Consider a communication network with four nodes n1, n2, n3 and n4 and five directed links l1 = (n1, n2), l2 = (n1, n3), l3 = (n2, n3), l4 = (n3, n2), l5 = (n2, n4) and l6 = (n3, n4). A message has to be sent from the source node n1 to the destination node n4. The network is unreliable. The probability that the link li is functioning is pi for i = 1, . . . , 5. The links behave physically independent of each other. A path from node n1 to node n4 is only functioning if each of its links is functioning. Use the inclusion-exclusion formula to find the probability that there is some functioning path from node n1 to node n4. How does the expression for this probability simplify when pi = p for all i?
Consider a communication network with four nodes n1, n2, n3 and n4 and five directed links l1 = (n1, n2), l2 = (n1, n3), l3 = (n2, n3), l4 = (n3, n2), l5 = (n2, n4) and l6 = (n3, n4). A message has to be sent from the source node n1 to the destination node n4. The network is unreliable. The probability that the link li is functioning is pi for i = 1, . . . , 5. The links behave physically independent of each other. A path from node n1 to node n4 is only functioning if each of its links is functioning. Use the inclusion-exclusion formula to find the probability that there is some functioning path from node n1 to node n4. How does the expression for this probability simplify when pi = p for all i?
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Consider a communication network with four nodes n1, n2, n3 and n4 and five directed
links l1 = (n1, n2), l2 = (n1, n3), l3 = (n2, n3), l4 = (n3, n2), l5 = (n2, n4) and l6 = (n3, n4). A
message has to be sent from the source node n1 to the destination node n4. The network is
unreliable. The probability that the link li is functioning is pi for i = 1, . . . , 5. The links behave
physically independent of each other. A path from node n1 to node n4 is only functioning if
each of its links is functioning. Use the inclusion-exclusion formula to find the probability that
there is some functioning path from node n1 to node n4. How does the expression for this
probability simplify when pi = p for all i?
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