Robots have been programmed to traverse the maze shown in the figure below and at each junction randomly choose which way to go. i (a) Construct the transition matrix for the Markov chain that models this situation. 1 3 1 2 3 4 1 0 1/2 1/2 0 1/3 1 21 2 19 27 3 4 27 0 1/3 1/3 2 1/4 1/4 0 1/2 0 1/3 2/3 0 4 (b) Suppose we start with 27 robots at each junction. Find the steady state distribution of robots. (Assume that it tak each robot the me amount of time travel between adjacent junctions.)
Robots have been programmed to traverse the maze shown in the figure below and at each junction randomly choose which way to go. i (a) Construct the transition matrix for the Markov chain that models this situation. 1 3 1 2 3 4 1 0 1/2 1/2 0 1/3 1 21 2 19 27 3 4 27 0 1/3 1/3 2 1/4 1/4 0 1/2 0 1/3 2/3 0 4 (b) Suppose we start with 27 robots at each junction. Find the steady state distribution of robots. (Assume that it tak each robot the me amount of time travel between adjacent junctions.)
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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Problem 1P
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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.
**Maze Diagram:**
- The maze consists of four junctions labeled 1, 2, 3, and 4.
- Junctions 1 and 2 are connected by a straight line.
- Junctions 2 and 4 are connected by a straight line.
- Junctions 3 and 4 are connected by a straight line.
- Junctions 1 and 3 are connected by a straight line.
- There is an additional diagonal line connecting junctions 2 and 3.
- Junctions 3 and 1 are connected by an arc around the bottom.
**(a) Construct the transition matrix for the Markov chain that models this situation:**
| | 1 | 2 | 3 | 4 |
|---|----|----|----|----|
| 1 | 0 | 1/3| 1/4| 0 |
| 2 | 1/2| 0 | 1/4| 1/3|
| 3 | 1/2| 1/3| 0 | 2/3|
| 4 | 0 | 1/3| 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.
| | Number |
|---|---------|
| 1 | 21 |
| 2 | 27 |
| 3 | 27 |
| 4 | 27 |
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