Leslie Lamport
Massachusetts Computer Associates, Inc.
Presented by
Lokendra
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Q. WHICH REQUEST WAS MADE FIRST?
A common
‘Resource’
request A
Node A
request B
Node B
A Distributed System
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Q. WHICH REQUEST WAS MADE FIRST?
A common
‘Resource’
request A
Solution
request B
A Global Clock ??
Node A
Node B
Global
Synchronization?
A Distributed System
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Q. WHICH REQUEST WAS MADE FIRST?
A common
‘Resource’
Solution
Individual Clocks?
request A
10:00 AM
Node A
request B
10:02 AM
Are individual clocks
accurate, precise?
One clock might
run faster/slower?
Node B
A Distributed System
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 Synchronization
in a Distributed System!
• Event Ordering : Which event occurred first?
• How to sync the clocks across the nodes?
 Can
we define notion of ‘happened-before’
without using physical clocks?
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 Develop
a logical model of event ordering
(without the use of physical clocks)
• Might result into Anomalous Behavior?
 Bring
in ‘Physical’ Clocks to integrate with
the logical model
• Fix anomalous behavior
 Make
sure that the ‘Physical’ Clocks are
synced.
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
The system is composed of a collection of processes

Each process consists of a sequence of events
(instructions/subprogram)
Process P :
instr1
instr2
instr3 … (Total Order)

‘Sending’ and ‘Receiving’ messages among processes
• ‘Send’ : an event
• ‘Receive’ : an event
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
1.
2.
a ‘Happened Before’ b : a→b
If a and b are events in the same process, and a
comes before b, then a → b.
If
a :message sent
b : receipt of the same message
then a → b.
3.
If a → b and b → c then a → c.
4.
Two distinct events a and b are said to be
concurrent if a -/->b and b -/->a
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p1 → p2
p1 → q2
p1 → r4
q2 -/-> p2
q3 -/-> p2
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

A clock Ci for each process Pi to be a function which assigns a
number Ci(a) to any event a in that process.
Logical Clock (Ci ) has no relation with the Physical Clock.
Clock Condition:
For any event a, b:

If a→b, then C(a) < C(b)

Converse NOT True!
• Concurrent processes?
Clock Condition is satisfied if :
C1. If a and b are events in process Pi, and a comes before b, then

Ci(a) < Ci(b).
C2. If a is the sending of a message by process Pi and b is the
receipt of that message by process Pj, then
Ci(a) < Cj(b)
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•A clock ticks through every event
•The clicks happen between the events
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
Following implementation rules are proposed to
satisfy the clock condition:
IR1. Each process Pi increments Ci between any two
successive events.
IR2. (a) If event a is the sending of a message m by
process Pi, then the message m contains a timestamp
Tm = Ci (a).
(b) Upon receiving a message m, process Pi sets Ci
greater than or equal to its present value and greater
than Tm.
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Correction of clocks
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 One
more relation < to break ties, arbitrary
total order of events
The total order relation => is defined as:
a => b, if and only if
(i) Ci(a) < Cj(b)
(ii) Ci(a) = Cj(b) and Pi< Pj

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I.
A process using the resource must release it
before it can be given to another process.
II.
Requests for the resource must be granted
in the order in which they were made.
I.
III.
Does not indicate what should be done when two
processes request for the resource at the same time?
If every process using the resource
eventually releases it, then every request is
eventually granted (no starvation)
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
Each process maintains its own request queue:

1.
The Algorithm:
Resource request:
1.
2.
2.
Resource request receipt.:
1.
2.
3.
3.
Pi removes request message Tm : Pi requests resource from its queue
sends the release message Pi releases resource to every other process.
Resource release receipt
1.
2.
5.
Pi receives Pi’s request message.
Pj then puts the message on its request queue
Pj sends an acknowledgement to Pi (timestamped later)
Resource release:
1.
2.
4.
Process Pi sends the message Tm : Pi requests resource to every other
Pi also puts the request message on its request queue.
Pj receive’s Pi’s resource release message.
Pj removes the Tm : Pi requests resource from its request queue.
Resource allocation.
Pi is allocated the resource when:
1.
2.
There is a Tm : Pi requests resource message in Pi ’s request queue which is ordered before and other
request in the queue by ).
Pi has received messages from every other process timestamped later than Tm .
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 NOTE:
• Each process independently follows these rules
• There is no central synchronizing process or
central storage.
• Can be viewed as State Machine C x S→ S
 C : set of commands for eg resource request
 S : Machine’s state
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
1.
Two possible ways to avoid such anomalous behavior:
Give the user the responsibility for avoiding anomalous
behavior.
•
2.
When the call is made, b be given a later timestamp than a.
Let S : set of all system events
Š : Set containing S + relevant external events
Let → denote the “happened before” relation for Š .
Strong Clock Condition:
For any events a; b in Š : if a → b then C(a) < C(b)

One can construct physical clocks, running quite
independently, and having the Strong Clock Condition,
therefore eliminating anomalous behavior.
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 PC1:
ĸ <<1
 PC2:
2
| dCi(t)/dt - 1 | < ĸ
For all i,j : |Ci(t) – Cj(t)| < ԑ
clocks don’t run at the same rate:
• They may drift further
 Need
holds
of an algorithm that PC2 always
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 Let
μ be a number such that a→b and a
occurs at t in Pi and b in Pj, then b occurs
later than t+ μ
• μ : less than the shortest transmission time
 To
avoid anomalous behavior, we need:
Ci(t+ μ) – Cj(t) > 0, guaranteed if ԑ/(1- ĸ) ≤ μ
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μm is the minimum delay of a message and
is known by the processes
 IR1’
: For each i, Ci is differentiable at t
and dCi(t)/dt >0
 IR2’:
• a) Pi sends a message at t, timestamp Tm=Ci(t)
• Upon receipt of m, Pj sets Cj(t’) to max (Cj(t’), Tm+
μm )
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 Lamport
clocks limitation:
• If (ab) then C(a) < C(b) but
• Reverse is not true!!
 Nothing can be said about events by comparing timestamps!
 If C(A) < C(B), then ??
 Need to maintain causality
• Causal delivery:
• If send(m) -> send(n) => deliver(m) -> deliver(n)
• Need a time-stamping mechanism such that:
 If T(A) < T(B) then A should have causally preceded B
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P1
P2
(1, 0 , 0)
e11
(2, 0, 0)
e12
(0, 1, 0)
e21
(2, 2, 0)
(3, 5, 2)
e13
(2, 3, 1)
e22
e23
(2,4,2)
e24
(2, 5, 2)
e25
(0, 0, 2)
(0, 0, 1)
P3
e32
e31
Each process i maintains a vector Vi
Vi[i] : number of events that have occurred at i
Vi[j] : number of events i knows have occurred at process j
Less
than
or equal:: ts(a) ≤ ts(b) if ts(a)[i] is ≤ ts(b)[i] for all i.
Causal
Delivery
For
(3,3,5)
if megis [sent
by≤P(3,4,5)
and ]ts(m) is (3, 4, 0) and you are P , you should already
1
3
have received exactly 2 messages from P1 and at least 4 from P2
ts(e11) = (1, 0, 0) and ts(e22) = (2, 2, 0), which shows e11  e22
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 ‘Happens
Before’ is just partial ordering
 To
make it total, arbitrary ties method can
be used
• But can lead to Anomalous behavior
 But
we can use synchronized clocks to
resolve
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