A traffic network is shown in the figure below. The reliability (probability of

Question

A traffic network is shown in the figure below. The reliability (probability of freeflowing without congestion) of link B is 0.7, link D is 0.8, and link E is 0.8; these are all statistically independent of each other and of other links in the network. The overall reliability of Link A is 0.7. However, if A is congested, then the reliability of C is 0.4, whereas if A is not congested, C has a reliability of 0.8.

Please answer the following questions using the terminology "A = A is free-flowing; B = B is free-flowing" and so on.

A. How do you write the event “A vehicle can travel from point 1 to point 2 without encountering congestion." in terms of A, B, C, D, and E? You may use "U" (capital u) to indicate unions, and "^" (caret, above the 6 on most keyboards) or “n” to indicate intersections. (Note that this answer will not be automatically graded.)

B. Find the probability of vehicles being able to travel freely from point 1 to point 2. (3 decimal places, 0.XXX)

C. If vehicles can flow freely, what is the probability that A is congested? (3 decimal places, 0.XXX)

Please show your work, not just the answer. I want to be able to understand the concepts used to solve the problem. Will rate/review. Thanks. :)

Explanation / Answer

A) A vehicle can ravel from point 1 to point 2=((AnB)U(CnDnE))

B) here P(A) =0.7 ; P(B) =0.7 ; P(D) =0.8 ; P(E) =0.8

also from given if A is congested reliabilty of C P(C|Ac) =0.4

and given if A is not congested reliabilty of C P(C|A) =0.8

therefore relaibilty of C =P(A)*P(C|A) +P(Ac)*P(C|Ac) =0.7*0.8+0.3*0.4 =0.68

therefore :relaibilty of system =probability of vehicles being able to travel freely from point 1 to point 2=P(at least one of the channel will work) =1-P(both upper and lower channel will not work)

=1-((1-0.7*0.7)*(1-0.68*0.8*0.8))=0.7119

c)here proabbilty that A is congested and vehicles can flow freely =P(bottom channel is working) =0.68*0.8*0.8=0.4352

hence If vehicles can flow freely, the probability that A is congested=P(Ac|R) =0.4352/0.7119 =0.6113

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.