Mostly finished ex4.

.vscode/settings.json

@@ -4,6 +4,8 @@
     "ggplot",
     "ggsave",
     "linebreak",
+    "lsroute",
+    "Mbits",
     "objval",
     "typst",
     "xlab",

typst/appendixes/4.typ

@@ -0,0 +1,13 @@
+#import "/typst/util.typ" as util: indent_par, code_figure
+
+==== Greedy Randomized
+#code_figure(
+  text(size: 0.8em, raw(read("/code/util/greedy_randomized.R"), lang: "R", block: true)),
+  caption: [Implementation of `GreedyRandomized`],
+)
+
+==== c.
+#code_figure(
+  text(size: 0.8em, raw(read("/code/4c.R"), lang: "R", block: true)),
+  caption: [Code used for exercise 4c],
+)

typst/exercises/3.typ

@@ -29,7 +29,7 @@ $ sum_i c_"ab" dot x_"ab" $
 
 #indent_par[Where $c_"ab"$ is the cost of the $a -> b$ link.]
 
-#indent_par[For both of the following cases, the code we have used is presented in the appendix.]
+#indent_par[The code we have used to calculate this is presented in the appendix.]
 
 #indent_par[We achieve the following results in table 9:]
 
@@ -50,3 +50,5 @@ $ sum_i c_"ab" dot x_"ab" $
 )
 
 #indent_par[The total cost ends end at 3. We conclude that the best solution is the route $1 -> 2 -> 3 -> 4$, with a cost of 3.]
+
+#pagebreak()

typst/exercises/4.typ

@@ -0,0 +1,75 @@
+#import "/typst/util.typ" as util: indent_par, code_figure
+
+#indent_par[The following figure 2, from the guide, represents our network.]
+
+#figure(
+	image("/images/4-diagram.png", width: 70%),
+	caption: [Network diagram]
+)
+
+==== a.
+
+#indent_par[Using the provided script `lsrouteA.R`, we obtained the following results for a kilometric solution in table 10:]
+
+#figure(
+	pad(1em, table(
+		columns: (auto, auto),
+		align: center,
+
+		[Maximum link load], [Average packet delay ($"ms"$)],
+		[0.999000], [2.055],
+	)),
+	kind: table,
+	caption: [Solution]
+)
+
+==== b.
+
+#indent_par[To develop the `GreedyRandomized` function, we used the following approach:]
+
+- Find all possible flows and shuffle them
+- For each flow, find the shortest path, taking into account the previously installed flows.
+
+#indent_par[In detail, we store a matrix `λ` with the installed traffic through each node, so we may compute the link delays using it. We update this matrix using delays calculated from `Tr` matrix and the speed of light.]
+
+#indent_par[This function is present in the appendix.]
+
+#indent_par[After running the provided script `lsrouteB.R`, we obtained the following results for a kilometric solution in table 11:]
+
+#figure(
+	pad(1em, table(
+		columns: (auto, auto),
+		align: center,
+
+		[Maximum link load], [Average packet delay ($"ms"$)],
+		[0.864000], [1.207],
+	)),
+	kind: table,
+	caption: [Solution]
+)
+
+#indent_par[The solution found via this method is substantially better than in the previous exercise, by both the maximum link load, which is lower, and the average packet delay.]
+
+#pagebreak()
+
+==== c.
+
+#indent_par[Using the solution from the previous exercise, we computed the rates matrix and used it to determine where we needed to add more capacity.]
+
+#indent_par[In detail, we normalize the matrix to the $[0.0, 1.0]$ interval and added it to the `Mu` matrix using `Mu = (1 + extra_capacity) * 1e9 / 8e3`. This makes it so that, as specified, we don't remove any capacity and only add it where necessary. However, this lead to a maximum link load of higher than 70%. To fix this, we multiplied the original by the lowest factor that would yield a < 70% maximum link load.]
+
+#indent_par[The code used for this, which includes the extra capacity, is present in the appendix.]
+
+#indent_par[After running our solution, we obtained the following solution in table 12:]
+
+#figure(
+	pad(1em, table(
+		columns: (auto, auto),
+		align: center,
+
+		[Maximum link load], [Average packet delay ($"ms"$)],
+		[0.699999], [1.163],
+	)),
+	kind: table,
+	caption: [Solution]
+)

typst/main.typ

@@ -56,6 +56,9 @@
 === 3. Exercise 3
 #include "exercises/3.typ"
 
+=== 4. Exercise 4
+#include "exercises/4.typ"
+
 #pagebreak()
 
 = Appendix
@@ -63,8 +66,11 @@
 === 1. Exercise 1
 #include "appendixes/1.typ"
 
-=== 2. Exercise 2 <appendix2>
+=== 2. Exercise 2
 #include "appendixes/2.typ"
 
-=== 3. Exercise 3 <appendix3>
+=== 3. Exercise 3
 #include "appendixes/3.typ"
+
+=== 4. Exercise 4
+#include "appendixes/4.typ"