Global Time in Distributed Real-Time Systems

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Global Time in Distributed Real-Time Systems

• Dr. Konstantinos Tatas

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OUTLINE

• Revision of real-time system
• Distributed real-time system requirements
• Global time
• Clock synchronization

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What is real-time? Is there any other kind?

• A real-time computer system is a computer system
  where the correctness of the system behavior
  depends not only on the logical results of the
  computations, but also on the physical time when
  these results are produced.
• By system behavior we mean the sequence of
  outputs in time of a system.

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Real-time means reactive

• A real-time computer system must react to stimuli
  from its environment
• The instant when a result must be produced is
  called a deadline.
• If a result has utility even after the deadline
  has passed, the deadline is classified as soft,
  otherwise it is firm.
• If severe consequences could result if a firm
  deadline is missed, the deadline is called hard.
• Example Consider a traffic signal at a road
  before a railway crossing. If the traffic signal
  does not change to red before the train arrives,
  an accident could result.

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Distributed RT system model

• From the POV of an outside observer, a real-time
  (RT) system can be decomposed into three
  communicating subsystems
• a controlled object (the physical subsystem, the
  behavior of which is governed by the laws of
  physics),
• a distributed computer subsystem (the cyber
  system, the behavior of which is governed by the
  programs that are executed on digital computers)
• a human user or operator
• The distributed computer system consists of
  computational nodes that interact by the exchange
  of messages.
• A computational node can host one or more
  computational components.

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Design Challenges in Distributed Systems

• Theoretically, a distributed system features the
  same design challenges as a centralized embedded
  system in terms of performance, power
  consumption, battery life, etc.
• However, an additional challenge exists
  synchronization between nodes

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Definition of time

• Newtonian physics time model is adequate for most
  temporal phenomena and is much simpler than
  relativistic time
• Time is modeled as an infinite set T with the
  following properties
• T is an ordered set, that is, if p and q are
  any two instants, then either p is simultaneous
  with q, or p precedes q, or q precedes p, where
  these relations are mutually exclusive. We call
  the order of instants on the timeline the
  temporal order.
• T is a dense set. This means that there is at
  least one q between p and r iff p is not the same
  instant as r, where p, q, and r are instants.

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Events in the time model

• A section of the time line between two different
  instants is called a duration.
• An event takes place at an instant of time and
  does not have a duration.
• If two events occur at the same instant, then the
  two events are said to occur simultaneously.
• Instants are totally ordered however, events are
  only partially ordered,
• Events can be totally ordered if another
  criterion is introduced to order events that
  occur simultaneously

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Causal order

• In many real time systems determining cause and
  effect relations between events is of interest,
  especially determining the primary event
• Temporal order is necessary but not sufficient to
  establish causal order

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Global time

• An important yet challenging task is maintaining
  a consistent global time in a distributed
  real-time system
• There is no global clock, only local clocks
• Local clocks drift arbitrarily
• No local clock is always correct
• A global time is an abstract notion that is
  approximated by properly selected microticks from
  the synchronized local physical clocks of an
  ensemble.

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Global time

• Assume a set of nodes, each one with its own
  local physical clock that ticks with
  granularity . Assume that all of the clocks are
  internally synchronized with a precision ?, i.e.,
  for any two clocks j, k, and all microticks i
• It is then possible to select a subset of the
  microticks of each local clock k for the
  generation of the local implementation of a
  global notion of time.
• We call such a selected local microtick i a
  macrotick (or a tick) of the global time.
• For example, every tenth microtick of a local
  clock k may be interpreted as the global tick,
  the macrotick , of this clock (see Fig. 3.2).
• If it does not matter at which clock k the
  (macro) tick occurs, we denote the tick ti
  without a superscript.
• A global time is thus an abstract notion that is
  approximated by properly selected microticks from
  the synchronized local physical clocks of an
  ensemble.

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Reasonable global time

• The global time t is called reasonable, if all
  local implementations of the global time satisfy
  the condition
• ggt?
• Then for a single event e, that is observed by
  any two different clocks of the ensemble, their
  global time-stamps can differ by at most one
  tick.
• This is the best we can achieve.

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Temporal order

• When to events differ by less than two ticks
  temporal order cannot be maintained

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Errors in duration measurement
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Internal clock synchronization

• The purpose of internal clock synchronization is
  to ensure that the real-time clocks of each
  correct node are within precision ?,
  independently of their drift rates.
• The global time ticks of each node must be
  periodically resynchronized within the ensemble
  of nodes to establish a global time base with
  specified precision.
• The period of resynchronization is called
  resynchronization interval. After that the clocks
  are left to drift again until they are
  resynchronized.

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Internal clock synchronization

• The synchronization algorithm must bring the
  clocks so close together that the amount of
  divergence during the next free-running
  resynchronization interval will not cause a clock
  to leave the precision interval.
• FG?
• Where F is the convergence function and G is the
  drift offset
• F2?Rint
• Where Rint is the length of the resynchronization
  interval and ? is the maximum specified drift rate

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Malicious clock

• clock synchronization can only be guaranteed in
  the presence of Byzantine errors if the total
  number of clocks N (3k 1), where k is the
  number of Byzantine faulty clocks.

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Central Master Synchronization

• the central master, periodically sends the value
  of its time counter in synchronization messages
  to all other nodes
• the slave records the time-stamp of message
  arrival.
• The difference between the masters time,
  contained in the synchronization message, and the
  recorded slaves time-stamp of message arrival,
  corrected by the known latency of the message
  transport, is a measure of the deviation of the
  clock of the master from the clock of the slave.
• The slave then corrects its clock by this
  deviation to bring it into agreement with the
  masters clock.
• Used at system startup
• Not fault-tolerant

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External clock synchronization

• External synchronization links the global time of
  a cluster to an external standard of time.
• For this purpose it is necessary to access a
  timeserver, i.e., an external time source that
  periodically broadcasts the current reference
  time in the form of a time message.
• GPS (Global Positioning System).
• The accuracy of a GPS receiver is better than 100
  ns and it has an authoritative long-term
  stability in some sense, GPS is the worldwide
  measurement standard for measuring the
  progression of time. Alternatively, the external
  time source can
• temperature compensated crystal oscillators
  (TCXO)
• Typical drift rate of better than 1 ppm, causing
  a drift offset of better 1 µs/s
• atomic clocks
• Rubidum clock typical drift rate in the order of
  10-12 causing a drift offset of about 1 µs in 10
  days.

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Example 1

• Given a clock synchronization system that
  achieves a precision of 90 µs, what is a
  reasonable granularity for the global time?
• What are the limits for the observed values for a
  time interval of 1.1 ms?

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Example 2

• Given a
• latency jitter of 20 µs,
• a clock drift rate of 10-5 s/s, and
• a resynchronization period of 1 s
• what precision can be achieved by the central
  master algorithm?

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Example 3

• A distributed system uses GPS for clock
  synchronization
• What is the reasonable granularity for the global
  time?
• What are the limits for the observed values for a
  time interval of 200 ms?

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References

• H. Kopetz, Real time systems Design principles
  for distributed systems Springer
• Kopetz, H. W. Ochsenreiter. (1987). Clock
  Synchronization in Distributed Real-Time Systems.
  IEEE Trans. Computers. Vol. 36(8). (pp. 933-940).
• Kopetz, H. (1992). Sparse Time versus Dense Time
  in Distributed Real-Time Systems. Proc. 14th Int.
  Conf. on Distributed Computing Systems. IEEE
  Press. (pp. 460-467).