Markov Chains and Decision Analysis

1. A major traffic problem in Baguio City can be seen in the intersection of Abanao and Maharlika. 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 0.75. Traffic is classified as having either a delay or a no-delay state, and the period considered is 30 minutes.

a. Draw the transition diagram in 2 periods. b. 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. c. What is the probability

2. Consider the three competing grocery stores in town, T'San Grocery, 654 Grocery and Sunlight Grocery. Consider the transition probabilities below:

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