Outline
• Theoretical Foundations - continued
– Lab 1
• Lamport’s algorithm for distributed mutual exclusion
–
–
–
–
Casual ordering of messages – continued
Global state
Cuts
Termination detection
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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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Lamport’s Clock
• 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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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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Lamport’s Distributed Mutual Exclusion Algorithm
• This algorithm is based on the total ordering using
Lamport’s clocks
– Each process keeps a Lamport’s logical clock
• Each process is associated with a unique id that can be used
to break the ties
– In the algorithm, each process keeps a queue,
request_queuei, which contains mutual exclusion
requests ordered by their timestamp and associated id
– Ri of each process consists of all the processes
– The communication channel is assumed to be FIFO
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Lamport’s Distributed Mutual Exclusion Algorithm – cont.
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Lamport’s Distributed Mutual Exclusion Algorithm – cont.
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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.
• In a system of vector clocks,
a  b iff t  t
a
b
where
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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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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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Global State
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Local State
• Local state
– For a site Si, its local state at a given time is
defined by the local context of the distributed
application, denoted by LSi.
• More notations
– mij denotes a message sent by Si to Sj
– send(mij) and rec(mij) denote the corresponding
sending and receiving event.
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Definitions – cont.
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Definitions – cont.
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Global State – cont.
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Definitions – cont.
Strongly consistent global state:
A global state is strongly consistent
if it is consistent and transitless
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Global State – cont.
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Chandy-Lamport’s Global State Recording Algorithm
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Cuts of a Distributed Computation
• A cut is a graphical representation of a global
state
– A consistent cut is a graphical representation of a
consistent global state
• Definition
– A cut of a distributed computation is a set C={c1,
c2, ...., cn}, where ci is a cut event at site Si in
the history of the distributed computation
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Cuts of a Distributed Computation – cont.
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Cuts of a Distributed Computation – cont.
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Cuts of a Distributed Computation – cont.
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Cuts of a Distributed Computation – cont.
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Cuts of a Distributed Computation – cont.
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Termination Detection
• Termination detection is to detect when a
distributed algorithm is terminated, such as
election, a deadlock detection, or token
generating algorithm
– A process can be active or idle
– A computation is said to have terminated if and only if
all the processes are idle and there are no messages in
transit
– Basic idea
• We are not going to cover the algorithm in detail
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Summary
• The absence of global time and the absence of shared
memory are two main characteristics of distributed
systems
– Two schemes, Lamport’s logical clocks and vector clocks are
used to order events
– Two algorithms for causal ordering of messages based on the
vector clock-based ideas are discussed
– Global states and cuts of a distributed system are also
covered
– These provide the theoretical foundations for other
distributed algorithms
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