Distributed Systems Foundations
Lecture 1
Main Characteristics of Distributed
Systems
• Independent processors,
sites, processes
• Message passing
• No shared memory
• No shared clock
• Independent failure
modes
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Distributed System Models
• Synchronous System: Known bounds on times
for message transmission, processing , bounds
on local clock drifts, etc.
– Can use timeouts
• Asynchronous System: No known bounds on
times for message transmission, processing,
bounds on local clock drifts, etc.
– More realistic, practical, but no timeout.
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CAUSALITY AND TIME
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What is a Distributed System?
• A simple model of a distributed system
proposed by Lamport in a landmark 1978
paper:
• “Time, Clocks and the Ordering of Events in a
Distributed System” Communications of the
ACM
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What is a Distributed System?
• A set of processes that communicate using
message passing.
• A process is a sequence of events
• 3 kinds of events:
– Local events
– Send events
– Receive events
• Local events on a process for a total order.
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Example of a Distributed System
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Happens Before or Causal Order
on Events
• Event e happens before (causally precedes)
event f, denoted e → f if:
1. The same process executes e before f ; or
2. e is send(m) and f is receive(m); or
3. Exists h so that e → h and h → f
• We define concurrent, e || f, as:
¬(e → f  f → e)
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Lamport Logical Clocks
• Assign “clock” value to each event such that
– if ab then clock(a) < clock(b)
• Assign each process a clock “counter”.
– Clock must be incremented between any two events
in the same process
– Each message carries the sender’s clock value
• When a message arrives set local clock to:
– max(local value, message timestamp + 1)
– This clock forms a partial order. If a total order is
needed use process ids to break ties—totally
ordered Lamport (or Logical) Clocks
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Example of a Logical Clock
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Vector clocks
1. Vector initialized to 0 at each process
Vi [j] = 0 for i, j =1, …, N
2. Process increments its element of the vector
in local vector before event:
Vi [i] = Vi [i] +1
3. Piggyback Vi with every message sent from
process Pi
4. When Pj receives message, compares vectors
element by element and sets local vector to
higher of two values
Vj [k] = max(Vj [k], Vi [k]) for k=1, …, N
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Comparing vector timestamps
Define
V = V’ iff V [i ] = V’[i ] for i = 1 … N
V  V’ iff V [i ]  V’[i ] for i = 1 … N
For any two events e, e’
e  e’ if and only if V(e) < V(e’)
Two events are concurrent if neither
V(e)  V(e’) nor V(e’)  V(e)
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Vector Clock Example
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Clock Synchronization
• Assume each process p has a physical clock Cp.
• Assume an accurate time source providing
Universal Coordinated Time (UCT)—atomic
clock or GPS.
• Clock Synchronization:
– Keep all clocks in a distributed system close to
each other, ie, synchronized.
• If UCT is t, and value of clock at process p is
Cp(t) then ideally, Cp(t) = t, ie, dCp(t)/dt = 1.
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Clock Synchronization
• The internal timer causes an interrupt h times
a second.
• When interrupt occurs, clock is incremented,
and clock keeps times since it was initialized.
• In reality, timers have drift ρ
therefore: 1- ρ =< dCp(t)/dt =< 1+ ρ
• Two clocks can drift 2 ρ Δt after Δt.
• If we want clocks not to differ by more than δ,
then resynch at least every δ/2ρ secs
Cristian’s Clock Synch Algorithm
[Distributed Computing 1989]
• A processor p requests time from UTC.
• UTC sends back current time t.
• What does p set local clock to?
t + Tround/2
• Tround = treceive –tsend.
• Assume minimum time is min.
• Error: +/- [Tround/2 –min]
• Time must be monotonic. What if t is less
than current time at p?
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