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Global States in a Distributed System By John Kor and Yvonne Cheng

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Initial Problem Example Garbage Collector Free’s up memory which is no longer in use Check’s if a reference to memory still exists What about in a distributed system

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Initial Problem Example (cont’d) A distributed system consists of multiple processes Each process is located on a different computer No sharing of processor or memory

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Initial Problem Example (cont’d) Each process can only determine its own “state” Problem: How do we determine when to garbage collect in a distributed system? How do we check whether a reference to memory still exists?

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System Model A distributed system consists of multiple processes Each process is located on a different computer Each process consists of “events” An event is either sending a message, receiving a message, or changing the value of some variable Each process has a communication channel in and out

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Our Garbage Collection Problem In order to test whether a certain property of our system is true, we cannot just look at each process individually A “snapshot” of the entire system must be taken to test whether a certain property of the system is true This “snapshot” is called a Global State

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Definition The global state of a distributed system is the set of local states of each individual processes involved in the system plus the state of the communication channels.

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Determinism Deterministic Computation At any point in computation there is at most one event that can happen next. Non-Deterministic Computation At any point in computation there can be more than one event that can happen next.

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Deterministic Computation

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Non-Deterministic Computation

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Determinism Deterministic computation A local event would reveal everything about the global state! The process will know other process’ state Non-Deterministic computation Because of branching, a local event cannot reveal what the next step will be

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Simple Algorithm Create a new process that collects the states of every other process Every process will save their state at an arbitrary time and send it to this new process

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Advantages Very simple Easy to implement

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Problems? Based on the assumption that all processes work on a synchronized global clock Wrong assumption!

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Problems (cont’d) State recorded by p m pq

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Problems (cont’d) pq m

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State recorded by q pq m

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Problems (cont’d) Global state recorded m pq m

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Another view p q m

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Process p has no record of sending m Process q HAS record of receiving m Problem? Global state does not show p sending m, therefore there is confusion as to where m came from Breaks the Consistency concept

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Consistency A global state is consistent if it could have been observed by an external observer If e e`, then both e and e` must reside within the same state For a successful Global State, all states must be consistent

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Solution Need to develop an asynchronous algorithm Cannot depend on a clock Must ensure consistency in all global states

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Assumptions Distributed system: Finite set of processes and channels; described by graph Processes Set of states, initial state, set of events Channels FIFO, error-free, infinite buffers, arbitrary but finite delay

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PART 2 Presented By: Yvonne

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Idea of a global state recording algorithm -each process records its own state -the two processes incident by one channel cooperate in recording the channel state

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Challenge -No global clock -Need a meaningful result -Superimposed on underlying computation

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Meaningful: The notion of Consistency -it could have been observed by an external observer -All feasible states are consistent

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An Example p q p q Sp0Sp0 Sp1Sp1 Sp2Sp2 Sp3Sp3 Sq0Sq0 Sq1Sq1 Sq2Sq2 Sq3Sq3 m1m1 m2m2 m3m3

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A Consistent State? p q Sp1Sp1 Sq1Sq1 p q Sp0Sp0 Sp1Sp1 Sp2Sp2 Sp3Sp3 Sq0Sq0 Sq1Sq1 Sq2Sq2 Sq3Sq3 m1m1 m2m2 m3m3

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Yes p q p q Sp0Sp0 Sp1Sp1 Sp2Sp2 Sp3Sp3 Sq0Sq0 Sq1Sq1 Sq2Sq2 Sq3Sq3 m1m1 m2m2 m3m3 Sp1Sp1 Sq1Sq1

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A Consistent State? p q Sp2Sp2 Sq3Sq3 m3m3 p q Sp0Sp0 Sp1Sp1 Sp2Sp2 Sp3Sp3 Sq0Sq0 Sq1Sq1 Sq2Sq2 Sq3Sq3 m1m1 m2m2 m3m3

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Yes p q p q Sp0Sp0 Sp1Sp1 Sp2Sp2 Sp3Sp3 Sq0Sq0 Sq1Sq1 Sq2Sq2 Sq3Sq3 m1m1 m2m2 m3m3 Sp2Sp2 Sq3Sq3 m3m3

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An inconsistent State p q p q Sp0Sp0 Sp1Sp1 Sp2Sp2 Sp3Sp3 Sq0Sq0 Sq1Sq1 Sq2Sq2 Sq3Sq3 m1m1 m2m2 m3m3 Sp1Sp1 Sq3Sq3

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Conducting algorithm: Using An Example -Processes: p and q -Channels: c and c’ -Token: t pq c c’

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An Example -p records its state t pq c c’

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An Example -q, c, and c’ record their states t pq c c’

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An Example -The composite global state! t pq c c’ t

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An Example -n: number of messages sent along c before p’s state is recorded -n’: number of message sent along c before c’s state is recorded pq c c’

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An Example - Reason of inconsistency: n<n’ t pq c c’ t pq c n = 0 n’ = 1

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Similar scenario c is recorded when the token is at process p. p sends the token through channel c, and the states of c’, p, and q are recorded. The recorded global state : no tokens in the system. The reason of inconsistency : n>n’

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Conclusion from the example A consistent global state requires n = n’

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Similar Conclusion m : number of messages received along c before q’s state is recorded m’ : number of messages received along c before c’s state is recorded To be consistency: m=m’

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Some other equations m’ : number of messages received along c before c’s state is recorded n’ : number of messages sent along c before c’s state is recorded m : number of messages received along c before p’s state is recorded n : number of messages sent along c before p’s state is recorded n = n’ m = m’ n’ >= m’ n >= m

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Other Fact The state of channel c that is recorded must be the sequence of messages sent along the channel before the sender’s state is recorded, excluding the sequence of messages received along the channel before the receiver’s state is recorded. Two cases: n’=m’ : c is empty n’>m’: c must be the (m’+1)st…n’th messages sent by p along c

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Put All Together: A brief sketch of the algorithm p sends a marker message along all its outgoing channels after it records its state and before it sends any other messages. On receipt of a marker message from channel c else state ( c ) = messages received on c since it had recorded its state excluding the marker. if p has not recorded its state record the state state ( c ) = EMPTY

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Chandy and Lamport Algorithm Features: Does not promise us to give us exactly what is there But gives us consistent state!!

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Algorithm in Action p q Sq0Sq0 Sq1Sq1 Sq2Sq2 Sq3Sq3 Sp0Sp0 Sp1Sp1 Sp2Sp2 Sp3Sp3 m1m1 m2m2 m3m3

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p q Sq0Sq0 Sq1Sq1 Sq2Sq2 Sq3Sq3 Sp0Sp0 Sp1Sp1 Sp2Sp2 Sp3Sp3 m1m1 m2m2 m3m3 q records state as S q 1, sends marker to p

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Algorithm in Action p q Sq0Sq0 Sq1Sq1 Sq2Sq2 Sq3Sq3 Sp0Sp0 Sp1Sp1 Sp2Sp2 Sp3Sp3 m1m1 m2m2 m3m3 p records state as S p 2, channel state as empty

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Algorithm in Action p q Sq0Sq0 Sq1Sq1 Sq2Sq2 Sq3Sq3 Sp0Sp0 Sp1Sp1 Sp2Sp2 Sp3Sp3 m1m1 m2m2 m3m3 q records channel state as m 3

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Algorithm in Action p q Sq0Sq0 Sq1Sq1 Sq2Sq2 Sq3Sq3 Sp0Sp0 Sp1Sp1 Sp2Sp2 Sp3Sp3 m1m1 m2m2 m3m3 Recorded Global State = ((S p 2, S q 1 ), (0,m 3 ) )

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Algorithm in Action p q Sq0Sq0 Sq1Sq1 Sq2Sq2 Sq3Sq3 Sp0Sp0 Sp1Sp1 Sp2Sp2 Sp3Sp3 m1m1 m2m2 m3m3 Recorded Global State = ((S p 2, S q 1 ), (0,m 3 ) ) Computation may not even have passed through the state recorded!

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What have we recorded The recorded consistent state can be anything!

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Properties of the recorded global state S i : global state when the algorithm starts S j : global state when the algorithm finishs S * : state recorded by the algorithm Then S * is reachable from S i S j is reachable from S *

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S * Is reachable from S i SiSi SjSj

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S j Is reachable from S * SiSi SjSj

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Still what good is it? Stable Properties A property Y is called a stable property iff for all states S` reachable from S Y(S) -> Y(S’)

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Detection of Stable Properties Outcome = false; while ( outcome == false ) { determine Global State S; outcome = Y (S); }

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Checkpoint S* serves as a checkpoint On a failure, restart the computation from S* Problem! Not able to restore to Sj SiSi SjSj S*S*

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Solution: Publishing A Broadcast medium A central recorder process records all the messages received by each process Processes record their states at their own time and send it to the recorder

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Determining Global State Recorder can construct global state from Checkpointed States of all processes Plus Messages recorded since last checkpoint

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Problems Publishing keeps track of all messages received by each process Expensive! Solution recorder takes checkpoint of process p at time t deletes all messages recd by p before t.

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Comparison

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Conclusion Global State detection difficult in Distributed Systems Snapshot algorithm may not give an actual state but is very helpful in detecting Stable Properties Publishing gives an asynchronous way of determining global states but is unscalable

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