1. Time, Clocks, and the Ordering of Events in a Distributed System
Leslie Lamport
Massachusetts Computer Associates, Inc.
Presented by
Lokendra

2. Problem! A Distributed System Q. WHICH REQUEST WAS MADE FIRST?
A common ‘Resource’
request B
request A
Node A
Node B
A Distributed System

3. Problem! A Distributed System Q. WHICH REQUEST WAS MADE FIRST?
A common ‘Resource’
Node A
Node B
request A
request B
A Distributed System
Solution
A Global Clock ??
Global Synchronization?

4. Problem! A Distributed System Q. WHICH REQUEST WAS MADE FIRST?
A common ‘Resource’
Node A
Node B
request A
request B
A Distributed System
Solution
Individual Clocks?
Are individual clocks accurate, precise?
One clock might run faster/slower?
10:02 AM
10:00 AM

5. Problem! 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?

6. Approach towards solution
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.

7. Partial Ordering 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

8. ‘Happened Before’ Relation
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.
If a → b and b → c then a → c.
Two distinct events a and b are said to be concurrent if a -/->b and b -/->a

9. Space Time Diagram
p1 → p2
p1 → q2
p1 → r4
q2 -/-> p2
q3 -/-> p2

10. Logical Clocks
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)

11. Space Time Diagram A clock ticks through every event
The clicks happen between the events

12. Logical Clocks
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.

13. Logical Clocks
Correction of clocks

14. Total Ordering of events
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

15. Mutual Exclusion Problem
A process using the resource must release it before it can be given to another process.
Requests for the resource must be granted in the order in which they were made.
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)

16. Solution -Distributed Algorithm
Each process maintains its own request queue:
The Algorithm:
Resource request:
Process Pi sends the message Tm : Pi requests resource to every other
Pi also puts the request message on its request queue.
Resource request receipt.:
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:
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
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:
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 .

17. Solution -Distributed Algorithm
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

18. Anomalous Behavior

19. Anomalous Behavior (contd)
Two possible ways to avoid such anomalous behavior:
Give the user the responsibility for avoiding anomalous behavior.
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.

20. Physical Clocks PC1: | dCi(t)/dt - 1 | < ĸ
ĸ <<1
PC2: For all i,j : |Ci(t) – Cj(t)| < ԑ
2 clocks don’t run at the same rate:
They may drift further
Need of an algorithm that PC2 always holds

21. Physical Clocks
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

22. Algorithm
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 )

23. Some related concepts Lamport clocks limitation:
If (ab) then C(a) < C(b) but
Reverse is not true!!
Nothing can be said about events by comparing time- stamps!
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

24. Vector Clocks (1, 0 , 0) (2, 0, 0) (3, 5, 2) e11 e12 e13 (0, 1, 0)
(2, 2, 0)
(2, 3, 1)
(2, 5, 2)
(0, 0, 1)
(0, 0, 2)
e21
e22
e23
e24
e31
e32 P1 P2 P3
(2,4,2)
e25
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.
For eg [ (3,3,5) ≤ (3,4,5) ]
ts(e11) = (1, 0, 0) and ts(e22) = (2, 2, 0), which shows e11  e22
Causal Delivery :
if m is sent by P1 and ts(m) is (3, 4, 0) and you are P3, you should already have received exactly 2 messages from P1 and at least 4 from P2

25. Distributed Failure Detection Algorithm

26. Conclusion ‘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

27. QUESTIONS ?