Clock Synchronization Nonanimated

Synchronizing Physical Clocks

Neeraj Mittal

The University of Texas at Dallas

August 9, 2012

Motivation

Types of Clock SynchronizationExternal SynchronizationInternal Synchronization

Algorithms for Clock SynchronizationCristians AlgorithmThe Berkeley AlgorithmNetwork Time Protocol (NTP)

Table of Contents

Motivation



Motivation

Applications such as real time object tracking need physicalclocks to work properly

Most hardware clocks have a non-zero drift rate

A clock with maximum drift rate of satisfies the followingproperty:

C (t): value of clock C at real time t t1 and t2: two instants of real time with t1 t2 Then

(1 )(t2 t1) C (t2) C (t1) (1 + )(t2 t1)

Typically, 106 seconds/second After 4 months, clock may have an error of 10.37 seconds

Although relative error is bounded, absolute error may growwith time

Table of Contents

Motivation



External Synchronization

Clocks of processes are synchronized with an external clock

External clock is assumed to be accurate (e.g., CoordinatedUniversal Time source)

Formal definition: S : clock of the server Ci : clock of process Pi , for i = 1, 2, . . . ,N D: constant Clocks are said to be externally synchronized if:

For all processes Pi , and for all real times t: |Ci (t)S(t)| D

Interpretation: Clocks are accurate to within the bound D

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Motivation



Internal Synchronization

Clocks of processes are synchronized with each other

Formal definition: Ci : clock of process Pi , for i = 1, 2, . . . ,N D: constant Clocks are said to be internally synchronized if:

For all pairs of processes Pi and Pj , and for all real times t:|Ci (t) Cj(t)| D

Interpretation: Clocks agree within the bound D

Internally synchronized clocks may show inaccurate time

Externally synchronized clocks are also internally synchronized

Table of Contents

Motivation



Cristians Algorithm

Client

Server

Client

Server

Client

Server

s

Server

Cristians Algorithm (Contd.)

Clients hardware may have a non-zero drift Drift introduces error in the estimation of the round trip time A typical hardware clock has maximum drift rate of only 106

seconds/second Any error in the estimate will be negligible if the round trip

time is small and can be ignored

Estimate of the current clock value of the server assumesrequest and reply messages incurred the same delay

Actual clock value of the server (when reply message isreceived by the client) can vary from s to s +Tround dependingon the actual delay incurred by request and reply messages

Skew in clients clock value just after synchronization lies in

the range Tround

2

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Motivation



The Berkeley Algorithm

Performs internal synchronization

Master-slave approach: One of the machines is chosen as master Other machines become slaves

Algorithm is polling based: Master periodically requests all slaves to send their clock values It then estimates the current clock value of each slave by

observing the round-trip time (similar to Cristians algorithm)

The Berkeley Algorithm (Contd.)

Slave S

Master

t1

Slave S

Master

t2

c

t1

Slave S

Master

t3t2t1

Master

The Berkeley Algorithm (Contd.)

Slaves

compute the average

Master

Master computes the average of all (estimated) clock valuesincluding its own once it has received clock values from allslaves

To each slave, it sends the amount by which the slaves clockrequires adjustment

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Motivation



Network Time Protocol

Used for distributing time information over the Internet

Service is provided by a network of servers arranged in ahierarchical manner

Servers at highest-level (root) are primary servers Directly connected to a time source (e.g., radio clock receiving

UTC)

Servers at lowest-level (leaf) are users workstations Servers at each level are synchronized with servers at a higher

level (to prevent cycles)

Clock accuracy decreases as level decreases

Network Time Protocol (Contd.)

A

B

A

B

A

B

B


Notation: o: actual offset of B s clock relative to that of As clock 1: transmission time for the first message 2: transmission time for the second message : total transmission time for the two messages oe : estimate of o

1 = Tr1 (T

s1 + o)

2 = (Tr2 + o) T

s2

= 1 + 2 = Tr1 T

s1 + T

r2 T

s2

Set oe asT r1 T

s1 + T

s2 T

r2

2


Subtracting 1 from 2, we obtain:

o = oe +2 1

2

This implies that:

|o oe | |2 1|

2

|2 + 1|

2=

2

Interpretation: oe is an estimate of oe with error bounded by

2

Client A computes many (oe , /2) pairs: Selects offset estimate with the least error for clock adjustment

MotivationTypes of Clock SynchronizationExternal SynchronizationInternal Synchronization

Algorithms for Clock SynchronizationCristian's AlgorithmThe Berkeley AlgorithmNetwork Time Protocol (NTP)

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Clock Synchronization Nonanimated