Chapter 16.pdf

# A assume that you are a motorist entering the traf fi

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• lbraithw
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a. Assume that you are a motorist entering the traf fi c system and receive a radio report of a traf fi c 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. b. What is the probability that in the long run the traf fi c will not be in the delay state? b. What is the long-run market share for each of these two products? c. A Red Pop advertising campaign is being planned to increase the probability of attracting Super Cola customers. Management believes that the new campaign will increase to 0.15 the probability of a customer switching from Super Cola to Red Pop. What is the projected effect of the advertising campaign on the market shares?   3. The computer center at Rockbottom University has been experiencing computer down- time. Let us assume that the trials of an associated Markov process are de fi ned as one-hour periods and that the probability of the system being in a running state or a down state is based on the state of the system in the previous period. Historical data show the following transition probabilities: 23610_ch16_ptg01_Web.indd 18 01/10/14 6:20 PM

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16-19 c. An important assumption of the Markov process models presented in this chapter 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 traf fi c problem? Explain. 6. Rock-Paper-Scissors is a simple game in which two players compete by simultaneously choosing rock, paper, or scissors. According to the classic rules of the game, paper beats rock, scissors beats paper, and rock beats scissors. After watching one particular player compete in this game for many rounds, you have observed that she chooses rock, paper, or scissors based on her previous choice according to the following transition probabilities: Problems To From Murphy’s Ashley’s Quick Stop Murphy’s Foodliner 0.85 0.10 0.05 Ashley’s Supermarket 0.20 0.75 0.05 Quick Stop Groceries 0.15 0.10 0.75 Next Choice Previous Choice Rock Paper Scissors Rock 0.27 0.42 0.31 Paper 0.36 0.15 0.49 Scissors 0.18 0.55 0.27 Assume you are competing against this player and that you must decide on all future choices now (before seeing any additional opponent choices). a. Given the opposing player last chose Rock, what is your best choice in the next round as her opponent? b. Given the opposing player last chose Rock, show the two-period tree diagram. c. Given the opposing player last chose Rock, calculate Π (2) and use this to fi nd the probability that the opposing player will choose Paper two rounds from now. 7. Data collected from selected major metropolitan areas in the eastern United States show that 2% of individuals living within the city limits move to the suburbs during a one-year period, while 1% of individuals living in the suburbs move to the city during a one- year period. Answer the following questions assuming that this process is modeled by a Markov process with two states: city and suburbs.
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• Spring '18
• Markov process, Markov chain, Andrey Markov, Markov decision process

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