feat(warmup): nb finalised for warmup coding

Author: TomMonks

content/13_warm_up.ipynb

@@ -5,11 +5,26 @@
    "id": "0be7dabf-cb34-4faf-abb1-e2c8e735beda",
    "metadata": {},
    "source": [
-    "# Implementing a warm-up period\n",
+    "# Coding a warm-up period in SimPy\n",
     "\n",
-    "We will implement warm-up as a single event that resets all of our results collection variables.  \n",
+    "## Why do you need a warm-up period?\n",
     "\n",
-    "This is a simpler approach than including lots of if statements in `simpy` processes."
+    "Typically when you are modelling a non-terminating system, you will need to deal with **initialisation bias**. That is the real system always has work-in-progress (e.g. patients in queues and in service), but the model starts from empty. One way to do this is to split the model's run length into warm-up and data collection periods. We discard all results in the warm-up period.\n",
+    "\n",
+    "> In this tutorial we will focus on coding a warm-up period rather than analysis to determine its length\n",
+    "\n",
+    "## But how do you code it?\n",
+    "\n",
+    "💪 We will implement warm-up as a **single event** that resets all of our results collection variables.  \n",
+    "\n",
+    "> This is a simpler approach than including lots of if statements in `simpy` processes.\n",
+    "\n",
+    "## Illustrative example model\n",
+    "\n",
+    "We will use a very simple model for this example.  This is a acute stroke pathway with a single arrival processes, a single type of resource, and a single treatment process.  This is a non-terminating system. There are always patients in the system - it does not start up from empty\n",
+    "\n",
+    "\n",
+    "![model image](img/acute_stroke_pathway.png \"stroke pathway\")"
    ]
   },
   {
@@ -34,7 +49,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 2,
    "id": "ea3d507f-9e6d-4ff0-8b90-f9c63c8a8bdf",
    "metadata": {},
    "outputs": [],
@@ -212,7 +227,11 @@
    "id": "7ff9beae-89cc-419c-b584-c05b81086865",
    "metadata": {},
    "source": [
-    "## 🥵 Warm-up period"
+    "## 🥵 Warm-up period\n",
+    "\n",
+    "The acute stroke pathway model starts from empty.  As it is a non-terminating system our estimate of waiting time is biased due to the empty period at the start of the simulation.  We can remove this initialisation bias using a warm-up period.  \n",
+    "\n",
+    "We will implement a warm-up through an **event** that happens once in a single run of the model.  The model will be run for the **warm-up period + results collection period**.  At the end of the warm-up period an event will happen where all variables in the current experiment are reset (e.g. empty lists and set quantitative values to 0)."
    ]
   },
   {
@@ -248,7 +267,7 @@
    "id": "94f0f9c5-22cb-493a-9f1f-4e2a8325beaa",
    "metadata": {},
    "source": [
-    "## 4. Pathway process logic\n",
+    "## 4. Stroke pathway process logic\n",
     "\n",
     "The key things to recognise are \n",
     "\n",
@@ -309,7 +328,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": 8,
    "id": "b3e686ce-5371-4471-a052-b9d43309bc85",
    "metadata": {},
    "outputs": [],
@@ -352,7 +371,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
+   "execution_count": 9,
    "id": "0d0ea6cf-7d95-4d2c-9690-fcdbdae35d84",
    "metadata": {},
    "outputs": [],
@@ -424,7 +443,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
+   "execution_count": 22,
    "id": "caf52390-5455-4fa1-bb22-60b5b91ad8d0",
    "metadata": {},
    "outputs": [
@@ -436,7 +455,13 @@
       "3.29: Stroke arrival.\n",
       "3.29: Patient 1 admitted to acute ward.(waited 0.00 days)\n",
       "4.06: Stroke arrival.\n",
-      "4.06: Patient 2 admitted to acute ward.(waited 0.00 days)\n"
+      "4.06: Patient 2 admitted to acute ward.(waited 0.00 days)\n",
+      "5.31: Stroke arrival.\n",
+      "5.31: Patient 3 admitted to acute ward.(waited 0.00 days)\n",
+      "5.53: Stroke arrival.\n",
+      "5.53: Patient 4 admitted to acute ward.(waited 0.00 days)\n",
+      "5.76: Stroke arrival.\n",
+      "5.76: Patient 5 admitted to acute ward.(waited 0.00 days)\n"
      ]
     },
     {
@@ -445,31 +470,31 @@
        "{'mean_acute_wait': 0.0}"
       ]
      },
-     "execution_count": 35,
+     "execution_count": 22,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "TRACE = True\n",
     "experiment = Experiment()\n",
-    "results = single_run(experiment, rep=0, wu_period=0.0, rc_period=5.0)\n",
+    "results = single_run(experiment, rep=0, wu_period=0.0, rc_period=6.0)\n",
     "results"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 36,
+   "execution_count": 23,
    "id": "ddedb4f1-207d-4295-9ae4-c49b2c7cdcaf",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/plain": [
-       "{'n_arrivals': 2, 'waiting_acute': [0.0, 0.0]}"
+       "{'n_arrivals': 5, 'waiting_acute': [0.0, 0.0, 0.0, 0.0, 0.0]}"
       ]
      },
-     "execution_count": 36,
+     "execution_count": 23,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -484,12 +509,12 @@
    "id": "660ea2e1-d9c2-4355-876c-43dfd9dab0fe",
    "metadata": {},
    "source": [
-    "## Quick check 1: Include a warm-up"
+    "## Quick check 2: Include a warm-up"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 37,
+   "execution_count": 24,
    "id": "72b5284a-1fcb-4126-b663-c0ef0002e4bf",
    "metadata": {},
    "outputs": [
@@ -516,7 +541,7 @@
        "{'mean_acute_wait': 0.0}"
       ]
      },
-     "execution_count": 37,
+     "execution_count": 24,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -530,7 +555,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 38,
+   "execution_count": 25,
    "id": "7f5e282b-0f41-41df-bdca-f128e7d418c1",
    "metadata": {},
    "outputs": [
@@ -540,7 +565,7 @@
        "{'n_arrivals': 3, 'waiting_acute': [0.0, 0.0, 0.0]}"
       ]
      },
-     "execution_count": 38,
+     "execution_count": 25,
      "metadata": {},
      "output_type": "execute_result"
     }