Question

answer a b

Assignment: Do the same as the given example for the following problem except do not attempt to graph the solution as the state vectors are not in 3-space. Answer any additional questions posed in the problem. A traffic officer is assigned to control the traffic at the eight intersections indicated in the figure. She is instructed to remain at each intersection for an hour and then to either remain at the same intersection or move to a neighboring intersection. To avoid establishing a pattern, she is told to choose her new intersection on a random basis, with each possible choice equally likely. For example, if she is at intersection 5, her next intersection can be 2, 4, 5, or 8, each with probability 1/4, Every day she starts at the intersection where she stopped the day before. a) For this scenario, what does the steady-state vector tells us? b) if her objective is to spend the same proportion of time at each intersection, is the strategy of random movement with equal probabilities from one intersection to another a good one? Why or why not?

Answer 1

1) a) Probability that a book borrowed from A will end up at C after 2 more circulations =

For this we need to find the square of the given probability martix, and find the value of the 3rd row in 1st column. So the value at that place after the cube (3rd power) of the matrix will be= 0.027

b) Probability that a book borrowed from B ends up at B after 3 more circulations =

For this we need to find the values of the matrix of the fourth power of this probability matrix. In this matrix we need to check the value present at the 2nd row in the 2nd column. So the value at that place after the fourth power of the matrix will be = 0.2401