Add R script for estimating average node latency at different levels of network load

svn:r17768

doc/design-paper/node-selection/vary-network-load.R

@@ -0,0 +1,93 @@
+## The waiting time for a node (assuming no overloaded nodes)
+## x: 1/bandwidth
+## q: selection probability
+## L: network load
+wait <- function(x,q,L) {
+  a <- q*L*x*x
+  b <- 2*(1-q*x*L)
+  return (x + a/b)
+}
+
+## The weighted wait time
+wwait <- function(x,q,L) {
+  return (q*wait(x,q,L))
+}
+
+## Average latency, returning NA for infinite
+netLatency <- function(x, q, L) {
+  if (any(x*q*L <0 | x*q*L >1)) {
+    return (NA)
+  } else {
+    return (sum(wwait(x, q, L)))
+  }
+}
+
+## Load in data files
+t1 <- read.table("opt_1e-6.pickle.dat", header=TRUE)
+t2 <- read.table("opt_1e-3.pickle.dat", header=TRUE)
+t3 <- read.table("opt_1e-1.pickle.dat", header=TRUE)
+t4 <- read.table("opt_0.75.pickle.dat", header=TRUE)
+t5 <- read.table("opt_0.5.pickle.dat", header=TRUE)
+t6 <- read.table("opt_0.25.pickle.dat", header=TRUE)
+t7 <- read.table("opt_0.1.pickle.dat", header=TRUE)
+tt <- read.table("opt_tor.pickle.dat", header=TRUE)
+
+## Node bandwidth and reciprocal
+bw <- t1$bw
+x <- 1/bw
+
+## Calculate network capcity
+capacity <- sum(bw)
+
+## Calculate selection probabilties that Tor uses
+torProb <- bw/sum(bw)
+
+## Load values to try
+varyLoad <- seq(0.01,0.93,0.01)
+latencyTor <- c()
+latency3 <- c()
+latency4 <- c()
+latency5 <- c()
+for (L in varyLoad) {
+  latencyTor <- append(latencyTor,
+                       netLatency(x, torProb, capacity*L))
+  latency3   <- append(latency3,
+                       netLatency(x, t3$prob, capacity*L))
+  latency4   <- append(latency4,
+                       netLatency(x, t4$prob, capacity*L))
+  latency5   <- append(latency5,
+                       netLatency(x, t5$prob, capacity*L))
+}
+
+## Output graph
+pdf("vary-network-load.pdf")
+
+## Set up axes
+yFac <- 1000
+xFac <- 100
+
+ylim <- range(na.omit(c(latencyTor, latency3, latency4, latency5)))
+ylim <- c(0,0.015) * yFac
+xlim <- c(0,1) * xFac
+plot(NA, NA,
+     xlim=xlim, ylim=ylim,
+     frame.plot=FALSE,
+     xlab = "Network load (%)",
+     ylab = "Average queuing delay (ms)",
+     main = "Latency for varying network loads")
+
+## Plot data
+col <- rainbow(8)
+lines(varyLoad*xFac, latency3*yFac, col=col[3])
+lines(varyLoad*xFac, latency4*yFac, col=col[4])
+lines(varyLoad*xFac, latency5*yFac, col=col[5])
+lines(varyLoad*xFac, latencyTor*yFac)
+
+## Plot points at which selection probabilities are optimal
+par(xpd=TRUE)
+points(c(0.9, 0.75, 0.5, 1)*xFac, rep(par("usr")[3], 4),
+       col=c(col[3:5], "black"), pch=20,
+       cex=2)
+
+## Close output device
+dev.off()