feat: Adding Little's law as an example

README.md

@@ -13,6 +13,7 @@
 - [D/D/c queues](simulating-ddc-queues.ipynb)
 - [multiple executors](simulating-mdc-queues.ipynb)
 - [interesting experiments](interesting-experiments.ipynb)
+- [Little's law](littles-law.ipynb)
 
 # Starting the Examples
 Installing the environment with [`pyenv`](https://github.com/pyenv/pyenv)

interactive-ddc-queues.ipynb

@@ -17,7 +17,7 @@
     {
      "data": {
       "application/vnd.jupyter.widget-view+json": {
-       "model_id": "d0eae19f26914d3fbb2865bc3b1837df",
+       "model_id": "fb98c8fcfb474c62b329c591f7ba9a83",
        "version_major": 2,
        "version_minor": 0
       },
@@ -39,9 +39,6 @@
     "from src.queue import Queue, timestamps_to_intervals\n",
     "\n",
     "SAMPLE_SIZE = 1000\n",
-    "ARRIVAL_RATE = 1\n",
-    "EXECUTION_RATE = 2\n",
-    "EXECUTORS = 2\n",
     "\n",
     "def display_queue_metrics(arrival_interval, execution_interval, executrs):\n",
     "    inter_arrival_time = np.full(shape=SAMPLE_SIZE, dtype=int, fill_value=arrival_interval)\n",
@@ -72,6 +69,10 @@
     "    fig.tight_layout()\n",
     "    plt.show()\n",
     "\n",
+    "    print(f'The mean queue length (L): {queue.length.mean()}')\n",
+    "    print(f'The arrival rate (λ): {1 / (arrival_interval / 1000)} ops/s')\n",
+    "    print(f'The mean wait time (W): {queue.wait_times.mean() / 1000} s')\n",
+    "\n",
     "interactive_plot = interactive(\n",
     "    display_queue_metrics,\n",
     "    arrival_interval=(0, 500),\n",
@@ -87,7 +88,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "15c94d85-6ec2-4ce1-b7cf-dbd6a1f0fbed",
+   "id": "c631f4cb-56ba-4dea-acd9-1397000ec9cb",
    "metadata": {},
    "outputs": [],
    "source": []