Purpose
To compare 2 drunkard walks

Moves between Home (0) Bar(4) which are absorbing states 1,2,3 points have left and righ prob as 0.5

> Q <- matrix(data = NA, nrow = 3, ncol = 3)
> Q[1, ] <- c(0, 0.5, 0)
> Q[2, ] <- c(0.5, 0, 0.5)
> Q[3, ] <- c(0, 0.5, 0)
> N <- solve(diag(3) - Q)
> C <- c(1, 1, 1)
> R <- matrix(data = NA, nrow = 3, ncol = 2)
> R[1, ] <- c(0.5, 0)
> R[2, ] <- c(0, 0)
> R[3, ] <- c(0, 0.5)
> N1 <- N
> NC1 <- N %*% C
> NR1 <- N %*% R

Moves between Home (0) Bar(4) which are absorbing states 1,2,3 points have left and righ prob as 2/3 and 1/3

> Q <- matrix(data = NA, nrow = 3, ncol = 3)
> Q[1, ] <- c(0, 2/3, 0)
> Q[2, ] <- c(1/3, 0, 2/3)
> Q[3, ] <- c(0, 1/3, 0)
> N <- solve(diag(3) - Q)
> C <- c(1, 1, 1)
> R <- matrix(data = NA, nrow = 3, ncol = 2)
> R[1, ] <- c(1/3, 0)
> R[2, ] <- c(0, 0)
> R[3, ] <- c(0, 2/3)
> N2 <- N
> NC2 <- N %*% C
> NR2 <- N %*% R

Comparison # of times man is in transient state sj if he begins at si

> print(N1)
     [,1] [,2] [,3]
[1,]  1.5    1  0.5
[2,]  1.0    2  1.0
[3,]  0.5    1  1.5
> print(N2)
     [,1] [,2] [,3]
[1,]  1.4  1.2  0.8
[2,]  0.6  1.8  1.2
[3,]  0.2  0.6  1.4

Comparison expected time before it get absorbed

> print(NC1)
     [,1]
[1,]    3
[2,]    4
[3,]    3
> print(NC2)
     [,1]
[1,]  3.4
[2,]  3.6
[3,]  2.2

Absorbtion probabilities

> print(NR1)
     [,1] [,2]
[1,] 0.75 0.25
[2,] 0.50 0.50
[3,] 0.25 0.75
> print(NR2)
           [,1]      [,2]
[1,] 0.46666667 0.5333333
[2,] 0.20000000 0.8000000
[3,] 0.06666667 0.9333333