Consistent%20cut

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Consistent cut
A cut is a set of events.

• (a ? consistent cut C) ? (b happened before
  a) ? b ? C
• If this is not true, then the cut is inconsistent

b
g
c
a
d
P1
e
m
f
P2
P3
k
h
i
j
Cut 1
Cut 2
(Not consistent)
(Consistent)
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Consistent snapshot

• The set of states immediately following a
  consistent cut forms a consistent snapshot of a
  distributed system.
• A snapshot that is of practical interest is the
  most recent one. Let C1 and C2 be two consistent
  cuts and C1 ? C2. Then C2 is more recent than C1.
• Analyze why certain cuts in the one-dollar bank
  are inconsistent.

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Consistent snapshot

• How to record a consistent snapshot? Note that
• 1. The recording must be non-invasive
• 2. Recording must be done on-the-fly.
• You cannot stop the system.

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Chandy-Lamport Algorithm

• Works on a
• (1) strongly connected graph
• (2) each channel is FIFO.
• An initiator initiates the algorithm by sending
  out a marker ( )

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White and red processes

• Initially every process is white.
• When a process receives a marker,
• it turns red if it has not already done so.
• Every action by a process, and every
• message sent by a process gets the
• color of that process.

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Two steps

• Step 1. In one atomic action, the initiator (a)
  Turns red (b) Records its own state (c) sends a
  marker along all outgoing channels
• Step 2. Every other process, upon receiving a
  marker for the first time (and before doing
  anything else) (a) Turns red (b) Records its own
  state (c) sends markers along all outgoing
  channels
• The algorithm terminates when (1) every process
  turns red, and (2) Every process has received a
  marker through each incoming channel.

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Why does it work?

• Lemma 1. No red message is received in a white
  action.

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Why does it work?
All white
All red
SSS
Easy conceptualization of the snapshot state

• Theorem. The global state recorded by
  Chandy-Lamport algorithm is equivalent to the
  ideal snapshot state SSS.
• Hint. A pair of actions (a, b) can be scheduled
  in any order, if there is no causal order between
  them, so (a b) is equivalent to (b a)

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Why does it work?
Let an observer observe the following
actions wi wk rk wj ri wl rj rl
? wi wk wj rk ri wl rj rl
Lemma 1 ? wi wk wj rk wl ri rj
rl Lemma 1 ? wi wk wj wl rk ri
rj rl done!
Recorded state
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Example 1. Count the tokens

• Let us verify that Chandy-Lamport snapshot
  algorithm correctly counts
• the tokens circulating in the system

token
C
token
no token
A
token
no token
no token
B
A
token
no token
no token
C
B
Are these consistent cuts?
How to account for the channel states? Use sent
and received variables for each process.
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Another example of distributed snapshot
Communicating State Machines
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Something unusual

• Let machine i start Chandy-lamport snapshot
  before it has sent M along ch1. Also, let machine
  j receive the marker after it sends out M along
  ch2. Observe that the snapshot state is
• down ? up M
• Doesnt this appear strange? This state was
  never reached during the computation!

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Understanding snapshot
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Understanding snapshot
The observed state is a feasible state that is
reachable from the initial configuration. It may
not actually be visited during a specific
execution. The final state of the original
computation is always reachable from the
observed state.
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Discussions

• What good is a snapshot if that state has never
  been visited by the system?
• - It is relevant for the detection of stable
  predicates.
• - Useful for checkpointing.

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Discussions

• What if the channels are not FIFO?
• Study how Lai-Yang algorithm works. It does not
  use any marker
• LY1. The initiator records its own state. When
  it needs to send a message m to another process,
  it sends a message (m, red).
• LY2. When a process receives a message (m, red),
  it records its state if it has not already done
  so, and then accepts the message m.
• Question 1. Why will it work?
• Question 1 Are there any limitations of this
  approach?

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Questions

• Distributed snapshot distributed read.
• Distributed reset distributed write
• How difficult is distributed reset?