1. Global State Recording
definitions
global state recording
FIFO
Chandy-Lamport’s algorithm
collecting global state
incremental snapshot
non-FIFO
Lai-Yang two color algorithm
Mittern’s vector clocks algorithm
consistent global snapshots
causality and zigzag paths
rollback dependency graph

2. Local State
local state LSi of a site (process) Si is an assignment of values to variables of Si
sending send(mij) and receiving rec(mij) of message mij from Si to Sj may influence LSi
we denote
time(send(mij) or rec(mij)) the sequence number of the state in the compuation after which send/receive occurs (note the difference with Singhal)
time(LSi) the state at which Si was recorded
to aid the reasoning we consider the messages sent/received by a process as belonging to local state
we define
that is
the message is in transit if it was sent but not received
the message is inconsistent if it was received but never sent

3. Global State
global state is a collection of local states of all processes and set of messages in the channels
notice Singhal does not use messages in his def. – ours is more precise
global state is consistent if it does not have any inconsistent messages, that is:
global state is transitless if there are no messages in transition, that is:
note that a consistent state is not necessarily transitless and v.v.
what are the global states on the picture above?

4. Chandy-Lamport’s Global State Recording Algorithm
9/10/2018
Chandy-Lamport’s Global State Recording Algorithm
works on arbitrary topology system with FIFO channels and arbitrary algorithm whose snapshot is taken (basic algorithm)
does not interfere with the operation of basic algorithm (does not delay, reorder or drop basic messages)
one process initiates recording by sending control messages (markers) multiple pro- cesses can also initiate
draw a tree process example
can C-L record an inconsistent state?

5. Global State Recorded by Chandy-Lamport’s Algorithm
does C-L record a (global) state that occurs in the computations?
not necessarily.
however, C-L records a state in a computation that is equivalent to the original computation.
moreover this equivalent computation shares with the original computation
a prefix up to start of snapshot
a suffix after the snapshot
the recorded state is between these two states
can C-L record a state where some P have messages in every channel? if yes which one?
can several independent snapshots run in parallel?

6. Collecting Global State
based on spanning tree constructed on the fly
sender of the first marker to arrive at a process is its parent
each marker carries the sender’s parent
by receiving marker process learns if it has children
if process is a leaf, after finishing state recording, it sends its state to its parent
each process waits for its children’s states, appends its own and forwards all info to its parent

7. Non-FIFO: Lai-Yang Algorithm
non-FIFO channel: is a set (rather than a queue) of messages, any message in the set can be received
messages can overtake one another
fair message receipt is assumed – eventually a sent message is received
two colors for processes and basic messages – white and red, no explicit markers
all processes start as white, when process sends a basic message it attaches its color
when process receives a differently colored message, it itself changes color
while white (red), process records all messages sent/received, after changing colors, the process sends message history to the initiator; based on sent/received histories, initiator calculates messages in transit
if only the number of messages in transit needed – may maintain counters in stead of histories

8. State Recording Using Causal Message Delivery
initiator broadcast token to all processes
each process records state and sends it to the initiator
processes do not send markers or coordinate local state recording
due to causal ordering of messages
if for Pi: rec(tokeni)  send(mij) then send(tokenj)  send(mij) therefore rec(tokenj)  rec(mij) hence state recording at Pj happens before mij receipt
channel state recording (Archaya-Badrinath)
append sequence numbers to all messages,
at each process record highest sent/received SN
together with local state send sent/received records for initiator to determine messages in transition

9. Consistent Global Snapshot
processes periodically asynchronously record local states (local checkpoints)
a global snapshot is a collection of local checkpoints
needed in distributed failure recovery, distributed event monitoring, debugging, etc.
global snapshot is consistent if no two checkpoints are causally related
even though checkpoints themselves are not causally related, they may not be a part of a global snapshot
ex: C11 and C32 are concurrent, yet there is no global snapshot that contains both of them
the objective in global snapshot recording is to select (out of available) the set of concurrent checkpoints.
note that unlike global state recording, the alg. does not have control over the snapshot taking time

10. Zigzag Path
checkpoint interval – part of computation between two successive checkpoints at the same process
zigzag path exists between checkpoints Cxi and Cyj if there exists a sequence of messages m1, …mn such that
m1 sent by Px after Cxi
mk received by Pz, mk+1 is sent by Pz in the same checkpoint interval
mn received by Py before Cyj
causal path - same as zigzag path but the messages are causally related
zigzag cycle is a zigzag path to the process itself
causal path
zigzag path

11. Zigzag Path
checkpoint interval – part of computation between two successive checkpoints at the same process
zigzag path exists between checkpoints Cxi and Cyj if there exists a sequence of messages m1, …mn such that
m1 sent by Px after Cxi
mk received by Pz then mk+1 is sent by Pz in the same checkpoint interval
mn received by Py before Cyj
causal path - same as zigzag path but the messages are causally related
zigzag cycle is a zigzag path to the process itself
zigzag cycle
zigzag path

12. Sufficient Condition for Consistent Snapshot
a consistent snapshot can be formed to include a set S of checkpoints if and only if no zigzag path exists between any two checkpoints in S [Netzer and Xu]
snapshot line – a line drawn through a set of checkpoints
due to the existence of a zigzag path, a snapshot line always crosses a message making two checkpoints causally related and resultant snapshot inconsistent
constructing consistent snapshot requires choosing checkpoints without zigzag path
zigzag path

13. Runtime Consistent Snapshot Construction Using R-Graph
definition of rollback-dependency graph (R-graph) [Wang]
basic message carries its checkpoint interval number
there is a zigzag path between two checkpoints if there is a path in R- graph
example computation
corresponding R-graph