Distributed Computing Notes

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Distributed Computing Notes

• CS422

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Time and Event Ordering

• Synchronizing clocks
• Lamports Logical Clock
• Event Ordering
• Vector Clock
• Causal Ordering of Events

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Clock Synchronization

• Message passing to synchronize clock
• message transit time not predictable
• can not be used to establish an event order
• Network Time Protocol

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Logical Time and Logical Clocks

• Within a process, events ordered by local clock
• two events within a process occur in the order
  they are observed
• Distributed events must be ordered using a
  logical clock
• The act (event) of sending a message occurs
  before the event of receiving the message.

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Lamports Logical Clock
Scheme to order event in a distributed system
using logical clocks Process execution
characterized by a sequence of events. Events
can be procedure invocation instruction
execution message exchange sending a
message receiving a message
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Definitions
Ascertain order of two events based on behavior
of underlying computation Happened Before
Relation (?) - Casual relationship between two
events. a ? b, events in same process, a
occurred before b a ? b, a is sending message, b
is receiving message if a ? b and b ? c, then a ?
c (Transitive) Casual affects - past events
influence future events
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Definitions
Causally Related Events - Event a causally
affects event b if a ? b. Concurrent Events ()
- events a and b are concurrent (ab) if a b
and b a. That is, no causal affect. For
any two events in a system either a ? b, b ? a,
or a b Note a ? b only represents a potential
causality.
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Example space-time diagram
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Logical clocks
Clock Ci for each process Pi in system Ci (a)
assigns a timestamp to event a at Pi Logical
clocks take monotonically increasing values
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Logical Clocks - Conditions
If a ? b, then C(a) lt C(b) C1 For any two
events a and b in a process Pi, if a occurs
before b then Ci(a) lt Ci(b) C2 If a is sending
a message m from Pi and b is receiving a message
m at Pj, then Ci(a) lt Cj(b)
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Logical Clocks - Implementation
IR1 Clock Ci is incremented before each event
in Pi Ci Ci 1 if a and b are successive
events in Pi and a ? b, then Ci(b) Ci(a)
1 IR2 If event a is sending message m by Pi,
then m is assigned timestamp tm Ci(a) (obtained
after applying IR1). On receiving (m, t) by Pj,
Cj max(Cj, tm 1)(on receiving m Cj is
incremented by IR1)
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Ordering of Events
Set of all events can be totally ordered (gt) if
a is any event at Pi, b any event at Pj then
agtb ? Ci(a) lt Cj(b) ? (Ci(a) Cj(b) ? Pi ? Pj)
where ? defines an arbitrary relation that orders
P
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Limitations of Lamports Clocks
a ? b ? C(a) lt C(b), but reverse not necessarily
true (rules of inference). For example, if a and
b are in different processes. C(a) lt C(b) ? Note
? represents a conditional relationship (if X
then Y, X is the antecedent and Y is the
consequent). The only time a conditional is
false (invalid) is when the antecedent is true
but the consequent if false.
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Causal Ordering of Messages
Maintaining the same causal relationship that
holds among message send events with the
corresponding message receive events.
Distinguish between causal ordering of events and
messages
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Global State

• Made difficult due to absence of global clock and
  shared memory
• Definitions
• Si Site i
• LSi Local State for Site i
• send(mij) send event of message mij by Si to Sj
• rec(mij) receive event of message mij by Sj
• time(x) time state x was recorded
• time(send(m)) time event send(m) occured.

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Local State

• Definitions
• Si Site i
• LSi Local State for Site i
• send(mij) send event of message mij by Si to Sj
• rec(mij) receive event of message mij by Sj
• time(x) time state x was recorded
• time(send(m)) time event send(m) occured.

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Local State

• for a message mij sent by Si to Sj
• send(mij) is in LSi iff time(send(mij)) lt
  time(LSi)
• rec(mij) is in LSi iff time(rec(mij)) lt time(LSj)
• Inconsistent
• inconsistent(LSi, LSj) mij send(mij) not in
  LSi and rec(mij) in LSj
• Transit
• transit(LSi, LSj) mij send(mij) in LSi and
  rec(mij) not in LSj

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Global State

• Global State (GS) collection of the local
  states of system sites. GS LSi, LS2, ..., LSn
• Does not guarantee consistency
• Consistent Global State A global state GS
  LSi, LS2, ..., LSn is consistent iff for all i
  and j, 1 lt i,j lt n inconsistent(LSi, LSj) is
  the null set.
• Consistent State gt every receive event has a
  corresponding send event
• Inconsistent Stategt there is at least one
  receive event for which not send event is recorded

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Global State

• Transitless Global State - All communication
  channels are empty.
• for all i, j 1lti,jltntransit(LSi, LSj) NULL
• Strongly Consistent State - State is both
  consistent and transitless. In other words,
  consistent global state with all communications
  channels empty.

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Chandy-Lamport (Snapshot) Algorithm

• Uses marker message to initiate algorithm
• Communication channels are FIFO
• Can be initiated by any process
• Several processes can initiate concurrently
• Each initiation requires a unique marker
  identifier (process-id, sequence number).
• All local state must be collected simple method
  is to include identifier in marker and each
  process then sends LS to the initiating process.

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Basic Algorithm

• R1 Marker Send Rule - P sends, channel C
• P records its local state (LSp)
• foreach outgoing channel C send marker before
  sending another message
• R2 Marker Receive Rule - Q receives, channel C
• if LSq NULL, then record state C NULL, go to R1
• else record state C sequence of messages
  received since LSq recorded and marker received.

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Discussion

• The collected global state may not correspond a
  real global state. This is due to distributed
  nature of the algorithm and propagation delays.
• However, the algorithm has the ability to detect
  stable properties such as process termination,
  computation completion, or deadlock.

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Distributed Coordination
Server implemented mutual exclusion Distributed
mutual exclusion Central server Distributed
manager ring-based