Physical Clocks

1
Physical Clocks
2
Topics

• Physical Clocks
• Clock Synchronization Algorithms

3
Readings

• Van Steen and Tanenbaum 5.1
• Coulouris 10.3

4
Introduction

• Electronic clocks in most servers and network
  devices keep inaccurate time.
• Small errors can add up over a long period.
• Assume two clocks are synchronized on January 1.
• One of the clocks consistently takes an extra
  0.04 milliseconds to increment itself by a
  second.
• On December 31 the clocks will differ by 20
  minutes

5
Introduction

• In some instances it is acceptable to measure
  time with some accuracy
• When we try to determine how many minutes left in
  an exam
• Making a soft boiled egg
• We can be relaxed about time in some instances
• The time it takes to drive to Toronto
• The number of hours studied for an exam

6
Introduction

• However, for many applications more precision is
  needed.
• Example Telecommunications
• Accurate timing is needed to ensure that the
  switches routing digital signals through their
  networks all run at the same rate.
• If not, slow running switches would not be able
  to cope with traffic and messages would be lost.

7
Introduction

• Example Global Positioning System (GPS)
• Ship, airplane and car navigation use GPS to
  determine location.
• GPS satellites that orbit Earth broadcast timing
  signals from their clocks.
• By looking at the signal from four (or more)
  satellites, the users position can be
  determined.
• Any tiny error could put you off course by a very
  long way.
• A nanosecond of error translates into a GPS error
  of one foot.

8
Introduction

• Other
• Need to know when a transaction occurs
• Equipment on a factory floor may need to know
  when to turn on or off equipment.
• Billing services
• E-mail sorting can be difficult if time stamps
  are incorrect
• Tracking security breaches
• Secure document transmissions

9
Clock Synchronization

• In a centralized system
• Time is unambiguous. A process gets the time by
  issuing a system call to the kernel. If process
  A gets the time and later process B gets the time
  then the value B gets is higher than (or possibly
  equal to) the value A got.
• Example UNIX make examines the times at which
  all the source and object files were last
  modified.
• If time (input.c) time(input.o) then recompile
  input.c
• If time (input.c) compilation is needed.

10
Clock Synchronization

• In a distributed system, achieving agreement on
  time is not easy.
• Assume no global agreement on time. Lets see
  what happens
• Assume that the compiler and editor are on
  different machines
• output.o has time 2144
• output.c is modified but is assigned time 2143
  because the clock on its machine is slightly
  behind.
• Make will not call the compiler.
• The resulting executable will have a mixture of
  object files from old and new sources.

11
Clock Synchronization

• When each machine has its own clock, an event
  that occurred after another event may
  nevertheless be assigned an earlier time.

12
Clock Synchronization

• Another example
• File synchronization after disconnected operation
• Synchronize workstation and laptop copies of
  402-a1.c
• Disconnect laptop
• Make some changes to 402-a1.c on the laptop.
• Reconnect and re-sync, hopefully copying laptop
  version over the workstation version.
• If laptops clock is behind workstation, the copy
  might go the other way around

13
Clocks

• Clocks should be synchronized. The question is
  this Is it possible to do so?
• A computer has a timer, not a clock.
• A timer is a precisely machined quartz crystal
  oscillating at a frequency that depends on how
  the crystal was cut and the amount of tension.

14
Clocks

• Two registers are associated with the crystal a
  counter and a holding register.
• Each oscillation of the crystal decrements the
  counter by one. When counter is 0, an interrupt
  is generated.
• Each interrupt is called a clock tick.
• At each clock tick, the interrupt procedure adds
  one to the time stored in memory. The counter is
  reinitialized by the value in the holding
  register.
• A timer can be programmed to generate an
  interrupt n times per second.

15
Clocks

• On each of the computers, the crystals will run
  at slightly different frequencies, causing the
  software clocks gradually to get out of sync.
  This is called clock skew or clock drift.
• Ordinary quartz clocks drift by 1 sec in 11-12
  days. (10-6 secs/sec).
• High precision quartz clocks drift rate is 10-7
  or 10-8 secs/sec

16
Physical Clocks

• Two problems
• How do we synchronize computer clocks with
  real-world clocks?
• How do we synchronize the computer clocks with
  each other?
• To answer these questions, we have to understand
  how time is measured.

17
Physical Clocks

• Since the invention of mechanical clocks (17th
  century) time is measured astronomically (mean
  solar day, mean solar second).
• The event of the suns reaching its highest
  apparent point is called transit of the sun.
• This event occurs at about noon each day.
• The interval between two consecutive transits of
  the sun is called the solar day.

18
Physical Clocks

• There are 24 hours in a day
• Each hour contains 3600 seconds.
• Each day contains 86400 seconds
• The solar second is defined as exactly 1/86400th
  of a solar day.

19
Physical Clocks

• Computation of the mean solar day.

20
Physical Clocks

• In the 1940s it was established that the period
  of the earths rotation is not constant.
• It is believed that 300 million years ago there
  were about 400 days per year.
• The length of the year (the time for one trip
  around the sun) is not thought to have changed
  the day has simply become longer.
• Short term variations in the length of the day
  also occur.

21
Physical Clocks

• Astronomers now compute the length of the day by
  measuring a large number of days and taking the
  average before dividing by 86,400. This is
  called the mean solar second.
• The invention of the atomic clock in 1948 made it
  easier to measure time more accurately.
• This is done by counting the transitions
  (changing energy state) of the cesium 133 atom. A
  second is defined as the time it takes the cesium
  133 atom to make exactly 9,192,631,770
  transitions.

22
Physical Clocks

• The atomic time is computed to make the atomic
  second equal to the mean solar second (in the
  year of its introduction in 1958).
• Currently about 50 labs have cesium 133 clocks.
• Each of them periodically tells the BIH (Bureau
  International d lHeure) in Paris how many times
  its clock ticked.
• BIH averages these values. This is referred to as
  International Atomic Time (TAI).

23
Universal Coordinated Time

• TAI is stable and available to anyone who wants
  to go to the trouble of buying a cesium clock.
• Problem86,400 TAI seconds is now about 3 msec
  less than a mean solar day since a solar day is
  getting longer.
• Using TAI means that over the course of years,
  noon would get earlier and earlier, until it
  would eventually occur in the wee hours of the
  morning.

24
Universal Coordinated Time

• Since the mean solar day gets longer, the BIH
  made necessary corrections ( by introducing leap
  seconds) resulting in Universal Coordinated Time
  (UTC).
• UTC is provided to those who need precise time
• National Institute of Standard Time (NIST)
  operates a shortwave radio station with call
  letters WWV from Fort Collins, Colorado with 1
  to 1 msec accuracy.
• Earth satellites also offer a UTC service
  accurate to 0.5 msec
• By telephone from NIST cheaper but less
  accurate.
• Need to compensate for signal propagation delay.

25
Physical Clock Coordination

• If one machine has a WWV receiver, the goal
  becomes keeping all the other machines
  synchronized to it.
• If no machines have WWV receivers, each machine
  keeps track of its own time the goal is to keep
  the machines synchronized.

26
Physical Clock Synchronization

• Model of system assumed by clock synchronization
  algorithms
• When UTC is t, the value of the clock on machine
  p is Cp(t).
• In a perfect world, Cp(t) t for all p and all
  t.
• dC/dt denotes the ratio of the change in the
  clock time to actual time.
• In perfect world dC/dt should be one

27
Physical Clock Coordination

• The relation between clock time and UTC when
  clocks tick at different rates.

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Physical Clock Coordination

• Each clock has a maximum drift rate ?.
• 1-? ?? dC/dt
• In time ?t a clock may drift ??t
• Assume two clocks are synchronized at time t.
  Assume that the clocks drift the maximum possible
  in ?t in opposite directions. In ?t, they
  are2??t apart.
• To limit drift to ?
• 2rDt?
• Dt? /(2r).
• resynchronize every d/2r seconds

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Christians Algorithm

• One time server (WWV) receiver all other
  machines stay synchronized with the time server.
• Periodically ( no more than ?/2? seconds), each
  machine sends a message to the time server asking
  for the current time.
• Time server machine responds with CUTC

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Cristian's Algorithm

• Getting the current time from a time server.

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Christians Algorithm

• CUTC could be smaller then requestors clock.
  Must not set the clock backwards (would this work
  for the makefile example?).
• Suppose that a timer is set to generate 100
  interrupts per second.
• Each interrupt would add 10 msec to the time.
• Instead the interrupt routine could add only 9
  msec each time until the correction has been
  made.
• A clock can be advanced gradually by adding 11
  msec at each interrupt.

32
Christians Algorithm

• Problem with client setting the clock to CUTC
• It takes a nonzero amount of time for the time
  servers reply to get back to the sender.
• The delay may be large and it varies with network
  load.
• T0 Starting time of the clients request
• T1 be the time that the client receives an
  answer (measured using the same clock).
• The best estimate of the message passing
  propagation time is this (T1-T0)/2
• The new time should be CUTC (T1-T0)/2

33
Christians Algorithm

• Problem with client setting the clock to CUTC
  (continued)
• Also should take into account time it takes the
  time server to handle the interrupt and process
  the incoming message. This is the interrupt
  handle time, I.
• The new time should be based on T1-T0 -I
• Christian suggested sending several messages and
  the fastest reply would be the most accurate
  since it presumably encountered the least traffic.

34
Christians Algorithm

• Single server may fail and thus render
  synchronization impossible (on a temporary
  basis).
• Christian suggests a group of synchronized time
  servers, each with a receiver for UTC time
  signals.
• A client multicasts its request to all servers
  and uses only the first reply obtained.

35
Christians Algorithm

• A faulty time server or an imposter time server
  that replied with deliberately incorrect times,
  could wreak havoc in a computer systems.
• It has been shown that if f is the number of
  faulty clocks out of a total of N, then we must
  have N 3f.
• The problem with faulty clocks is partially
  addressed by the Berkeley algorithm.

36
Berkeley Algorithm

• Suitable when no machine has a WWV receiver.
• The time server (daemon) is active
• Time daemon polls every machine periodically to
  ask what time is there
• Based on the answers, it computes an average time
• Tells all other machines to advance their clocks
  to the new time or slow their clocks down until
  some specified reduction has been achieved.
• Propagation is taken into account.
• The time daemons time is set manually by
  operator periodically.

37
The Berkeley Algorithm

• The time daemon asks all the other machines for
  their clock values using a polling mechanism and
  providing current time
• The machines answer indicating how they differ
  from time sent.
• The time daemon tells everyone how to adjust
  their clock based on a calculation of the
  average time value.

38
The Berkeley Algorithm

• The master takes a fault-tolerant average.
• A subset of clocks is chosen that do not differ
  from one another by more than a specified amount
  and the average is taken of readings from only
  these clocks.
• Should the master fail, then another can be
  elected (discussed later) using one of the
  election algorithms.

39
Network Time Protocols (NTP)

• Christians method and Berkeley algorithm
  intended for intranets
• NTP intended to provide the ability to externally
  synchronize clients across the Internet to UTC.

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Network Time Protocol (NTP)

• The NTP service is provided by a network of
  servers located across the Internet.
• Primary servers receive UTC.
• Secondary servers are synchronized with primary
  servers.
• The servers are connected in a logical hierarchy
  called a synchronization subnet whose levels are
  called strata.

41
An example synchronization subnet in an NTP
implementation
42
Network Time Protocols (NTP)

• Layered client-server architecture, based on UDP
  message passing.
• The clocks belonging to servers with high stratum
  numbers are liable to be less accurate than those
  with low stratum numbers since errors are
  introduced at each level of synchronization.
• If a strata 1 server fails, it may become a
  strata 2 server that is being synchronized
  through another strata 1 server.
• Accuracy range of 1-50 msec

43
Network Time Protocols (NTP)

• A 1999 survey of NTP servers shows the following
• 175,000 servers running NTP in the Internet
• 300 are stratum 1 servers
• Over 20,000 are stratum 2 servers
• Over 80,000 are stratum 3 servers

44
Using Coordination Algorithms

• Cristians method and the Berkeley algorithm are
  intended primarily for use within an intranet.
• NTP is intended for the Internet.

45
Is it Enough to Synchronize Physical Clocks?

• Values received by a UTC receiver is accurate
  within a range.
• At best we can synchronize clocks to within 10-30
  milliseconds of each other.
• We have to synchronize frequently, to avoid clock
  drift.
• The synchronization algorithms are good, but not
  always sufficient.

46
Is it Enough to Synchronize Physical Clocks?

• Replication of data and processing is an approach
  often used for reliability and performance
  reasons.
• Reliability
• If one replica is unavailable or crashes, use
  another
• Avoid single points of failure
• Performance
• Placing copies of data close to the processes
  using them can improve performance through
  reduction of access time.
• If there is only one copy, then the server could
  become overloaded.

47
Is it Enough to Synchronize Physical Clocks?

• Problems with replication include
• Whenever a copy is modified, that copy becomes
  different from the rest.
• Modifications have to be carried out on all
  copies to ensure consistency.
• Assume that update 1 is issued at 1000 and
  update 2 is issued at 10000001.
• Due to network delays, replica 2 receives update
  2 before update 1.
• How is replica 2 to know that there is an earlier
  update?