitely often in a non-stabilizing setting.

– We proposed a snap-stabilizing algorithms for each conflicting property.

• Future work– Committee coordination with priorities– Committee coordination in dynamic networks


THANK YOU !

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Maximal Concurrency .vs Fairness?


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Choosing the maximum ID?

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No progress!

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TOKEN CIRCULATION

PROGRE

SS

Snap-stabilization 2-Phase CC with

Maximal Concurrency

FAIRNESS

Snap-stabilization 2-Phase CC with

Fairness

Snap-stabilizing Committee Coordination

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