1. Distributed Snapshot

2. Think about these on the internet?
-- How many messages are in transit
on the internet?
-- What is the global state of a distributed system of N processes?
How do we compute these?

3. One-dollar bank
Let a $1 coin circulate in a network of a million banks. How can someone count the total $ in circulation? If not counted “properly,” then one may think the total $ in circulation to be one million.

4. Importance of snapshots
Major uses in
- deadlock detection
- termination detection
- rollback recovery
- global predicate computation

5. Consistent cut If this is not true, then the cut C is inconsistent
A cut is a set of events. If a cut C is consistent then
(a ∈ C) ⋀ (b ≺ a) ⇒ b ∈ C
If this is not true, then the cut C is inconsistent
time

6. Consistent snapshot
The set of states immediately following the events (actions) in 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.

7. 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.

8. 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 ( )

9. 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.

10. 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.

11. Why does it work?
Lemma 1. No red message is received in a white action.

12. Why does it work? SSS All white All red
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)

13. Why does it work? Let an observer observe the following actions:
w[i] w[k] r[k] w[j] r[i] w[l] r[j] r[l] … 
w[i] w[k] w[j] r[k] r[i] w[l] r[j] r[l] … [Lemma 1]
w[i] w[k] w[j] r[k] w[l] r[i] r[j] r[l] … [Lemma 1]
w[i] w[k] w[j] w[l] r[k] r[i] r[j] r[l] … [done!]
Recorded state

14. Example 1: Count the tokens
Let us verify that Chandy-Lamport snapshot algorithm correctly counts
the tokens circulating in the system 2
token C
token
no token A
no token
token
no token B A
no token
token
no token C 1 3 B
Are these consistent cuts?
How to account for the channel states?
Use sent and received variables for each process.

15. Example 2: Communicating State Machines

16. 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’
Doesn’t this appear strange? This state was never reached during the computation!

17. Understanding snapshot

18. 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.

19. 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.

20. 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?

21. Food for thought Distributed snapshot = distributed read.
Distributed reset = distributed write
How difficult is distributed reset?

22. Distributed debugging
(Marzullo and Neiger, 1991)
e, VC(e)
observer
Distributed system

23. Distributed debugging

24. Distributed debugging
Possibly ϕ:
At least one consistent global state S is reachable
from the initial global state, such that φ(S) = true.
Definitely ϕ:
All computations pass through some consistent global state S
such that φ(S) = true.
Never ϕ:
No computation passes through some consistent global state S
such that φ(S) = true.
Definitely ϕ ⇒Possibly ϕ

25. Examples ϕ = x+y =12 (true at S21) Possibly ϕ
ϕ = x+y > 15 (true at S32) Definitely ϕ
ϕ = x=y=5 (true at S40 and S22) Never ϕ
*Neither S40 and S22 is a consistent state*

26. Global State Collection

27. Global state collection
Some applications
- computing network topology
- termination detection
- deadlock detection
Chandy-Lamport algorithm does a partial job. Each process generates a fragment of the global state, but these pieces have to be “stitched together” to form a global state.

28. A simple exercise s(i) s(j) i j s(k) s(l) k l At the end, each process
Once the pieces of a consistent global state become available, consider collecting the global state via all-to-all broadcast
At the end, each process
will compute a set V, where
V= {s(i): 0 ≤ i ≤ N-1 }
s(i)
s(j) i j
s(k)
s(l) k l

29. All-to-all broadcast
Assume that the topology is a strongly connected graph
V.i
W.i
(i,k)
V.k
W.k
(j,i)
V.j
W.j
Acts like a “pump”