In the field of computer networking there is an imprecise relationship between the level of use of a network communication bandwidth and the latency experience in peer-to-peer communication. Let X be a fuzzy set of use levels (in terms of the percentage of full bandwidth used) and Y be a fuzzy set of latencies (in millisecond) with the following membership function: (0.2 0.5 0.8 1.0, 0.6, 0.1) + (10 ' 20 + --+ 40 60 + 80 100) (03 06 09 10 08

Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter20: Queuing Theory
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5. In the field of computer networking there is an imprecise relationship between the level of use of
a network communication bandwidth and the latency experience in peer-to-peer communication.
Let X be a fuzzy set of use levels (in terms of the percentage of full bandwidth used) and Y be a
fuzzy set of latencies (in millisecond) with the following membership function:
(0.2 0.5 0.8 1.0 0.6 0.1
+
40
X =
+-
(10
20
60 80 100S
(0.3 0.6 0.9
Y =
1.0. 0.8. 0.3)
+
4
+
+
l0.5 ' 1'1.5
8
20
a) Find the Cartesian product represented by the relation R = X × Y
b) Now, suppose we have second fuzzy set of bandwidth usage given by:
0.9. 1 0.5)
+-
60 ' 80 ' 100S
(0.3 0.6 0.7
+-
(10 ' 30
Z
40
Find S = Z1x6 ° Røx6
i. using max-min composition and
ii. max-product composition
Transcribed Image Text:5. In the field of computer networking there is an imprecise relationship between the level of use of a network communication bandwidth and the latency experience in peer-to-peer communication. Let X be a fuzzy set of use levels (in terms of the percentage of full bandwidth used) and Y be a fuzzy set of latencies (in millisecond) with the following membership function: (0.2 0.5 0.8 1.0 0.6 0.1 + 40 X = +- (10 20 60 80 100S (0.3 0.6 0.9 Y = 1.0. 0.8. 0.3) + 4 + + l0.5 ' 1'1.5 8 20 a) Find the Cartesian product represented by the relation R = X × Y b) Now, suppose we have second fuzzy set of bandwidth usage given by: 0.9. 1 0.5) +- 60 ' 80 ' 100S (0.3 0.6 0.7 +- (10 ' 30 Z 40 Find S = Z1x6 ° Røx6 i. using max-min composition and ii. max-product composition
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