Logical Clocks 2

1
Logical Clocks (2)
2
Topics

• Logical clocks
• Totally-Ordered Multicasting
• Vector timestamps

3
Readings

• Van Steen and Tanenbaum 5.2
• Coulouris 10.4
• L. Lamport, Time, Clocks and the Ordering of
  Events in Distributed Systems, Communications of
  the ACM, Vol. 21, No. 7, July 1978, pp. 558-565.
• C.J. Fidge, Timestamps in Message-Passing
  Systems that Preserve the Partial Ordering,
  Proceedings of the 11th Australian Computer
  Science Conference, Brisbane, pp. 56-66, February
  1988.

4
Problems with Lamport Clocks

• Lamport timestamps do not capture causality.
• With Lamports clocks, one cannot directly
  compare the timestamps of two events to determine
  their precedence relationship.
• If C(a) lt C(b) is not true then a ? b is also not
  true.
• Knowing that C(a) lt C(b) is true does not allow
  us to conclude that a ? b is true.
• Example In the first timing diagram, C(e) 1
  and C(b) 2 thus C(e) lt C(b) but it is not the
  case that e ? b

5
Problems with Lamport Clocks

• Why is this important?
• For the banking example, it doesnt matter what
  order operations are executed at each replica.
• It only matters that all replicas execute the
  operations in the same order. This is total
  order.
• Causal order is used when a message received by a
  process can potentially affect any subsequent
  message sent by that process. Those messages
  should be received in that order at all
  processes. Unrelated messages may be delivered
  in any order.
• Do Lamport timestamps support causal order?
• NO

6
Example ApplicationBulletin Board

• The Internets electronic bulletin board service
  (network news)
• Users (processes) join specific groups
  (discussion groups).
• Postings, whether they are articles or reactions,
  are multicast to all group members.
• Could use a totally-ordered multicasting scheme.
• Should be doing this?

7
Display from a Bulletin Board Program

• Users run bulletin board applications which
  multicast messages
• One multicast group per topic (e.g.
  os.interesting)
• Require reliable multicast - so that all members
  receive messages
• Ordering

Bulletin board
os.interesting
From
Subject
Item
23
A.Hanlon
Mach


24
G.Joseph
Microkernels
25
A.Hanlon
Re Microkernels
26
T.LHeureux
RPC performance
Figure 11.13 Colouris
27
M.Walker
Re Mach
end

8
Example Application Bulletin Board

• A totally-ordered multicasting scheme does not
  imply that if message B is delivered after
  message A, that B is a reaction to A.
• Totally-ordered multicasting is too strong in
  this case.
• The receipt of an article precedes the posting of
  a reaction.
• The receipt of the reaction to an article should
  always follow the receipt of the article.

9
Example Application Bulletin Board

• If we look at the bulletin board example, it is
  allowed to have items 26 and 27 in different
  order at different sites.
• Items 25 and 26 may be in different order at
  different sites.

10
Problem with Lamport Clocks

• The main problem is that a simple integer clock
  cannot order both events within a process and
  events in different processes.
• C. Fidge developed an algorithm that overcomes
  this problem.
• Fidges clock is represented as a vector
  v1,v2,,vn with an integer clock value for each
  process (vi contains the clock value of process
  i). This is a vector timestamp.

11
Fidges Algorithm

• Properties of vector timestamps
• vi i is the number of events that have occurred
  so far at Pi
• If vi j k then Pi knows that k events have
  occurred at Pj

12
Fidges Algorithm

• The Fidges logical clock is maintained as
  follows
• Initially all clock values are set to the
  smallest value (e.g., 0).
• The local clock value is incremented at least
  once before each event in a process, q i.e.,
  vqq vqq 1
• Let vq be piggybacked on the message sent by
  process q to process p We then have
• For i 1 to n do
• vpi max(vpi, vq i )
• vpp vpp 1

13
Fidges Algorithm

• For two vector timestamps, va and vb
• va ? vb if there exists an i such that vai ?
  vbi
• va vb if for all i vai vbi
• va lt vb if for all i vai vbi AND va is not
  equal to vb
• Events a and b are causally related if va lt vb or
  vblt va .

14
Example
P2
P1
P3
0,1,0
e
a
1,0,0
0,0,1
j
b
2,0,0
f
2,2,0
k
3,0,0
c
0,0,2
g
2,3,2
d
4,0,0
2,4,2
h
0,0,3
l
i
4,5,2
15
Causality and Modified Vector Timestamps

• What I just presented is the original Fidges
  vector timestamp.
• With a slight adjustment, vector timestamps can
  be used to guarantee causal message delivery.
• We will illustrate this adjustment, the
  definition of causality and the motivation
  through an example.

16
Example Application Bulletin Board

• Vector timestamps can be used to guarantee causal
  message delivery.
• Each process Pi has an array Vi where Vij
  denotes the number of events that process Pi
  knows have taken place for Pj.
• In this application events refers to the
  sending of a message.
• Thus if Vij 6 then Pi knows that Pj has sent
  6 messages.

17
Example Application Bulletin Board

• Vector timestamps are assumed to be updated only
  when posting or receiving articles i.e., when a
  message is sent or received.
• Let Vq be piggybacked on the message sent by
  process Pq to process Pp When process Pp
  receives the message, then Pp does the following
• For i 1 to n do
• Vpi max(Vpi, Vq i )
• Thus if process q knows that process i sent 5
  messages (Vq i 5 and Vpi 3) then process p
  didnt know about the latest two messages sent by
  process i.

18
Example Application Bulletin Board

• When p sends a message, it does the following
• Vpp Vpp 1
• This is basically saying that the number of
  messages process p has sent is incremented by
  one.

19
Example Application Bulletin Board

• When a process Pi posts (sends) an article, it
  multicasts that article with timestamp Vi
• Process Pj posts a reaction. Lets call this
  message r. Assume that the value of the timestamp
  is Vj
• Note that Vj gt Vi
• Message r may arrive at Pk before message a.
• Pk will postpone delivery of r to the display of
  the bulletin board until all messages that
  causally precede r have been received as well.

20
Example Application Bulletin Board

• Message r (from Pj ) is delivered to Pk iff the
  following conditions are met
• Vjj Vkj1
• This condition is satisfied if r is the next
  message that Pk was expecting from process Pj
• Assume that Vkj5. This means that Pk knows Pj
  sent 5 messages and that it should be waiting for
  the 6th message.
• If Vjj 8 then messages 6,7 are lost.
• Vji Vki for all i not equal to j
• This condition is satisfied if Pk has seen at
  least as many messages as seen by Pj when it sent
  message r.
• Assume for some i that Vji 2 and Vki 1
  and thus Vji gt Vki for some i. This
  indicates that Pi sent a message that was
  received by Pj but not Pk

21
Example Application Bulletin Board
0,0,0
P2
P1
P3
0,0,0
0,0,0
Post a
1,0,0
a
e
1,0,0
1,0,0
c
1,0,1
r Reply a
d
g
b
1,0,1
1,0,1
Message a arrives at P2 before the reply r from
P3 does
22
Example Application Bulletin Board
0,0,0
P2
P1
P3
0,0,0
0,0,0
Post a
1,0,0
a
d
1,0,0
g
1,0,1
r Reply a
Buffered
b
c
1,0,1
1,0,0
Deliver r
The message a arrives at P2 after the reply from
P3 The reply is not delivered right away.
23
Summary

• No notion of a globally shared clock.
• Local (physical) clocks must be synchronized
  based on algorithms that take into account
  network latency.
• Knowing the absolute time is not necessary.
• Logical clocks can be used for ordering purposes.