Add M/M/c (split) queue-theory analyzer, RANDOM load-balancer policy, and end-to-end comparison reports (#26)

* mmc split + notebook mmc split + random lb algo

* tests for mmc

Author: GioeleB00

…queue_limit/asyncflow_mm1_notebook.ipynb asyncflow_queue_limit/asyncflow_mm1.ipynbasyncflow_queue_limit/asyncflow_mm1_notebook.ipynb renamed to asyncflow_queue_limit/asyncflow_mm1.ipynb asyncflow_queue_limit/asyncflow_mm1_notebook.ipynb renamed to asyncflow_queue_limit/asyncflow_mm1.ipynb

@@ -93,20 +93,18 @@
         "\n",
         "```mermaid\n",
         "graph LR;\n",
-        "    %% Definiamo i nodi con i loro dettagli\n",
         "    rqs1[\"<b>RqsGenerator</b><br/>id: rqs-1\"]\n",
         "    client1[\"<b>Client</b><br/>id: client-1\"]\n",
         "    app1[\"<b>Server</b><br/>id: app-1<br/>Endpoint: /api\"]\n",
         "\n",
-        "    %% Definiamo le connessioni (edge) con latenza\n",
         "    rqs1 -- \"Edge: gen-client<br/>Latency: 0.0001\" --> client1;\n",
         "    client1 -- \"Request<br/>Edge: client-app<br/>Latency: 0.0001\" --> app1;\n",
         "    app1 -- \"Response<br/>Edge: app-client<br/>Latency: 0.0001\" --> client1;"
       ]
     },
     {
       "cell_type": "code",
-      "execution_count": 3,
+      "execution_count": null,
       "metadata": {
         "tags": [
           "build"
@@ -148,7 +146,7 @@
         "    e_app_client = Edge(id=\"app-client\", source=\"app-1\", target=\"client-1\", latency=0.0001, dropout_rate=0.0)\n",
         "\n",
         "    settings = SimulationSettings(\n",
-        "        total_simulation_time=900,\n",
+        "        total_simulation_time=2400,\n",
         "        sample_period_s=0.05,\n",
         "    )\n",
         "\n",
@@ -160,9 +158,7 @@
         "        .add_edges(e_gen_client, e_client_app, e_app_client)\n",
         "        .add_simulation_settings(settings)\n",
         "    ).build_payload()\n",
-        "    return payload\n",
-        "\n",
-        "payload = build_payload()\n"
+        "    return payload\n"
       ]
     },
     {
@@ -174,7 +170,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 21,
+      "execution_count": null,
       "metadata": {
         "tags": [
           "run"
@@ -190,6 +186,7 @@
         }
       ],
       "source": [
+        "payload = build_payload()\n",
         "env = simpy.Environment()\n",
         "runner = SimulationRunner(env=env, simulation_input=payload)\n",
         "results: ResultsAnalyzer = runner.run()\n",
@@ -306,7 +303,7 @@
     },
     {
       "cell_type": "code",
-      "execution_count": 22,
+      "execution_count": 28,
       "metadata": {
         "tags": [
           "mm1"
@@ -322,13 +319,13 @@
             "--------------------------------------------------------------------\n",
             "sym  metric                      theory   observed        abs   rel%\n",
             "--------------------------------------------------------------------\n",
-            "λ    Arrival rate (1/s)       33.333333  33.204444  -0.128889  -0.39\n",
-            "μ    Service rate (1/s)       66.666667  66.638004  -0.028663  -0.04\n",
-            "rho  Utilization               0.500000   0.498281  -0.001719  -0.34\n",
-            "L    Mean items in system      1.000000   1.034536   0.034536   3.45\n",
-            "Lq   Mean items in queue       0.500000   0.526294   0.026294   5.26\n",
-            "W    Mean time in system (s)   0.030000   0.031157   0.001157   3.86\n",
-            "Wq   Mean waiting time (s)     0.015000   0.015850   0.000850   5.67\n",
+            "λ    Arrival rate (1/s)       33.333333  33.150833  -0.182500  -0.55\n",
+            "μ    Service rate (1/s)       66.666667  66.556885  -0.109782  -0.16\n",
+            "rho  Utilization               0.500000   0.498083  -0.001917  -0.38\n",
+            "L    Mean items in system      1.000000   1.012994   0.012994   1.30\n",
+            "Lq   Mean items in queue       0.500000   0.504967   0.004967   0.99\n",
+            "W    Mean time in system (s)   0.030000   0.030557   0.000557   1.86\n",
+            "Wq   Mean waiting time (s)     0.015000   0.015232   0.000232   1.55\n",
             "====================================================================\n"
           ]
         }