Time%20and%20Clock

1
Time and Clock

• Primary standard rotation of earth
• De facto primary standard atomic clock
• (1 atomic second 9,192,631,770 orbital
  transitions of Cs 133 atom.
• 86400 atomic sec 1 solar day 3 ms).
• What is GPS?

• There is nothing called simultaneous
• in the physical world.

2
Sequential and Concurrent events

• Sequential Totally ordered in time. Total
  ordering is feasible in a single process that has
  only one clock. This is not true in a distributed
  system.
• Two issues are important here
• How to synchronize physical clocks ?
• Can we define sequential and concurrent events
  without using physical clocks?

3
Causality

• Causality helps determine sequential and
  concurrent events
• without using physical clocks.
• Joke ? Re joke (? implies causally ordered
  before)
• Message sent ? message received
• Local ordering a ? b ? c (based on the local
  clock)

4
Defining causal relationship

• Rule 1. If a, b are two events in a single
  process P, and the time of a is less than the
  time of b then a ? b.
• Rule 2. If a sending a message, and b
  receipt of that message, then a ? b.
• Rule 3. a ? b ? b ? c ? a ? c

5
Example of causality

• a ? d since (a ? b ? b ? c ? c ? d)
• e ? d since (e ? f ? f ? d)
• (Thus ? defines a PARTIAL order).
• Is g ? f or f ? g? NO. They are concurrent.
• Concurrency absence of causal order.

6
Logical clocks

• LC is a counter. Its value respects causal
  ordering as follows
• a ? b ? LC(a) lt LC(b)
• Note that LC(a) lt LC(b) does NOT imply a ? b.

• Each process maintains its logical clock as
  follows
• LC1. Each time a local event takes place,
  increment LC.
• LC2. Append the value of LC to outgoing
  messages.
• LC3. When receiving a message, set LC to
• 1 max (local LC, message LC)

7
Total order

• So, does total order exist in a distributed
  system?
• It is important to define a total order for some
  applications.
• Causal order is strengthened to define a total
  order (ltlt) among events.
• The (id, LC) value sent out with each message is
  called its timestamp.

• Let a, b be events in processes i and j
  respectively. Then
• a ltlt b iff LC(a) lt LC(b) OR LC(a) LC(b) and
  i lt j
• a ? b ? a ltlt b, but the converse is not true.

8
Vector clock

• Causality detection can be an important issue is
  applications like group communication.
• Logical clocks do not detect causal ordering.
  Vector clocks do.
• a ? b ? VC(a) lt VC(b)

9
Vector clocks

• Example
• 3, 3, 4, 5, 3, 2, 1, 4 lt
• 3, 3, 4, 5, 3, 2, 2, 5
• But,
• 3, 3, 4, 5, 3, 2, 1, 4 and
• 3, 3, 4, 5, 3, 2, 2, 3
• are not comparable

• Define. VC(a) lt VC(b) iff
• ?i 0 i N-1 VC(a)i VC(b)i, and
• ? j 0 j N-1 VC(a)j lt VC(b)j,

10
Implementing VC

• Actions of process j
• VC1. Increment VCj) for each local event.
• VC2. Append local VC to every outgoing message.
• VC3. When a message with a vector timestamp T
  arrives, first increment the jth component VCj
  of the local vector clock, and then update it as
  follows
• ?k 0 k N-1 VCk max(Tk, VCk).

11
Physical clock synchronization

• Question 1.Why is physical clock synchronization
  important?
• Question 2.With atomic clocks becoming
  affordable, should we care about physical clock
  synchronization? Cant we use GPS?

12
Classification

• Types of Synchronization
• External Synchronization
• Internal Synchronization
• Phase Synchronization

• Types of clocks
• Unbounded 0, 1, 2, 3, . . .
• Bounded 0, 1, 2, . . . M-1, 0, 1, . . .
• Unbounded clocks are not realistic, but are
  easier to deal with in algorithms

13
Terminologies

• What are these?
• Drift rate ?
• Clock skew ?
• Resynchronization interval R
• Challenges
• (Drift is unavoidable)
• Accounting for propagation delay
• Processing delay
• Faulty clocks

14
Internal synchronization

• A simple averaging algorithm

• Step 1. Read every clock in the system.
• Step 2. Discard outliers and substitute them by
  the value of the local clock.
• Step 3. Update the clock using the average of
  these values.
• Synchronization is maintained if
• n gt 3t1
• where t is the number of faulty
• (may be 2-faced) clocks. Why?

Some clocks may be faulty
15
Internal synchronization

• A simple averaging algorithm

• If there are t faulty clocks, then
• the maximum difference between
• the averages computed by two
• non-faulty nodes is be 3td /n
• To keep the clocks synchronized,
• 3td /n lt d
• So, 3t lt n

Some clocks may be faulty
16
Cristians method

• Client pulls data from a time server.
• For accuracy, it computes the round
• trip time (RTT), and compensates for this
• delay while adjusting its own clock

Time server
17
Network Time Protocol

• Tiered architecture

• Broadcast mode
• -least accurate
• Procedure call
• -medium accuracy
• Peer-to-peer mode
• -higher level servers
• use this for max accuracy

Time server
18
P2P mode of NTP

• Let Qs time be ahead of Ps time by ?. Then
• T2 T1 TPQ ?
• T4 T3 TQP - ?
• RTT y TPQ TQP T2 T4 -T1 -T3
• ? (T2 -T4 -T1 T3) / 2 -(TPQ - TQP) / 2
• Ping several times, and obtain the smallest value
  of y. Use it to calculate ?

T2
T3
Q
P
T1
T4
x
Between y/2 and -y/2