Question

A major traffic problem in the Greater Cincinnati area involves traffic attempting to cross the Ohio River from Cincinnati to Kentucky using Interstate 75. Let us assume that the probability of no traffic delay in one period, given no traffic delay in the preceding period, is 0.8 and that the probability of finding a traffic delay in one period, given a delay in the preceding period, is 0.7. Traffic is classified as having either a delay or a no-delay state, and the period considered is 30 minutes.

- Assume that you are a motorist entering the traffic system and
receive a radio report of a traffic delay. What is the probability
that for the next 60 minutes (two time periods) the system will be
in the delay state? Note that this result is the probability of
being in the delay state for two consecutive periods. If required,
round your answer to three decimal places.

- What is the probability that in the long run the traffic will
not be in the delay state? If required, round your answers to three
decimal places.

- An important assumption of the Markov process model presented
here has been the constant or stationary transition probabilities
as the system operates in the future. Do you believe this
assumption should be questioned for this traffic problem?
Explain.

The input in the box below will not be graded, but may be reviewed and considered by your instructor.

Answer #1

A major traffic problem in the Greater Cincinnati area involves
traffic attempting to cross the Ohio River from Cincinnati to
Kentucky using Interstate 75. Let us assume that the probability of
no traffic delay in one period, given no traffic delay in the
preceding period, is 0.85 and that the probability of finding a
traffic delay in one period, given a delay in the preceding period,
is 0.65. Traffic is classified as having either a delay or a
no-delay state,...

A major traffic problem in the Greater Cincinnati area involves
traffic attempting to cross the Ohio River from Cincinnati to
Kentucky using Interstate 75. Let us assume that the probability of
no traffic delay in one period, given no traffic delay in the
preceding period, is 0.85 and that the probability of finding a
traffic delay in one period, given a delay in the preceding period,
is 0.65. Traffic is classified as having either a delay or a
no-delay state,...

Problem 16-05 (Algorithmic)
A major traffic problem in the Greater Cincinnati area involves
traffic attempting to cross the Ohio River from Cincinnati to
Kentucky using Interstate 75. Let us assume that the probability of
no traffic delay in one period, given no traffic delay in the
preceding period, is 0.9 and that the probability of finding a
traffic delay in one period, given a delay in the preceding period,
is 0.6. Traffic is classified as having either a delay or...

Problem 16-05 (Algorithmic)
A major traffic problem in the Greater Cincinnati area involves
traffic attempting to cross the Ohio River from Cincinnati to
Kentucky using Interstate 75. Let us assume that the probability of
no traffic delay in one period, given no traffic delay in the
preceding period, is 0.9 and that the probability of finding a
traffic delay in one period, given a delay in the preceding period,
is 0.6. Traffic is classified as having either a delay or...

What tools could AA leaders have used to increase their
awareness of internal and external issues?
???ALASKA AIRLINES: NAVIGATING CHANGE
In the autumn of 2007, Alaska Airlines executives adjourned at
the end of a long and stressful day in the
midst of a multi-day strategic planning session. Most headed
outside to relax, unwind and enjoy a bonfire
on the shore of Semiahmoo Spit, outside the meeting venue in
Blaine, a seaport town in northwest
Washington state.
Meanwhile, several members of...

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