Transcript Fuzzy Logic and its Application to Web Caching

Fuzzy Logic and its Application
to Web Caching
By
P.M.Pavan Kiran
What is fuzzy logic?
A type of logic that recognizes
more than simple true and false
values. With fuzzy logic,
propositions can be represented
with degrees of truthfulness
and falsehood.
A Simple Example
The Statement Today is sunny can be
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100% true if there are no clouds
80% true if there are a few clouds
50% true if it's hazy and
0% true if it rains all day
Classical Set
young = { x  P | age(x)  20 }
characteristic function:
myoung(x) =
myoung(x)
1
0
{
1 : age(x)  20
0 : age(x) > 20
A=“young”
x [years]
Fuzzy Set
Classical Logic
Fuzzy Logic
Element x belongs to set A
or it does not:
m(x){0,1}
Element x belongs to set A
with a certain
degree of membership:
m(x)[0,1]
mA(x)
1
0
mA(x)
A=“young”
1
x [years]
0
A=“young”
x [years]
Types of Membership Functions
Trapezoid: <a,b,c,d>
m(x) 1
0a
Triangular: <a,b,d>
m(x)
1
0
b
c d x
Singleton: (a,1) and (b,0.5)
m(x)
1
a
b
d
x
0
a
b
x
Operators on Fuzzy Sets
Union
mAB(x)=max{mA(x),mB(x)}
1
mA(x)
mB(x)
0
Intersection
mAB(x)=min{mA(x),mB(x)}
1
x
mA(x)
mB(x)
0
x
mAB(x)=min{1,mA(x)+mB(x)} mAB(x)=mA(x)  mB(x)
1
0
mA(x)
mB(x)
1
x
0
mA(x)
mB(x)
x
Fuzzy Sets & Linguistic Variables
A linguistic variable combines several fuzzy sets.
linguistic variable : temperature
linguistics terms (fuzzy sets) : { cold, warm, hot }
m(x)
1
0
mcold
mwarm
20
mhot
60
x [C]
Fuzzy Rules
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causal dependencies can be expressed in
form of if-then-rules
general form:
if <antecedent> then <consequence>
example:
if temperature is cold and oil is cheap
then heating is high
linguistic variables
linguistic values/terms (fuzzy sets
Fuzzy Rule Base
Heating
Oil price:
Temperature :
cold
warm
hot
cheap
high
high
medium
normal
high
medium
low
expensive
medium
low
low
if temperature is cold and oil price is low then heating is high
if temperature is hot and oil price is normal then heating is low
Fuzzy Knowledge Base
fuzzy knowledge base
Fuzzy Data-Base:
Definition of linguistic input and output variables
Definition of fuzzy membership functions
m(x) m
cold
1
0
mwarm
20
mhot
60
x [C]
Fuzzy Rule-Base:
if temperature is cold and oil price is cheap
then heating is high
….
An Example
In order to illustrate some
basic concepts in Fuzzy
Logic, consider a simplified
example of a thermostat
controlling a heater fan
illustrated in Figure 1.
The room temperature
detected through a sensor is
input to a controller which
outputs a control force to
adjust the heater fan speed.
Conventional Thermostat
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A conventional thermostat works like an on-off switch
(Figure 2).
If we set it at 78oF then the heater is activated only
when the temperature falls below 75oF .
When it reaches 81oF the heater is turned off. As a
result the desired room temperature is either too
warm or too hot.
Fuzzy Thermostat
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A fuzzy thermostat works in shades of gray where the
temperature is treated as a series of overlapping ranges.
For example, 78oF is 60% warm and 20% hot. The controller is
programmed with simple if-then rules that tell the heater fan
how fast to run.
As a result, when the temperature changes the fan speed will
continuously adjust to keep the temperature at the desired
level.
Figure 2
Designing a Fuzzy Controller
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Our first step in designing such a fuzzy controller is
to characterize the range of values for the input and
output variables of the controller
Then we assign labels such as cool for the
temperature and high for the fan speed, and we
write a set of simple English-like rules to control the
system. .
Design Contd…..
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Inside the controller all temperature
regulating actions will be based on how the
current room temperature falls into these
ranges and the rules describing the system
behavior. The controller's output will vary
continuously to adjust the fan speed
The Rule Base
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The temperature controller described above can be defined in
four simple rules:
IF temperature IS cold THEN fan_speed IS high
IF temperature IS cool THEN fan_speed IS medium
IF temperature IS warm THEN fan_speed IS low
IF temperature IS hot THEN fan_speed IS zero
The Process
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A fuzzy controller works similar to a conventional system: it
accepts an input value, performs some calculations, and
generates an output value. This process is called the Fuzzy
Inference Process and works in three steps illustrated in Figure
3:
(a) Fuzzification where a crisp input is translated into a fuzzy
value,
(b) Rule Evaluation, where the fuzzy output truth values are
computed, and
(c) Defuzzification where the fuzzy output is translated to a
crisp value.
Fuzzification
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During the fuzzification step
the crisp temperature value
of 78oF is input and
translated into fuzzy truth
values.
For this example, 78oF is
fuzzified into warm with
truth value 0.6 (or 60%) and
hot with truth value 0.2 (or
20%).
Rule Evaluation
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For 78oF only the last
two of the four rules will
fire.
IF temperature IS warm
THEN fan_speed IS low
with truth value 0.6
IF temperature IS hot THEN
fan_speed IS zero with truth
value 0.2
Defuzzification
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During the defuzzification step
the 60% low and 20% zero
labels are combined using a
calculation method called the
Center of Gravity (COG) in
order to produce the crisp
output value of 13.5 RPM for
the fan speed
The Steam turbine Contrller
The Membership functions
The Rule Base
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rule 1: IF temperature IS cool AND pressure
IS weak, THEN throttle is P3.
rule 2: IF temperature IS cool AND pressure
IS low, THEN throttle is P2.
rule 3: IF temperature IS cool AND pressure
IS ok, THEN throttle is Z.
rule 4: IF temperature IS cool AND pressure
IS strong, THEN throttle is N2.
Fuzzification and Rule Inferencing
Fuzzification and Rule Inferencing
Defuzzification
Why Web Caching?
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It is widely recognized that slow web sites are
primary source of user dissatisfaction.
Web Caching is a mechanism widely
employed to reduce the latency to retrieve
web pages.
What is web Caching?
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The idea of web caching is to store popular
web objects “closer” to the user who requests
them such that they can be retrieved faster.
Caching also has the effect of reducing the
load on the web servers and traffic over
network.
Web Caching
Web caching can be implemented at different
levels
 They are
1.Client
2.Server
3.Network
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Web Caching
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The web server and web browser are
responsible for caching at server and client
side respectively. Proxy servers are used for
caching at the network level.
A proxy server acts as an intermediary
between clients and web servers.
Proxy server
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Many organizations use proxy servers in front of their
LANs to save network bandwidth and speed up web
page requests serving them locally.
Upon receiving requests from multiple clients the
proxy server checks from its cache whether the page
is already present.
Proxy Server
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In Case of a cache miss the proxy server forwards
the request to the web server. Once the page is
returned by the server, the proxy sends it back to the
client and stores a copy in the local cache for further
requests.
If the cache is full one or more pages have to be
evicted from the cache.
The Replacement Policies
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The efficiency and performance of proxy caches
depend on their design and management.
Replacement policies play a key role for effectiveness
of caching.
The goal of these policies is to make best use of the
available resources by dynamically selecting the
pages to cached or evictes.
The fuzzy Database for web caching
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1. Identification of the input output variables.
2. Definition of the membership functions.
3. Construction of the rule base.
The Variables
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The proper choice of process state input
variable is essential to the characterization of
the operation of a fuzzy system.
Three variables as input are chosen, they
being
Size, Frequency of access, Access recency, i.e
time elapsed since the last access.
The Variables
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The output variable is probability of
replacement.
The membership functions of each of these
variables is plotted from the analysis of
various proxy servers and their workloads.
The Membership functions
The rule base
The process
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Measurement of the values of the input data
from the server.
Fuzzification
Inference from fuzzy rules using Max-Min
Inference.
Defuzzification using the COG method.
The performance
The End
Thank You