云计算基础分布式时间与时钟
文世挺 博士 浙江大学宁波理工学院(SL605-2)
wensht@nit.zju.edu.cn
15058033236
2014.2.21
物理时间
分布式系统中时间戳作用？






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准确度量系统性能
保证数据“up-to-date”和正确性
并发处理程序的时序事件逻辑排序
消息发送端和接收端的同步
联合活动协调
共享对象并发存取的串行化
……
3
物理时间 Physical time

Solar time (太阳时)




1 sec = 1 day / 86400
Problem: days are of different
lengths (due to tidal friction, etc.)
mean solar second: averaged over
many days
Greenwich Mean Time
(GMT 格林尼治)


The mean solar time at Royal
Observatory in Greenwich, London
Greenwich located at longitude 0,
the line that divides east and west
4
协调世界时间Coordinated Universal
Time (UTC)
国际原子时(TAI: International atomic time)




1 秒  Cesium-133 原子发生 9,192,631,770 次状态转变
TAI time is simply the number of Cesium-133 transitions since
midnight on Jan 1, 1958.
Accuracy: better than 1 second in six million years
Problem: Atomic clocks do not keep in step with solar time
协调世界时间Coordinated Universal Time (UTC)


Based on the atomic time (TAI) and introduced from 1 Jan 1972
A leap second is occasionally inserted or deleted to keep in step with
solar time when the difference btw a solar-day and a TAI-day is over
800ms
5
计算机时钟 Computer Clocks

石英振荡器驱动CMOS时钟电路



电脑关机情况下是通过电池供电驱动CMOS时钟
电路
时钟电路主要由两部分组成：计数器（counter）
和寄存器（register）。石英振荡器每震荡一次，
计数器减1；当计数器为0时产生一个中断，同
时从寄存器重新读取数值。不停重复。。。
操作系统（OS）捕获中断信号维护计算机时
钟


e.g., 60 or 100中断为1sec
可编程中断控制器Programmable Interrupt Controller
(PIC)
CPU
counter
register
6
时钟漂移和偏移Clock drift and
clock skew

时钟漂移Clock Drift

Clocks tick at different rates




Ordinary quartz clocks drift
by ~ 1sec in 11-12 days.
(10-6 secs/sec).
High precision quartz clocks
drift rate is ~ 10-7 or 10-8
secs/sec
Create ever-widening gap in
perceived time
时钟偏移（补偿）Clock
Skew (offset)

Difference between two
clocks at one point in time
7
(完美时钟)Perfect clock
8
Drift with a slow computer clock
9
Drift with a fast computer clock
10
Dealing with drift

No good to set a clock backward


Illusion of time moving backwards can confuse
message ordering and software development
environments
Go for gradual clock correction


If fast: Make clock run slower until it synchronizes
If slow: Make clock run faster until it synchronizes
11
线性补偿函数Linear compensating
function

操作系统可以调整中断的频
率


e.g.: if the system generates
an interrupt every 17 ms but
clock is too slow: generates
an interrupt at (e.g.) 15 ms
调整系统时间的斜率
Adjustment changes slope of
system time: Linear
compensating function
12
再同步Resynchronization

同步周期After synchronization period is reached



周期性再同步(Resynchronize periodically), or
当斜率达到阈值时同步(The skew is beyond a threshold)
主动调节时间
UNIX adjtime system call:
int adjtime(struct timeval *delta, struct timeval *old-delta)
 adjusts the system's notion of the current time, advancing
or retarding it, by the amount of time specified in the struct
timeval pointed to by delta. “old-delta”, output parameter,
returns time left uncorrected since last call of “adjtime”

13
Getting UTC from Top Sources

在每个计算机上安装GPS接收器


连接 WWV (http://tf.nist.gov) 无线接收器



误差：± 1 ms of UTC
从Boulder or DC 获取时间广播
误差：± 3 ms of UTC (depending on distance)
安装 GOES 接收器 (Geostationary Operational
Environmental Satellites,
http://www.goes.noaa.gov/)

误差：± 0.1 ms of UTC
Not practical for every machine
– Cost, size, convenience, environment
14
Getting UTC for Client Computers

Client Computer 和 time server 同步时间



和更准确的时钟同步，or
和UTC时间源同步（connected to UTC time
source）
Also called external clock synchronization
15
Synchronizing Clocks by using RPC

Simplest synchronization technique


Make an RPC to obtain time from the server
Set the local clock to the server time
What’s the time?
server
client
10:25:18
没有考虑网络延迟
16
Cristian’s algorithm
Compensate for network delays (assuming
symmetric)
 client sends a request at T0
 server replies with the current clock value
T T
T

T

Tserver
2
 client receives response at T1
 client sets its clock to:
1
client
server
0
Cristian’s algorithm: example


Send request at 5:08:15.100 (T0)
Receive response at 5:08:15.900 (T1)


Response contains 5:09:25.300 (Tserver)
Round-trip time is T1 − T0
5:08:15.900 - 5:08:15.100 = 800 ms


Best guess: timestamp was generated 400 ms ago
Set the local time to Tserver + round-trip-time/2
5:09:25.300 + 400 = 5:09.25.700

Accuracy: ± round-trip-time/2
Tserver
server
client
T0
T1
18
Cristian’s algorithm: error bound
Tmin: Minimum message travel
time
(
)
19
Problems with Cristian’s algorithm


Server might fail
Subject to malicious interference
20
（伯克利算法）Berkeley Algorithm





Proposed by Gusella & Zatti, 1989 and
implemented in BSD version of UNIX
Aim: synchronize clocks of a group of machines
as close as possible (also called internal
synchronization)
Assumes no machine has an accurate time
source (i.e., no differentiation of client and server)
Obtains average from participating computers
Synchronizes all clocks to average
21
（伯克利算法）Berkeley Algorithm

1.
One machine is elected (or designated) as the master;
others are slaves:
Master polls all slaves periodically, asking for their time

2.
When results are collected, compute the average

3.
Cristian’s algorithm can be used to obtain more accurate clock
values from other machines by counting network latency
Including master’s time
Send each slave the offset that its clock need be
adjusted

Avoids problems with network delays by sending “offset”
instead of “timestamp”
22
（伯克利算法）Berkeley Algorithm

Algorithm has provisions for ignoring
readings from clocks whose skew is too large


Compute a fault-tolerant average
Any slave can take over the master if master
fails
23
Berkeley Algorithm: example
24
Berkeley Algorithm: example
25
Berkeley Algorithm: example
+0:05
3:00
+0:15
3:25
2:50
9:10
3. Send offset to each client
26
网络时间协议Network Time
Protocol (NTP)




NTP 是非常常用的互联网时间协议，它的准确性也非常高 (RFC
1305, http://tf.nist.gov/service/its.htm ).
计算机操作系统需要安装NTP软件协议。客户端软件周期性的从一个
或多个获取时间更新（计算其平均值）
时间服务器监听NTP协议 ，端口123，响应UDP/IP协议传送一个NTP
数据的包（which is a 64-bit timestamp in UTC seconds since Jan 1,
1900 with a resolution of 200 pico-s）.
Many NTP client software for PC only gets time from a single server
(no averaging). The client is called SNTP (Simple Network Time
Protocol, RFC 2030), a simple version of NTP.
27
NTP synchronization subnet
第一层组织：客户机器直接连接到准确
的时间服务器。
第二层组织：客户机器和第一层组织机
器同步。
。。。
28
NTP goals

使得客户机可以跨越Internet和UTC进行准确同步）
（有消息延迟）


提供可靠的时间同步服务（Provide reliable service）




Survive lengthy losses of connectivity
Redundant paths
Redundant servers
使得客户端可以频繁同步Enable clients to
synchronize frequently


Use statistical techniques to filter data and improve quality of
results
Adjustment of clocks by using offset (for symmetric mode)
提供抗干扰能力Provide protection against
interference

Authenticate source of data
29
NTP Synchronization Modes

Multicast (for quick LANs, low accuracy)


Remote Procedure Call (medium accuracy)



server periodically multicasts its time to its clients in the subnet
server responds to client requests with its actual timestamp
like Cristian’s algorithm
Symmetric mode (high accuracy)

used to synchronize between the time servers (peer-peer)
All messages delivered unreliably with UDP
30
Symmetric mode

The delay between the arrival of a request (at server B) and
the dispatch of the reply is NOT negligible:
Ti-2 Ti-1
Server B
Server A

m
Ti-3
m’
Ti
time
Delay = total transmission time of the two messages
di = (Ti – Ti-3 ) – (Ti-1– Ti-2)

Offset of clock A relative to clock B:

Offset of clock A: oi 
(Ti  2  Ti 3 )  (Ti 1  Ti )
2

Set clock A: Ti + oi
(Ti 1 

Accuracy bound: di /2
di
)
2
31
Symmetric mode (another
expression)
T
i-2
Server B
Server A

Ti-1
m’
m
Ti-3
di
2
Ti
time
Delay = total transmission time of the two messages
di = (Ti – Ti-3 ) – (Ti-1– Ti-2)

Clock A should set its time to (the best estimate of B’s time at Ti):
Ti-1 + di/2, which is the same as Ti + oi
32
Symmetric NTP example
Server B
Server A
Ti-2 =800 Ti-1 =850
m
Ti-3 =1100
m’
Ti =1200
time
Offset oi=((800 – 1100) + (850 – 1200))/2 = – 325
Set clock A to: Ti + oi = 1200 – 325 = 875
Note: Server A need to adjusts it current clock (1200ms)
by gradual slowdown its pace until -325ms is compensated.
33
Improving accuracy

Data filtering from a single source



Peer-selection: synchronize with lower stratum servers


Retain the multiple most recent pairs < oi, di >
Filter dispersion: choose oj corresponding to the smallest dj
lower stratum numbers, lower synchronization dispersion
The stratum of a server is dynamically changing,
depending on which server it synchronize with
34
Simple Network Time Protocol
(SNTP) RFC 2030


Targeted for machines that have no need of full NTP
implementation, particularly for machines at the end of
synchronization subnet (client nodes)
SNTP operate in one of the following modes:



单播模式（Unicast mode）, the client sends a request to a
designated server
组播模式（Multicast mode）, the server periodically
broadcast/multicast its time to the subnet and does not serve
any requests from clients
任播模式（Anycast mode）, the client broadcast/multicast a
request to the local subnet and takes the first response for time
synchronization
35
逻辑时间
使用逻辑时间的动机

Cannot synchronize physical clocks perfectly
in distributed systems. [Lamport 1978]

Main function of computer clocks – order
events


If two processes don’t interact, there is no need
to sync clocks.
This observation leads to “causality（因果关系）”
37
因果关系（Causality）

Order events with happened-before ()
relation

ab


a could have affected the outcome of b
a || b


a and b take place in different processes that don’t
exchange data
Their relative ordering does not matter (they are
concurrent)
38
Definition of happened-before
Definition of “” relationship:
1.
If a and b take place in the same process

2.
If a and b take place in the different processes

3.
a comes before b, then a  b
a is a “send” and b is the corresponding “receive”, then a  b
Transitive: if a  b and b  c, then a  c
Partial ordering – unordered events are concurrent
39
Logical Clocks

A logical clock is a monotonically increasing
software counter. It need not relate to a
physical clock.


Corrections to a clock must be made by adding,
not subtracting
Rule for assigning “time” values to events

if a  b then clock(a) < clock(b)
40
Event counting example



Three processes: P0, P1, P2, events a, b,
c, …
A local event counter in each process.
Processes occasionally communicate with
each other, where inconsistency occurs, …
Bad ordering: e  h, f  k
41
Lamport’s algorithm, 1978
Each process Pi has a logical clock Li. Clock synchronization
algorithm:
1.
Li is initialized to 0;
2.
Update Li:



LC1: Li is incremented by 1 for each new event happened in Pi
LC2: when Pi sends message m, it attaches t = Li to m
LC3: when Pj receives (m,t) it sets Lj := max{Lj, t} , and then applies
LC1 to increment Lj for event receive(m)
42
Problem: Identical timestamps
Concurrent events (e.g., a, g) may have the same timestamp
43
Make timestamps unique
Append the process ID (or system ID) to the
clock value after the decimal point:

e.g. if P1, P2 both have L1 = L2 = 40, make L1 =
40.1, L2 = 40.2
44
Problem: Detecting causal relations



If a  b, then L(a) < L(b), however:
If L(a) < L(b), we cannot conclude that a  b
It is not very useful in distributed systems.
L(g) < L(c ), but g || c

Solution: use vector clocks
45
Vector of Timestamps
Suppose there are a group of people and each needs to
keep track of events happened to others.
Requirement: Given two events, you need to tell whether
they are sequential or concurrent.
Solution: you need to have a vector of timestamps, one
element for each member.
(3,0,0)
(?,?,?)
46
Vector clocks
Each process Pi keeps a clock Vi which is a vector of N
integers
 Initialization: for 1 ≤ i ≤ N and 1 ≤ k ≤ N, Vi[k] := 0
 Update Vi :



VC1: when there is a new event in Pi, it sets Vi[i] := Vi[i] +1
VC2: when Pi sends a message m out, it attaches t = Vi to m
VC3: when Pj receives (m,t), for 1 ≤ k ≤ N, it sets Vj[k] := max{Vj[k],
t[k]}, then applies VC1 to increment Vj[j] for event receive(m,t)
Note: Vi[j] is a timestamp indicating that Pi knows all events
that happened in Pj upto this time.
47
Vector timestamps: example
48
Vector timestamps: example
49
Vector timestamps: example
50
Vector timestamps: example
51
Vector timestamps: example
52
Vector timestamps: example
53
Vector timestamps: example
54
Detecting “” or “||” events by time
vectors

Define
V = V’ iff V[i] = V’[i]) for i = 1, …, N
V ≤ V’ iff V[i] ≤ V’[i]) for i = 1, …, N
V < V’ iff V ≤ V’ and V ≠ V’


V(e)  timestamp vector of an event e
For any two events a and b,


a  b iff V(a) < V(b), a ≠ b
a || b iff neither V(a) ≤ V(b) nor V(b) ≤ V(a)
55
Detecting “” or “||” events: an
example
56
Summary on vector timestamps



不需要同步物理时钟
能排序随机事件
能识别并发事件 (but cannot order them)
57
An Application of Timestamp
Vectors: causally-ordered multicast
Multicast: a sender sends a message to a group of receivers.
Every message must be received by all group members.
Causally ordered multicast: if m1  m2, m1 must be received
before m2 by all receivers.
(2,2,0)
(1,0,0)
(0,0,0)
(1,2,0)
(0,0,0)
(0,0,0)
(1,1,0)
(1,0,1) (1,2,2)
58
Algorithm of Causally-Ordered
Multicast
Each group member keeps a timestamp vector of n components (n group
members), all initialized to 0.
1. When Pi multicasts a message m, it increments i-th component of its
time vector Vi and attaches Vi to m.
2. When Pj with Vj receives (m, Vi) from Pi:
if (Vj [k]  Vi[k] for all k, k≠ i), then
Vj [i] := Vi [i]; // Vi [i] is always greater than Vj [i]
Vj [j] := Vj [j] + 1;
(2,2,0) (3,2,0)
(1,0,0)
Deliver m;
(0,0,0)
otherwise
(1,2,0)
Delay m until “if” is met.
(0,0,0)
(0,0,0)
(1,1,0)
(3,3,0)
?
(1,0,1) (1,2,2)
59
Causal-Order Preserved



If m1  m2, m1 is received by (delivered to) all recipients before
m2.
If m1 || m2, m1 and m2 can be received in arbitrary order by
recipients.
Total ordered multicast: for case of m1 || m2, m1 and m2 must
be received in the same order by all recipients (i.e., either all
(3,2,0)
m1 before(1,0,0)
m2, or all m2 before(2,2,0)
m1).
(0,0,0)
(1,2,0)
(0,0,0)
(0,0,0)
(1,1,0)
(1,3,0)
(3,4,0)
(1,0,1) (1,2,2)
?
(3,3,
4)
60
谢谢各位!