Started work on exercise 13.

.vscode/settings.json

@@ -21,6 +21,7 @@
     "logseq",
     "maxs",
     "packetsize",
+    "pktnet",
     "pnet",
     "Pollaczek",
     "pracma",

code/13.R

@@ -15,6 +15,5 @@ flows <<- list(
   list(rate = 5 * k, route = c(3))
 )
 
-throughput <- approx_kleinrock(link_capacities, flows, packet_size)
-
-str(throughput)
+approx <- approx_kleinrock(link_capacities, flows, packet_size)
+str(approx)

code/kleinrock.R

@@ -1,31 +1,36 @@
 # Calculates the throughput of a network using the kleinrock approximation
 approx_kleinrock <- function(link_capacities, flows, packet_size) {
-  # (Bits / s)
-  λ_total <- 0
-  λ <- replicate(length(link_capacities), 0)
+  # Calculate the arrival rates per link and for the whole network
+  # (bits / s)
+  λ_network <- 0
+  λ_per_link <- replicate(length(link_capacities), 0)
   for (flow in flows) {
-    λ_total <- λ_total + flow$rate
-    for (node_idx in flow$route) {
-      λ[node_idx] <- λ[node_idx] + flow$rate
+    λ_network <- λ_network + flow$rate
+    for (link_idx in flow$route) {
+      λ_per_link[link_idx] <- λ_per_link[link_idx] + flow$rate
     }
   }
 
-  # (Packets / s)
-  μ <- link_capacities / packet_size
+  # Then calculate the service rates
+  # (packets / s)
+  μ_per_link <- link_capacities / packet_size
 
-  # (Packets)
-  l <- λ / (μ - λ)
-  l_sum <- sum(l)
+  # Then the average packets per link and in the network
+  # (packets)
+  avg_packets_per_link <- λ_per_link / (μ_per_link - λ_per_link)
+  avg_packets_network <- sum(avg_packets_per_link)
 
-  total_wait <- l_sum / sum(λ_total)
-  waits_flows <- 1 / (μ - λ)
-  waits <- sapply(flows, function(flow) {
-    sum(sapply(flow$route, function(node_idx) waits_flows[node_idx]))
+  # And finally the average packet delay per link, then flow and in the network
+  # (seconds)
+  avg_packet_delay_network <- sum(avg_packets_per_link) / λ_network
+  avg_packet_delay_per_link <- 1 / (μ_per_link - λ_per_link)
+  avg_packet_delay_per_flow <- lapply(flows, function(flow) {
+    sum(sapply(flow$route, function(link_idx) avg_packet_delay_per_link[link_idx]))
   })
 
   list(
-    waits = waits,
-    total_wait = total_wait,
-    l_sum = l_sum
+    avg_packet_delay_per_flow = avg_packet_delay_per_flow,
+    avg_packet_delay_network = avg_packet_delay_network,
+    avg_packets_network = avg_packets_network
   )
 }

typst/exercises/12.typ

@@ -23,3 +23,5 @@
 ==== d. Remarking
 
 #indent_par[After a packet is processed, it can be re-evaluated, similarly to the first step of classification, so that further equipment down the line can have a better idea of the nature of this packet.]
+
+#pagebreak()

typst/exercises/13.typ

@@ -0,0 +1,56 @@
+#import "@preview/tablex:0.0.6": tablex, rowspanx, colspanx
+#import "/typst/util.typ" as util: indent_par, code_figure
+
+#indent_par[The following code 10 is our implementation of the kleinrock approximation. It takes the link capacities, flows and packet size similarly to the `pnet` simulator.]
+
+#code_figure(
+  text(size: 0.8em, raw(read("/code/kleinrock.R"), lang: "R", block: true)),
+  caption: "Code for Kleinrock approximation",
+)
+
+#indent_par[To test the simulator, we've used the following network from the course slides (`pktnet`, page 14).]
+
+#figure(
+  image("/images/13-diagram.png", width: 75%),
+	caption: "3-DTMC"
+)
+
+#pagebreak()
+
+#indent_par[We developed the following code 11 to test our implementation and obtained the results in table 18:]
+
+#code_figure(
+  text(size: 0.8em, raw(read("/code/13.R"), lang: "R", block: true)),
+  caption: "Code for testing the Kleinrock approximation",
+)
+
+#figure(
+	pad(1em, tablex(
+		columns: (auto, 1fr, 1fr, 1fr),
+		align: center + horizon,
+
+
+		rowspanx(2)[ Flow ],
+		colspanx(2)[ Average packet delay ($"μs"$) ],
+		rowspanx(2)[ Average packets (network) ],
+
+		[ Per flow ],
+		[ Network ],
+
+		[1],
+		[600],
+		rowspanx(3)[644.4],
+		rowspanx(3)[14.5],
+
+		[2],
+		[800],
+
+		[3],
+		[400],
+
+	)),
+	kind: table,
+	caption: [Results]
+)
+
+#indent_par[Our values are the same as calculated manually, and thus we conclude our script is valid.]

typst/main.typ

@@ -92,3 +92,8 @@
 
 === 12. Exercise 12
 #include "exercises/12.typ"
+
+== G. Packet switched networks
+
+=== 13. Exercise 13
+#include "exercises/13.typ"