Outline
• Theoretical Foundations - continued
– Vector clocks - review
– Casual ordering of messages
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Announcements
• This is no TA for this class
– I will do the grading and everything else by myself
• Homework #1 is due this Thursday, Feb. 6, 2003
– Turn your homework in hardcopy
– For the last problem, attach a hardcopy of your
program
• Lab 1 will be assigned today
– You can work as a team with most two members on
each team
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Lamport’s Logical Clocks – review
• Implementation rules
– [IR1] Clock Ci is incremented between any two
successive events in process Pi
Ci := Ci + d ( d > 0)
– [IR2] If event a is the sending of message m by
process Pi, then message m is assigned a
timestamp tm = Ci(a). On receiving the same
message m by process Pj, Cj is set to
Cj := max(Cj, tm + d)
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An Example
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Total Ordering Using Lamport’s Clocks
• If a is any event at process Pi and b is any
event at process Pj, then a => b if and only if
either
Ci (a)  C j (b) or
Ci (a)  C j (b) and Pi  Pj
– Where  is any arbitrary relation that totally
orders the processes to break ties
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A Limitation of Lamport’s Clocks - review
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Vector Clocks
• Implementation rules
– [IR1] Clock Ci is incremented between any two
successive events in process Pi
Ci[i] := Ci[i] + d ( d > 0)
– [IR2] If event a is the sending of message m by
process Pi, then message m is assigned a
timestamp tm = Ci(a). On receiving the same
message m by process Pj, Cj is set to
Cj[k] := max(Cj[k], tm[k])
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Vector Clocks – cont.
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Vector Clocks – cont.
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Vector Clocks – cont.
• Assertion
– At any instant,
i, j : Ci [i]  C j [i]
• Events a and b are casually related if ta < tb or tb
< ta. Otherwise, these events are concurrent
• In a system of vector clocks,
a  b iff t  t
a
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Causal Ordering of Messages
• The causal ordering of messages tries to
maintain the same causal relationship that
holds among “message send” events with the
corresponding “message receive” events
– In other words, if Send(M1) -> Send(M2), then
Receive(M1) -> Receive(M2)
– This is different from causal ordering of events
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Causal Ordering of Messages – cont.
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Causal Ordering of Messages – cont.
• The basic idea
– It is very simple
– Deliver a message only when no causality
constraints are violated
– Otherwise, the message is not delivered
immediately but is buffered until all the
preceding messages are delivered
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Birman-Schiper-Stephenson Protocol
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Schiper-Eggli-Sando Protocol
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Schiper-Eggli-Sando Protocol – cont.
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Schiper-Eggli-Sando Protocol – cont.
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Regarding Lab 1
• For this project, you can work as a team with
at most two members per team
– Each team only needs to turn in one report
– However, all the members are required to
understand all the parts as you may be tested on
the midterm or the final exam
• Three processes
– Bank Account Server
– Bank Office Clients
– Bank Office Mutual Exclusion Processes
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