Problem 16-05 (Algorithmic)

A major traffic problem in the Greater Cincinnati area involvestraffic attempting to cross the Ohio River from Cincinnati toKentucky using Interstate 75. Let us assume that the probability ofno traffic delay in one period, given no traffic delay in thepreceding period, is 0.8 and that the probability of finding atraffic delay in one period, given a delay in the preceding period,is 0.65. Traffic is classified as having either a delay or ano-delay state, and the period considered is 30 minutes.

1. Assume that you are a motorist entering the traffic system andreceive a radio report of a traffic delay. What is the probabilitythat for the next 60 minutes (two time periods) the system will bein the delay state? Note that this result is the probability ofbeing in the delay state for two consecutive periods. If required,round your answer to three decimal places.
   
   
   
2. What is the probability that in the long run the traffic willnot be in the delay state? If required, round your answers to threedecimal places.
   
   
   
3. An important assumption of the Markov process model presentedhere has been the constant or stationary transition probabilitiesas the system operates in the future. Do you believe thisassumption should be questioned for this traffic problem?Explain.
   
   The input in the box below will not be graded, but may be reviewedand considered by your instructor.