Time
This powerpoint presentation has been adapted from:
1) www.cse.buffalo.edu/~bina/cse486/.../TimeGlobalState
sApr20.ppt
Contents
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

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Introduction
Clocks, events and process states
Synchronizing physical clocks
Logical time & logical clocks
Contents




Introduction
Clocks, events and process states
Synchronizing physical clocks
Logical time & logical clocks
Time
Introduction
 Why time is important in distributed
systems?
A quantity that needs to be measured
accurately
• to know at what time of day a particular event
occurred at a particular computer
• is important for auditing purposes
• to maintain the consistency of distributed data
Contents




Introduction
Clocks, events and process states
Synchronizing physical clocks
Logical time & logical clocks
Time
 Clocks, events and process states
 How to timestamp events in terms of
their execution?
Consider the following notations
•ϸ
– A collection of N processes pi, i = 1,2, .. N (p executes on a
single processor)
• si
– The state of pi (each p has a state, the state changed when
it is executed)
• Actions of pi
– Operations that transform pi’s state (p executes with a
series of actions.
– Send or receive message between pi
Time
 Clocks, events and process states
e
• Event: occurrence of a single action
Relation between the events(i)
• The series of events for a single process p
• e.g., e i e` : e occurs before e` at pi
history(pi ) = hi = <ei0, ei1, ei2, …>
• The series of event e in process pi
Time
 Clocks, events and process states
 How to timestamp the events (e)?
Clock in computer:
• Each computer has its own physical clock
• Is a device that counts oscillations occurring in a
crystal at a definite frequency
• The OS reads the node’s hardware time: Hi(t)
» The counts of oscillation since an original point
• Then, scale it and add offset to produce software
clock, Ci(t) = Hi(t)+
» To timestamp of an event
Time
 Clocks, events and process states
 Computer clocks tend not to be in a perfect
agreement.
Netw ork
Clock drift
• Clocks count time at different rates
Clock skew
• The instantaneous (direct) difference between the
readings of any two clocks
Why? Oscillators are subject to physical variations
• Frequency, temperature
Time
 Clocks, events and process states
 How to synchronize computer clocks?
Use external source that provide highly accurate
time
Use atomic oscillator
Used by International Atomic Time
Time
 Clocks, events and process states
 What is the international standard for time
keeping?
Coordinated Universal Time (UTC)
• Based on atomic time
• Time is coordinated with astronomical time
• UTC signal is broadcasted from land-based radio station to
satellites covering many parts of the world
Contents




Introduction
Clocks, events and process states
Synchronizing physical clocks
Logical time & logical clocks
Time
Synchronizing physical clocks
 How to know at what time of the day an
event occurs?
Two types of synchronization:
• External
• Internal
Notations:
• Ci : pi’s clock
• I : an interval of real time
Time
Synchronizing physical clocks
 External synchronization
 For a synchronization bound D > 0, and for a source S of
UTC time, |S(t)-Ci(t)| < D, for i = 1, 2, … N and for all real
times t in I
 Clocks Ci are accurate to within the bound D
 Internal synchronization
 For a synchronization bound D > 0, |Ci(t)-Cj(t)| < D for i,
j =1,2, … N, and for all real times t in I
 Clocks Ci agree within the bound D
 Clocks that are internally synchronized are not necessarily
externally synchronized
 If the system ϸ is externally synchronized with a bound D, then the
same system is internally synchronized with a bound of 2D.
Time
Synchronizing physical clocks
 Synchronization in a synchronous system
 there will be a minimum time of transmission where no other
processes executed at the same time and no other network traffic
existed.
 Maximum time of transmission in synchronous mode is always set
(i.e., time out is applied)
 Protocol
• Sender: send M(t)
• Receiver: set time to t + Ttrans
 Bounds are known in synchronous system
• min < Ttrans < max (constant)
 Optimum transmission time,
• Ttrans = (min+max) / 2
• Receiver’s clock = t + (min+max) / 2
t
t + min
t +Ttrans
t+max
Time
Synchronizing physical clocks
 The common practice in distributed system is
asynchronous;
The factors lead to message delay are not bounded
(no upper bound max)
The Internet is asynchronous
Ttrans = min + x, where x ≥ 0, the value of x is not
known
Methods for synchronizing clock in asynchronous
distributed systems:
• Cristian’s method
• The Berkeley algorithms
• The Network Time Protocol
Time
Synchronizing physical clocks
 Cristian’s method of synchronizing clocks
 Use time server
 Protocol
• mr – process p requests the time from server
• mt – process receives the time (t is inserted in the
message)
• Tround - process p records the round-trip (send requestget reply)
• Estimated time: t + Tround/2
mr
p
mt
Time server,S
Time
Synchronizing physical clocks
 Cristian’s method of synchronizing
clocks
Accuracy analysis
• If the minimum delay of a message transmission is
min, then accuracy: (Tround/2 – min)
t + min
t
t +Tround-min
t +Tround/2
t +Tround
Time and Global State
Synchronizing physical clocks
 The Berkeley algorithms
Internal synchronization using a coordinator
computer (master). Other computers that their
clocks need to be synchronized is known as
slaves
1.
2.
3.
4.
5.
The master polls the slaves’ clocks
The master estimates the slaves’ clocks by roundtrip time
The master averages the slaves’ clock values
The master sends back to the slaves the amount
that the slaves’ clocks should adjust
Slave adjust its clock
Time
Synchronizing physical clocks
 The Network Time Protocol (NTP)
An architecture for a time service and a protocol to
distribute time information over the Internet
Aims:
• External synchronization
– Enable clients across the Internet to be synchronized
accurately to UTC
• Reliability
– Can survive lengthy losses of connectivity
» Redundant server & redundant path between servers
• Scalability
– Enable clients to resynchronize sufficiently frequently to offset
the rates of drift found in most computers
• Security
– Protect against interference with the time service
Time
Synchronizing physical clocks
 NTP service is provided by servers located
across the Internet
Primary servers are connected directly to a time
source, e.g. radio clock receiving UTC
Secondary servers are synchronized to primary
servers
Time
Synchronizing physical clocks
 Network Time Protocol Architecture
1
2
3
2
3
3
Note: Arrows denote synchronization control, numbers denote strata.
Source: Wikipedia
Time
Synchronizing physical clocks
 3 modes of NTP synchronization:
Multicast mode
• Intended for use on a high speed LAN
• One or more servers multicast the time to other servers in
the LAN
• Low accuracy but sufficient
Procedure-call mode
• Similar to Christian’s
• Higher accuracy than multicast
Symmetric mode
• Use by the servers that supply time information in LANs
• The highest accuracy
Contents




Introduction
Clocks, events and process states
Synchronizing physical clocks
Logical time & logical clocks
Time
Logical time and logical clocks
 Events in a single process is ordered
uniquely by times shown in the local clock
 Clock is unable to be synchronized perfectly.
Hence physical time is not accurate to
determine the occurrence of events
Time
Logical time and logical clocks
 Happened-before relation
It is also sometimes known as the relation of
causal ordering or potential causal ordering.
Time
Logical time and logical clocks
 Logical clocks- a simple mechanism to capture HB
order numerically. Known as Lamport timestamps
algorithm (it is a software counter).
LC1
• Li is incremented before each event is issued
at process pi : Li :=Li+1
LC2:
(a) When a process pi sends a message m, it
adjoin the value t = Li on m
(b) On receiving (m,t), a process Pj computes
Lj := max(Lj, t) and then applies LC1 before
timestamping the event receive(m)
Time
Logical time and logical clocks
 Totally ordered logical clocks algorithm
Assumption
Ti : local timestamp of e that is an event
occurring at pi
Tj : local timestamp of e` that is an event
occurring at pj
The timestamps of two events e and e` are (Ti, i), (Tj, j)
When (Ti, i) < (Tj, j), if and only if Ti < Tj , or Ti = Tj and i < j
Time
Logical time and logical clocks
 Vector Clocks algorithm
Each process pi keeps a vector clock Vi
VC1: Initially, Vi[j]=0, for i, j = 1,2…, N
VC2: Just before pi timestamps an event, it sets
Vi[i] := Vi[i] +1
VC3: pi includes the value t= Vi in every message it
sends
VC4: When pi receives a timestamp t in a message,
it sets Vi[j] :=max(Vi[j], t[j]), for j=1,2…,N
End of the Chapter…