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Snap-stabilizing Committee Coordination Borzoo Bonakdarpour Stephane Devismes Franck Petit IEEE International Parallel and Distributed Processing Symposium (IPDPS’11) May17, 2011

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2 Motivation Generation distributed code from high-level component- based models. May 17, 2011 IEEE International Parallel and Distributed Processing Symposium (IPDPS'11) Behavioral Behavioral atomic components Synchronizing with a set of Synchronizing with a set of rendezvous interactions

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3 Simple Rendezvous May 17, 2011 IEEE International Parallel and Distributed Processing Symposium (IPDPS'11) s Sender r1r1 Receiver1 Interactions: sr 1 r 2 r 3 Priorities: sr1r1 r2r2 Receiver2 r2r2 r3r3 Receiver3 r3r3 r2r2 Most process algebras have similar syntax and semantics

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4 Motivation May 17, 2011 IEEE International Parallel and Distributed Processing Symposium (IPDPS'11) How do we generate distributed code by starting from such high-level models?

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5 Motivation May 17, 2011 IEEE International Parallel and Distributed Processing Symposium (IPDPS'11) C1C1C1C1 C1C1C1C1 C4C4C4C4 C4C4C4C4 C2C2C2C2 C2C2C2C2 C3C3C3C3 C3C3C3C3 C6C6C6C6 C6C6C6C6 C5C5C5C5 C5C5C5C5 C7C7C7C7 C7C7C7C7 I1I1 I2I2 I3I3 Conflict resolution (exclusion) (exclusion)

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

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7 Distributed Committee Coordination May 17, 2011 IEEE International Parallel and Distributed Processing Symposium (IPDPS'11) C1C1C1C1 C3C3C3C3 C2C2C2C2

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

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

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10 Why another Committee Coordination Algorithm? May 17, 2011 IEEE International Parallel and Distributed Processing Symposium (IPDPS'11) [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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11 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 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 May 17, 2011 IEEE International Parallel and Distributed Processing Symposium (IPDPS'11)

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12 Maximal Concurrency in CC Let P 1 be a set of professors that are all in infinite-time meetings. Let P 2 be a set of professors waiting to enter a committee meeting. Let Π be the set of committees that all their members are in P 2. If Π ≠ Ø then a committee in Π meets. Let P 1 be a set of professors that are all in infinite-time meetings. Let P 2 be a set of professors waiting to enter a committee meeting. Let Π be the set of committees that all their members are in P 2. If Π ≠ Ø then a committee in Π meets. May 17, 2011 IEEE International Parallel and Distributed Processing Symposium (IPDPS'11)

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13 Maximal Concurrency May 17, 2011 IEEE International Parallel and Distributed Processing Symposium (IPDPS'11) C1C1C1C1 C3C3 C2C2 The meetings lasts indefinitely An idle meeting eventually convenes

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14 Professor Fairness Every professor wants to participate in a committee meeting infinitely often. May 17, 2011 IEEE International Parallel and Distributed Processing Symposium (IPDPS'11) Every professor eventually participates in a committee meeting that it is a member of. Assumption Fairness Otherwise, distributed committee coordination is [2] Otherwise, distributed committee coordination is impossible [2] [2] Y.-K. Tsay and R. Bagrodia. Some impossibility results in interprocess synchronization. Distributed Computing, 6(4):221–231, 1993.

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15 Impossibility of Fairness and Maximal Concurrency May 17, 2011 IEEE International Parallel and Distributed Processing Symposium (IPDPS'11) C1C1C1C1 C3C3C3C3 C2C2C2C2 MaximalConcurrencyMaximalConcurrency MaximalConcurrencyMaximalConcurrency We design an algorithm for each property

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16 2-Phase Discussion Time May 17, 2011 IEEE International Parallel and Distributed Processing Symposium (IPDPS'11) C1C1C1C1 C2C2 Phase1 Essential discussion (all professors have to participate) Essential discussion (all professors have to participate) Phase2 Voluntary discussion The meeting continues for a finite time Voluntary discussion The meeting continues for a finite time

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

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18 Snap-stabilizing Committee Coordination May 17, 2011 IEEE International Parallel and Distributed Processing Symposium (IPDPS'11) 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. 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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19 Snap-stabilization 2-Phase CC May 17, 2011 IEEE International Parallel and Distributed Processing Symposium (IPDPS'11) CommitteeCoordination Self-stabilizing Circulating Token || Our algorithm is parallel composition of two modules

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20 Snap-stabilizing 2-Phase CC May 17, 2011 IEEE International Parallel and Distributed Processing Symposium (IPDPS'11) C1C1C1C1 C3C3 C2C2 Step1 Looking for a committee to participate L L L L L L L

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21 Snap-stabilizing 2-Phase CC May 17, 2011 IEEE International Parallel and Distributed Processing Symposium (IPDPS'11) C1C1C1C1 C3C3 C2C2 Step2 Choosing a committee, where all other members are also looking L L L L L L L

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22 Snap-stabilizing 2-Phase CC May 17, 2011 IEEE International Parallel and Distributed Processing Symposium (IPDPS'11) C1C1C1C1 C3C3 C2C2 Step3 Getting ready to participate in committee, where all members are looking or waiting L L L L L L L W W W W

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23 Snap-stabilizing 2-Phase CC May 17, 2011 IEEE International Parallel and Distributed Processing Symposium (IPDPS'11) C1C1C1C1 C3C3 C2C2 Step3 Committee meeting convenes, where all members are waiting. L L L W W W W L L W W W W

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24 Snap-stabilizing 2-Phase CC with Maximal Concurrency May 17, 2011 IEEE International Parallel and Distributed Processing Symposium (IPDPS'11) C1C1C1C1 C3C3 C2C2 Step4 After essential discussion, professors may leave the meeting. A token holder releases the token. L W W W W W W W W D D D D

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25 Maximal Snap-stabilization 2-Phase CC with Maximal Concurrency ¬LegitimateStates(p) ∧ (State = idle) Pointer := null; ¬LegitimateStates (p) ^ (State = idle) State := looking, Pointer := null; ¬LegitimateStates(p) ∧ (State = idle) Pointer := null; ¬LegitimateStates (p) ^ (State = idle) State := looking, Pointer := null; May 17, 2011 IEEE International Parallel and Distributed Processing Symposium (IPDPS'11) Stabilizing Actions

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

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

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

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THANK YOU !

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30 Maximal Concurrency.vs Fairness? May 17, 2011 IEEE International Parallel and Distributed Processing Symposium (IPDPS'11) C1 C2 L 1 2 3 L C3 C4 C5 4 5 6 7 Choosing the maximum ID?

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31 Maximal Concurrency.vs Fairness? May 17, 2011 IEEE International Parallel and Distributed Processing Symposium (IPDPS'11) C1 C2 L 1 2 3 L C3 C4 C5 4 5 6 7 Choosing the maximum ID?

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32 Maximal Concurrency.vs Fairness? May 17, 2011 IEEE International Parallel and Distributed Processing Symposium (IPDPS'11) C1 C2 L 1 2 3 L C3 C4 C5 4 5 6 7 Choosing the maximum ID?

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33 Maximal Concurrency.vs Fairness? May 17, 2011 IEEE International Parallel and Distributed Processing Symposium (IPDPS'11) C1 C2 L 1 2 3 L C3 C4 C5 4 5 6 7 Choosing the maximum ID?

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34 Maximal Concurrency.vs Fairness? May 17, 2011 IEEE International Parallel and Distributed Processing Symposium (IPDPS'11) C1 C2 L 1 2 3 L C3 C4 C5 4 5 6 7 Choosing the maximum ID? No progress!

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35 Maximal Concurrency.vs Fairness? May 17, 2011 IEEE International Parallel and Distributed Processing Symposium (IPDPS'11) TOKEN CIRCULATION PROGRESS Snap-stabilization 2- Phase CC with Maximal Concurrency FAIRNESS Snap-stabilization 2- Phase CC with Fairness

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