matrix for the Markov chain that models this situation. 3 1/4 1/4 1/2 0 1/3 2/3 0 robots at each junction. Find the steady state distribution of robots. (Assume that it takes each robot the same amo

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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Robots have been programmed to traverse the maze shown in the figure below and at each junction randomly choose which way to go.
(a) Construct the transition matrix for the Markov chain that models this situation.
1
3
4
1
2
3
1
Ø
3
4
2
3
0
1/2
1/2
0
1/3
0
1/3
1/3
2
1/4
1/4
0
1/2
0
(b) Suppose we start with 27 robots at each junction. Find the steady state distribution of robots. (Assume that it takes each robot the same amount of time to travel between two adjacent junctions.)
1/3
2/3
0
Transcribed Image Text:Robots have been programmed to traverse the maze shown in the figure below and at each junction randomly choose which way to go. (a) Construct the transition matrix for the Markov chain that models this situation. 1 3 4 1 2 3 1 Ø 3 4 2 3 0 1/2 1/2 0 1/3 0 1/3 1/3 2 1/4 1/4 0 1/2 0 (b) Suppose we start with 27 robots at each junction. Find the steady state distribution of robots. (Assume that it takes each robot the same amount of time to travel between two adjacent junctions.) 1/3 2/3 0
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