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Synchronization

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									  Synchronization
          in
Distributed Systems
     Chapter 6
Guide to Synchronization Lectures
• Synchronization in shared memory systems
  (2/19/09)
• Event ordering in distributed systems (2/24)
  – Logical time, logical clocks, time stamps,
• Mutual exclusion in distributed systems
  (2/26)
• Election algorithms (3/3)
• Data race detection in multithreaded
  programs (3/5)
              Background
• Synchronization: coordination of actions
  between processes.
• Processes are usually asynchronous, (operate
  without regard to 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 easy if you can accurately
    time stamp events, but in a distributed system
    the clocks may not always be synchronized
  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: the difference in time values
  between different physical clocks
• If an application expects the time associated
  with a file, message, or other object to be correct
  (independently of its local clock), clock skew can
  lead to failure.
 Various Ways of Measuring Time
• The sun
  – Mean solar second – gradually getting longer
• 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)
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)
  – 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 determine 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
      Lamport‟s Logical Time
• Leslie Lamport suggested the following
  method to order events in a distributed
  system.
• "Events" are defined by the application. The
  granularity may be as coarse as a
  procedure or as fine-grained as a single
  instruction.
             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
Happened Before Relation (a  b)
• a  b: (page 244-245)
  – in the same [sequential] process/thread,
  – in different processes, (messages)
  – transitivity: if a  b and b  c, then a  c
• 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.
         Concurrent Events
• Happened-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

• For 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, set its time-
  stamp tsm to Ci, the time of the send event
  after following previous step.
• When the message is received the local time
  must be greater than tsm . The rule is (Cj =
  max{Cj, tsm} + 1).
• Clock management can be handled as a
  middleware protocol
       Lamport‟s Logical Clocks (2)
Event a: P1 sends m1                             Event c: P3
to P2 at t = 6,                                  sends m3 to P2
Event b: P2 receives                             at t = 60
m1 at t = 16.                                    Event d: P2
If C(a) is the time m1                           receives m3 at t
was sent, and C(b) is                            = 56
the time m1 is                                   Do C(c) and C(d)
received, do C(a) and                            satisfy the
C(b) satisfy the                                 conditions?
correctness conditions
?




     Figure 6-9. (a) Three processes, each with its own clock.
     The clocks “run” at different rates.
   Lamport‟s Logical Clocks (3)




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 mi is received
   message

                            Network Layer


Figure 6-10. The positioning of Lamport‟s logical clocks in distributed systems
Figure 5.3 (Advanced Operating Systems,Singhal and Shivaratri)
How Lamport‟s logical clocks advance

            e11     e12         e13     e14      e15      e16     e17
   P1




    P2      e21           e22     e23            e24            e25




            Which events are causally related?
            Which events are concurrent?
                                                       eij represents event j
                                                       on processor i
       A Total Ordering Rule
• A total ordering of events can be obtained
  if we ensure that no two events 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
Figure 5.3 - Singhal and Shivaratri


           e11    e12         e13     e14   e15   e16    e17
   P1




    P2     e21          e22     e23         e24         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
             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”?
• Problem: lack of consistency.
  – Both values should be the same
• Solution: make sure both sites see/process
  the messages in the same order.
    Implementing Total Order
• Assumptions:
  – Updates are multicast to all sites, including
    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 numbers
            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 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.
• 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.
       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 comes first.
• Lamport clocks do not capture causality
Figure 5.4
                                  Time

Space
                e11               e12
        P1      .                (2)
                (1)


        P2            e21                e22
                        (1)                (3)


                  e31          e32               e33
        P3
                  (1)             (2)            (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.
• 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.
• Then deliver the message to the application.
Figure 5.5. Singhal and Shivaratri


P1    (1, 0 , 0)            (2, 0, 0)                              (3, 5, 2)
          e11                      e12                             e13



           (0, 1, 0)                                          (2,4,2)    (2, 5, 2)
                              (2, 2, 0)     (2, 3, 1)
 P2
                e21                       e22           e23     e24      e25




                       (0, 0, 1)                (0, 0, 2)
 P3
                           e31                     e32
         Establishing Causal Order
• If event a has timestamp ts(a), then ts(a)[i]-1 is the
  number of events at Pi that causally preceded a.
• 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(e23) = (2, 3, 1). Two events in P1
  and one event in P3 “happened before” e23.
   – Even though P1 and P3 may have executed other events,
     they don‟t have a causal effect on e23.
Happened Before/Causally Related
 Events - Vector Clock Definition
• Events a and b are causally related if
   – ts(a) < ts(b) or
   – ts(b) < ts(a)
• Otherwise, we say the events are concurrent.
• a → b iff ts(a) < ts(b)
  (a happens before b iff the timestamp of a is less
  than the timestamp of b)
• 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 or equal: ts(a) ≤ ts(b) if each
  component of ts(a)[i] is ≤ ts(b)[i]
• Equal: ts(a) = ts(b) iff every component in ts(a)[i]
  is equal to ts(b)[i] . (In this case a and b are the
  same events)
• Less than: ts(a) < ts(b) iff ts(a) is less than or
  equal to ts(b) , but ts(a) is not equal ts(b) . In other
  words, at least one component of ts(a) is strictly
  less than the corresponding component of ts(b) .
• Concurrent: ts(a) || ts(b) if ts(a) isn‟t less than
  ts(b) and ts(b) isn‟t less than ts(a) .
Figure 5.4
                                     Time


                    e11             e12
      P1                           (2)
                     (1)


      P2              e21                   e22
                          (1)                  (3)


                   e31            e32                e33
      P3
                    (1)             (2)              (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, 3, 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 all that 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[i] to max{VCi[i] , ts(m)[k]} for each k.
   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 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)                 (1, 1, 0)
           m
P1
                      (1, 1, 0)
                        VC1 m*

P2
                              (0, 0, 0)   (1, 0, 0)   (1, 1, 0)
                                VC2         VC2         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.
      Revised Lecture Schedule
•   10/14: Finished L12, started L13
•   10/16: L13 + start L14
•   10/21: L14 + L15
•   10/23: L16: Detecting Race Conditions in
    Multithreaded Programs.
    – This lecture is based on papers 10 and 11
      from the reading list.

								
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