Markov Chain Chap 9 - 20

> trmatrix <- function(n, p, r) {
+     p_l <- r * (1 - p)
+     p_r <- p * (1 - r)
+     p_0 <- r * p + (1 - p) * (1 - r)
+     Q <- matrix(data = 0, nrow = n, ncol = n)
+     diag(Q) <- rep(p_0, n)
+     for (i in 1:(n - 1)) Q[i, (i + 1)] <- p_r
+     for (i in 2:n) Q[i, (i - 1)] <- p_l
+     Q[1, 1] <- 1 - p
+     Q[1, 2] <- p
+     Q[n, n] <- 1 - r
+     Q[n, (n - 1)] <- r
+     return(Q)
+ }
> n <- 20
> p <- 0.6
> r <- 0.3
> Q1 <- trmatrix(n, p, r)
> coefs <- t(Q1) - diag(n)
> wts1 <- solve(rbind(c(rep(1, n)), coefs)[1:n, ], c(1, rep(0,
+     (n - 1))))
> s1 <- p/r
> wts1 <- as.data.frame(wts1)
> p <- 0.3
> r <- 0.6
> Q1 <- trmatrix(n, p, r)
> coefs <- t(Q1) - diag(n)
> wts2 <- solve(rbind(c(rep(1, n)), coefs)[1:n, ], c(1, rep(0,
+     (n - 1))))
> s2 <- p/r
> wts2 <- as.data.frame(wts2)
> p <- 0.5
> r <- 0.5
> Q1 <- trmatrix(n, p, r)
> coefs <- t(Q1) - diag(n)
> wts3 <- solve(rbind(c(rep(1, n)), coefs)[1:n, ], c(1, rep(0,
+     (n - 1))))
> s3 <- p/r
> wts3 <- as.data.frame(wts3)
> p <- 0.3
> r <- 0.3
> Q1 <- trmatrix(n, p, r)
> coefs <- t(Q1) - diag(n)
> wts4 <- solve(rbind(c(rep(1, n)), coefs)[1:n, ], c(1, rep(0,
+     (n - 1))))
> s4 <- p/r
> wts4 <- as.data.frame(wts4)

> par(mfrow = c(2, 2))
> plot(1:n, wts1[, 1], col = "blue", pch = 19, main = paste("traffic intensity",
+     s1, " ", "0.6/0.3"))
> plot(1:n, wts2[, 1], col = "blue", pch = 19, main = paste("traffic intensity",
+     s2, " ", "0.3/0.6"))
> plot(1:n, wts3[, 1], col = "blue", pch = 19, main = paste("traffic intensity",
+     s3, " ", "0.5/0.5"))
> plot(1:n, wts4[, 1], col = "blue", pch = 19, main = paste("traffic intensity",
+     s4, " ", "0.3/0.3"))