1. Outline Theoretical Foundations - continued
Casual ordering of messages – review
Global state
Cuts
Termination detection
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2. Vector Clocks Implementation rules
[IR1] Clock Ci is incremented between any two successive events in process Pi
Ci[i] := Ci[i] + d ( d > 0)
[IR2] If event a is the sending of message m by process Pi, then message m is assigned a timestamp tm = Ci(a). On receiving the same message m by process Pj, Cj is set to
Cj[k] := max(Cj[k], tm[k])
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3. Vector Clocks – cont. In a system of vector clocks, where 4/22/2019
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4. Causal Ordering of Messages
The causal ordering of messages tries to maintain the same causal relationship that holds among “message send” events with the corresponding “message receive” events
In other words, if Send(M1) -> Send(M2), then Receive(M1) -> Receive(M2)
This is different from causal ordering of events
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5. Birman-Schiper-Stephenson Protocol
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6. Schiper-Eggli-Sando Protocol
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7. Schiper-Eggli-Sando Protocol – cont.
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8. Schiper-Eggli-Sando Protocol – cont.
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9. Global State
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10. Local State Local state More notations
For a site Si, its local state at a given time is defined by the local context of the distributed application, denoted by LSi.
More notations
mij denotes a message sent by Si to Sj
send(mij) and rec(mij) denote the corresponding sending and receiving event.
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11. Definitions – cont.
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12. Definitions – cont.
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13. Global State – cont.
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14. Definitions – cont. Strongly consistent global state:
A global state is strongly consistent
if it is consistent and transitless
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15. Global State – cont.
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16. Chandy-Lamport’s Global State Recording Algorithm
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17. Cuts of a Distributed Computation
A cut is a graphical representation of a global state
A consistent cut is a graphical representation of a consistent global state
Definition
A cut of a distributed computation is a set C={c1, c2, ...., cn}, where ci is a cut event at site Si in the history of the distributed computation
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18. Cuts of a Distributed Computation – cont.
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19. Cuts of a Distributed Computation – cont.
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20. Cuts of a Distributed Computation – cont.
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21. Cuts of a Distributed Computation – cont.
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22. Cuts of a Distributed Computation – cont.
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23. Termination Detection
Termination detection is to detect when a distributed algorithm is terminated, such as election, a deadlock detection, or token generating algorithm
A process can be active or idle
A computation is said to have terminated if and only if all the processes are idle and there are no messages in transit
Basic idea
We are not going to cover the algorithm in detail
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24. Summary
The absence of global time and the absence of shared memory are two main characteristics of distributed systems
Two schemes, Lamport’s logical clocks and vector clocks are used to order events
Two algorithms for causal ordering of messages based on the vector clock-based ideas are discussed
Global states and cuts of a distributed system are also covered
These provide the theoretical foundations for other distributed algorithms
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