Synchronization
in
Distributed Systems
Chapter 6
Guide to Synchronization Lectures
• Synchronization in shared memory systems
• Event ordering in distributed systems
– Logical time, logical clocks, time stamps,
• Mutual exclusion in distributed systems
– Centralized, decentralized, etc.
– Election algorithms
• Data race detection in multithreaded
programs
Background
• Synchronization: coordination of actions
between processes.
• Processes are usually asynchronous, (operate
independent of events in other processes)
• Sometimes need to cooperate/synchronize
– For mutual exclusion
– For event ordering (was message x from process P
sent before or after message y from process Q?)
Introduction
• Synchronization in centralized systems is
primarily accomplished through shared
memory
– Event ordering is clear because all events are
timed by the same clock
• Synchronization in distributed systems is
harder
– No shared memory
– No common clock
Clock Synchronization
• Some applications rely on event ordering
to be successful
– See page 232 for some examples
– Event ordering is easier if you can accurately
time-stamp events, but in a distributed system
the clocks may not always be synchronized
• Is it possible to synchronize clocks in a
distributed system?
Physical Clocks - pages 233-238
• Physical clock example: counter + holding
register + oscillating quartz crystal
–
–
–
–
The counter is decremented at each oscillation
Counter interrupts when it reaches zero
Reloads from the holding register
Interrupt = clock tick (often 60 times/second)
• Software clock: counts interrupts
– This value represents number of seconds since some
predetermined time (Jan 1, 1970 for UNIX systems;
beginning of the Gregorian calendar for Microsoft)
– Can be converted to normal clock times
Clock Skew
• In a distributed system each computer has
its own clock
• Each crystal will oscillate at slightly
different rate.
• Over time, the software clock values on
the different computers are no longer the
same.
Clock Skew
• Clock skew(offset): the difference between
the times on two different clocks
• Clock drift : the difference between a clock
and actual time
• Ordinary quartz clocks drift by ~ 1sec in
11-12 days. (10-6 secs/sec)
• High precision quartz clocks drift rate is
somewhat better
Various Ways of Measuring Time*
• The sun
– Mean solar second – gradually getting longer as
earth’s rotation slows.
• International Atomic Time (TAI)
– Atomic clocks are based on transitions of the cesium
atom
– Atomic second = value of solar second at some fixed
time (no longer accurate)
• Universal Coordinated Time (UTC)
– Based on TAI seconds, but more accurately reflects
sun time (inserts leap seconds to synchronize atomic
second with solar second)
Getting the Correct (UTC) Time*
• WWV radio station or similar stations in
other countries (accurate to +/- 10 msec)
• UTC services provided by earth satellites
(accurate to .5 msec)
• GPS (Global Positioning System)
(accurate to 20-35 nanoseconds)
Clock Synchronization Algorithms*
• In a distributed system one machine may
have a WWV receiver and some technique
is used to keep all the other machines in
synch with this value.
• Or, no machine has access to an external
time source and some technique is used
to keep all machines synchronized with
each other, if not with “real” time.
Clock Synchronization Algorithms
• Network Time Protocol (NTP):
– Objective: to keep all clocks in a system synchronized to
UTC time (1-50 msec accuracy) – not so good in WAN
– Uses a hierarchy of passive time servers
• The Berkeley Algorithm:
– Objective: to keep all clocks in a system synchronized to
each other (internal synchronization)
– Uses active time servers that poll machines periodically
• Reference broadcast synchronization (RBS)
– Objective: to keep all clocks in a wireless system
synchronized to each other
Three Philosophies of Clock
Synchronization
• Try to keep all clocks synchronized to
“real” time as closely as possible
• Try to keep all clocks synchronized to
each other, even if they vary somewhat
from UTC time
• Try to synchronize enough so that
interacting processes can agree upon an
event order.
– Refer to these “clocks” as logical clocks
6.2 Logical Clocks
• Observation: if two processes (running on
separate processors) do not interact, it
doesn’t matter if their clocks are not
synchronized.
• Observation: When processes do interact,
they are usually interested in event order,
instead of exact event time.
• Conclusion: Logical clocks are sufficient
for many applications
Formalization
• The distributed system consists of n
processes, p1, p2, …pn (e.g, a MPI group)
• Each pi executes on a separate processor
• No shared memory
• Each pi has a state si
• Process execution: a sequence of events
– Changes to the local state
– Message Send or Receive
Two Versions
• Lamport’s logical clocks: synchronizes
logical clocks
– Can be used to determine an absolute
ordering among a set of events although the
order doesn’t necessarily reflect causal
relations between events.
• Vector clocks: can capture the causal
relationships between events.
Lamport’s Logical Time
• Lamport defined a “happens-before”
relation between events in a process.
• "Events" are defined by the application. The
granularity may be as coarse as a
procedure or as fine-grained as a single
instruction.
Happened Before Relation (a  b)
• a  b: (page 244-245)
– in the same [sequential] process,
– send, receive in different processes,
(messages)
– transitivity: if a  b and b  c, then a  c
• If a  b, then a and b are causally related;
i.e., event a potentially has a causal effect
on event b.
Concurrent Events
• Happens-before defines a partial order of
events in a distributed system.
• Some events can’t be placed in the order
• a and b are concurrent (a || b) if
!(a  b) and !(b  a).
• If a and b aren’t connected by the
happened-before relation, there’s no way
one could affect the other.
Logical Clocks
• Needed: method to assign a “timestamp” to
event a (call it C(a)), even in the absence of a
global clock
• The method must guarantee that the clocks
have certain properties, in order to reflect the
definition of happens-before.
• Define a clock (event counter), Ci, at each
process (processor) Pi.
• When an event a occurs, its timestamp ts(a) =
C(a), the local clock value at the time the event
takes place.
Correctness Conditions
• If a and b are in the same process, and
a  b then C (a) < C (b)
• If a is the event of sending a message
from Pi, and b is the event of receiving the
message by Pj, then Ci (a) < Cj (b).
• The value of C must be increasing (time
doesn’t go backward).
– Corollary: any clock corrections must be
made by adding a positive number to a time.
Implementation Rules
• Between any two successive events a & b in
Pi, increment the local clock (Ci = Ci + 1)
– thus Ci(b) = Ci(a) + 1
• When a message m is sent from Pi, set its
time-stamp tsm to Ci, the time of the send
event after following previous step.
• When the message is received at Pj the local
time must be greater than tsm . The rule is
(Cj = max{Cj, tsm} + 1).
Lamport’s Logical Clocks (2)
Event a: P1 sends m1
to P2 at t = 6,
Event b: P2 receives
m1 at t = 16.
If C(a) is the time m1
was sent, and C(b) is
the time m1 is
received, do C(a) and
C(b) satisfy the
correctness conditions
?
Figure 6-9. (a) Three processes, each with its own clock.
The clocks “run” at different rates.
Lamport’s Logical Clocks (3)
Event c: P3
sends m3 to
P2 at t = 60
Event d: P2
receives m3
at t = 56
Do C(c) and
C(d) satisfy
the
conditions?
Figure 6-9. (b) Lamport’s algorithm corrects the clocks.
Application Layer
Application sends message mi
Deliver mi to application
Adjust local clock,
Timestamp mi
Adjust local clock
Middleware layer
Middleware sends
message
Message mi is received
Network Layer
Figure 6-10. The positioning of Lamport’s logical clocks in distributed systems
Handling clock management as a middleware operation
Figure 5.3 (Advanced Operating Systems,Singhal and Shivaratri)
How Lamport’s logical clocks advance
P1
P2
e11
e21
e12
e13
e22
e14
e23
e15
e24
e16
e17
e25
Which events are causally related?
Which events are concurrent?
eij represents event j
on processor i
A Total Ordering Rule
(does not guarantee causality)
• A total ordering of events can be obtained
if we ensure that no two events happen at
the same time (have the same timestamp).
• Why? So all processors can agree on an
unambiguous order.
• How? Attach process number to low-order
end of time, separated by decimal point;
e.g., event at time 40 at process P1 is
40.1,event at time 40 at process P2 is 40.2
Figure 5.3 - Singhal and Shivaratri
P1
P2
e11
e21
e12
e13
e22
e23
e14
e15
e24
e16
e17
e25
What is the total ordering of the events in these
two processes?
Example: Total Order Multicast
• Consider a banking database, replicated
across several sites.
• Queries are processed at the
geographically closest replica
• We need to be able to guarantee that DB
updates are seen in the same order
everywhere
Totally Ordered Multicast
Update 1: Process 1 at Site A adds $100 to an
account, (initial value = $1000)
Update 2: Process 2 at Site B increments the
account by 1%
Without synchronization,
it’s possible that
replica 1 = $1111,
replica 2 = $1110
• Message 1: add $100.00
Message 2: increment account by 1%
• The replica that sees the messages in the
order m1, m2 will have a final balance of
$1111
• The replica that sees the messages in the
order m2, m1 will have a final balance of
$1110
The Problem
• Site 1 has final account balance of $1,111
after both transactions complete and Site 2
has final balance of $1,100.
• Which is “right”? Either, from the standpoint
of consistency.
• Problem: lack of consistency.
– Both values should be the same
• Solution: make sure both sites see/process
all messages in the same order.
Implementing Total Order
• Assumptions:
– Updates are multicast to all sites, including
(conceptually) the sender
– All messages from a single sender arrive in
the order in which they were sent
– No messages are lost
– Messages are time-stamped with Lamport
clock values.
Implementation
• When a process receives a message, put
it in a local message queue, ordered by
timestamp.
• Multicast an acknowledgement to all sites
• Each ack has a timestamp larger than the
timestamp on the message it
acknowledges
• The message queue at each site will
eventually be in the same order
Implementation
• Deliver a message to the application only when
the following conditions are true:
– The message is at the head of the queue
– The message has been acknowledged by all other
receivers. This guarantees that no update messages
with earlier timestamps are still in transit.
• Acknowledgements are deleted when the
message they acknowledge is processed.
• Since all queues have the same order, all sites
process the messages in the same order.
Causality
• Causally related events:
– Event a may causally affect event b if a  b
– Events a and b are causally related if either
a  b or b  a.
– If neither of the above relations hold, then
there is no causal relation between a & b. We
say that a || b (a and b are concurrent)
Vector Clock Rationale
• Lamport clocks limitation:
– If (ab) then C(a) < C(b) but
– If C(a) < C(b) then we only know that either
(ab) or (a || b), i.e., b a
• In other words, you cannot look at the clock
values of events on two different processors
and decide which one “happens before”.
• Lamport clocks do not capture causality
Lamport’s Logical Clocks (3)
m2 ’
m3 ’
Figure 6-12.
Suppose we add a message to the
scenario in Fig. 6.12(b).
• Tsnd(m1) < Tsnd(m3’).
(6) < (32)
• Does this mean
send(m1)  send(m3’)?
But …
• Tsnd(m1) < Tsnd(m2’).
(6) < (20)
• Does this mean
send(m1)  send(m2)?
Figure 5.4
Time
Space
P1
P2
e11
.(1)
e12
(2)
e21
e22
(1)
P3
e31
(1)
(3)
e32
(2)
e33
(3)
C(e11) < C(e22) and C(e11) < C(e32) but while e11  e22, we cannot say
e11  e32 since there is no causal path connecting them. So, with
Lamport clocks we can guarantee that if C(a) < C(b) then
b
a , but by looking at the clock values alone we cannot say
whether or not the events are causally related.
Vector Clocks – How They Work
• Each processor keeps a vector of values,
instead of a single value.
• VCi is the clock at process i; it has a component
for each process in the system.
– VCi[i] corresponds to Pi‘s local “time”.
– VCi[j] represents Pi‘s knowledge of the “time”
at Pj (the # of events that Pi knows have
occurred at Pj
• Each processor knows its own “time” exactly,
and updates the values of other processors’
clocks based on timestamps received in
messages.
Implementation Rules
• IR1: Increment VCi[i] before each new event.
• IR2: When process i sends a message m it sets
m’s (vector) timestamp to VCi (after incrementing
VCi[i])
• IR3: When a process receives a message it
does a component-by-component comparison of
the message timestamp to its local time and
picks the maximum of the two corresponding
components. Adjust local components
accordingly.
• Then deliver the message to the application.
Review
• Physical clocks: hard to keep synchronized
• Logical clocks: can provide some notion of
relative event occurrence
• Lamport’s logical time
–
–
–
–
happened-before relation defines causal relations
logical clocks – don’t capture causality
total ordering relation
use in establishing totally ordered multicast
• Vector clocks
– Unlike Lamport clocks, vector clocks capture causality
– Have a component for each process in the system
Figure 5.5. Singhal and Shivaratri
P1
(1, 0 , 0)
(2, 0, 0)
e11
P2
(0, 1, 0)
e21
(3, 0, 0)
e12
e13
(2, 2, 0)
e22
(0, 0, 1)
P3
e31
(2, 3, 1)
e23
(0, 0, 2)
e32
(4, 5, 2)
e14
(2,4,2)
e24
(2, 5, 2)
e25
(0, 0, 3)
e33
Vector clock values. In a 3- process system, VC(Pi) = vc1, vc2, vc3
Establishing Causal Order
• When Pi sends a message m to Pj, Pj knows
– How many events occurred at Pi before m was sent
– How many relevant events occurred at other sites before
m was sent (relevant = “happened-before”)
• In Figure 5.5, VC(e24) = (2, 4, 2). Two events in P1
and two events in P3 “happened before” e24.
– Even though P1 and P3 may have executed other events,
they don’t have a causal effect on e24.
Happened Before/Causally Related
Events - Vector Clock Definition
• a → b iff ts(a) < ts(b)
(a happens before b iff the timestamp of a is less
than the timestamp of b)
• Events a and b are causally related if
– ts(a) < ts(b) or
– ts(b) < ts(a)
• Otherwise, we say the events are concurrent.
• Any pair of events that satisfy the vector clock
definition of happens-before will also satisfy the
Lamport definition, and vice-versa.
Comparing Vector Timestamps
• Less than: ts(a) < ts(b) iff at least one
component of ts(a) is strictly less than the
corresponding component of ts(b) and all
other components of ts(a) are either less
than or equal to the corresponding
component in ts(b).
• (3,3,5) ≤ (3,4,5), (3, 3, 3) ═ (3, 3, 3),
(3,3,5) ≥ (3,2,4), (3, 3 ,5) | | (4,2,5).
Figure 5.4
Time
e11
P1
P2
(1, 0, 0)
e12
(2, 0, 0)
e21
e22
(0, 1, 0)
P3
e31
(0, 0,1)
(2, 2, 0)
e32
(0, 0, 2)
e33
(0, 0, 3)
ts(e11) = (1, 0, 0) and ts(e32) = (0, 0, 2), which shows that the
two events are concurrent.
ts(e11) = (1, 0, 0) and ts(e22) = (2, 2, 0), which shows that
e11
e22
Causal Ordering of Messages
An Application of Vector Clocks
• Premise: Deliver a message only if
messages that causally precede it have
already been received
– i.e., if send(m1)  send(m2), then it should be
true that receive(m1)  receive(m2) at each
site.
– If messages are not related (send(m1) ||
send(m2)), delivery order is not of interest.
Compare to Total Order
• Totally ordered multicast (TOM) is
stronger (more inclusive) than causal
ordering (COM).
– TOM orders all messages, not just those that
are causally related.
– “Weaker” COM is often what is needed.
Enforcing Causal Communication
• Clocks are adjusted only when sending or
receiving messages; i.e, these are the only
events of interest.
• Send m: Pi increments VCi[i] by 1 and
applies timestamp, ts(m).
• Receive m: Pi compares VCi to ts(m); set
VCi[k] to max{VCi[k] , ts(m)[k]} for each k,
k ≠ i.
Message Delivery Conditions
• Suppose: PJ receives message m from Pi
• Middleware delivers m to the application iff
– ts(m)[i] = VCj[i] + 1
• all previous messages from Pi have been delivered
– ts(m)[k] ≤ VCi[k] for all k ≠ i
• PJ has received all messages that Pi had seen before
it sent message m.
• In other words, if a message m is received
from Pi, you should also have received
every message that Pi received before it
sent m; e.g.,
– if m is sent by P1 and ts(m) is (3, 4, 0) and you
are P3, you should already have received
exactly 2 messages from P1 and at least 4
from P2
– if m is sent by P2 and ts(m) is (4, 5, 1, 3) and if
you are P3 and VC3 is (3, 3, 4, 3) then you
need to wait for a fourth message from P2 and
at least one more message from P1.
Figure 6-13. Enforcing Causal Communication
P0
VC0
VC0
(1, 0, 0)
m
(1, 1, 0)
P1
(1, 1, 0)
VC1 m*
P2
(0, 0, 0)
VC2
(1, 0, 0)
VC2
(1, 1, 0)
VC2
P1 received message m from P0 before sending
message m* to P2; P2 must wait for delivery of m
before receiving m*
(Increment own clock only on message send)
Before sending or receiving any messages, one’s
own clock is (0, 0, …0)
History
• ISIS and Horus were middleware systems
that supported the building of distributed
environments through virtually
synchronous process groups
• Provided both totally ordered and causally
ordered message delivery.
– “Lightweight Causal and Atomic Group Multicast”
– Birman, K., Schiper, A., Stephenson, P, ACM Transactions on
Computer Systems, Vol 9, No. 3, August 1991, pp 272-314.
Location of Message Delivery
• Problems if located in middleware:
– Message ordering captures only potential causality;
no way to know if two messages from the same
source are actually dependent.
– Causality from other sources is not captured.
• End-to-end argument: the application is better
equipped to know which messages are causally
related.
• But … developers are now forced to do more
work; re-inventing the wheel.